Among the 122 family of iron-based superconductors, BaFe_2-xNi_xAs₂ pnictides are relatively understudied so far. Due to a lack of direct probes, an interplay between multiple-band effects, magnetism, and superconductivity remain ambiguous.

In the stoichiometric state, BaFe₂As₂ shows long antiferromagnetic order with a spin density wave below T_m ≈ 138 K. With electron (Fe,Ni) substitution, spin density wave is gradually suppressed, and a superconductivity emerges. In the optimally doped composition BaFe_0.9Ni_0.1As₂, the temperature of the superconducting transition reaches a maximum T_c ≈ 22 K. Despite both, underdoped (UD) and overdoped (OVD) compositions have similar T_c = 0–22 K range, there is a fundamental difference between these two parts of the doping phase diagram: a coexistence between spin density wave and superconductivity takes place in the UD region, being fully absent in the OVD region.

Here, using incoherent multiple Andreev reflection effect spectroscopy, we present local and direct study of the superconducting order parameter of UD BaFe_0.92Ni_0.08As₂ and OVD BaFe_0.88Ni_0.12As₂ compounds with similar T_c ≈ 18 K. We compare the determined superconducting gap structure, and discuss possible influence of the spin density wave to the superconducting properties.

T.E. Kuzmicheva, S.A. Kuzmichev, K.S. Pervakov, V.A. Vlasenko
JETP Letters 118, issue 7 (2023)

In the paper "Life, the Universe, and everything-42 fundamental questions"  Roland Allen and Suzy Lidstr\"om presented personal selection of the fundamental questions. Based on the condensed matter experience, we suggest the answers to some questions concerning the vacuum energy, black hole entropy and the origin of gravity. In condensed matter we know both the many-body phenomena emerging on the macroscopic level and the microscopic (atomic) physics, which generates this emergence. It appears that the same macroscopic phenomenon may be generated by essentially different microscopic backgrounds. This points to various possible directions in study of the deep quantum vacuum of our Universe.

 For example, there are at least 6 different scenarios of emergent gravity, which are supported by different condensed matter systems. In particular, the spin-triplet $p$-wave superfluid $^3$He-B supports the Akama-Diakonov theory, in which the gravitational tetrads emerge as the order parameter of symmetry breaking phase transition, while metric is represented by the fermionic quartet.  The chiral superfluid $^3$He-A supports the scenario in which the gravitational tetrads emerge together with Weyl fermions and gauge fields in the vicinity of the topological Weyl points in the energy spectrum of fermionic quasiparticles.  The gravitational tetrads may also emerge as the elasticity tetrads, which describe the elasticity theory in crystals. Condensed matter also demonstrates that metric may emerge from the non-quadratic vielbein, where the dimension of spin space is larger than the dimension of coordinate space, etc.

In all the condensed matter scenarios of emergent gravity, tetrads are the primary emergent objects, while metric is the secondary object, which is the bilinear form of tetrads.  This would suggest that geometry is the secondary emergent phenomenon. Whatever scenario (if any) is preferred by Nature, the gravity is not described by Einstein metric theory and requires the extended theory in terms of tetrads such as the Einstein-Cartan-Sciama-Kibble theory.

We also discuss the condensed matter views on the  cosmological constant problem and on the black hole thermodynamics. In particular, the answer to the question "Why does conventional physics predict a cosmological constant that is vastly too large?" is the following. The so-called conventional physics ignores the condensed matter lesson that in the full equilibrium the diverging zero-point energy of quantum fields is cancelled by  the atomic (trans-Planckian) degrees of freedom. The reason for cancellation is the general laws of thermodynamics, which are the same for relativistic and non-relativistic vacua (ground states).

G.E. Volovik
JETP Letters 118, issue 7 (2023)

A strong suppression of tunneling between graphene sheets in a magnetic field was found due to the appearance of a correlation Coulomb gap in the tunneling density of states. The origin of this phenomenon lies in a radical change in the tunneling transport of charge carriers in a strong magnetic field - there is a transition from effective resonant tunneling to the mode of strong blocking of this process. In the absence of a magnetic field, the electrons in each of the graphene layers weakly interact with each other and can tunnel into the adjacent graphene layer almost unhindered. In a magnetic field, due to the appearance of a strong correlation electron-electron Coulomb interaction inside the layers, for interlayer tunneling it is necessary to expend additional energy for the extraction of an electron from a correlated state in one layer and its injection into another. The total energy costs of these processes are determined by the Coulomb interaction inside the graphene layers and set the value of the resulting energy gap ∆. The value of the correlation Coulomb gap ∆ measured by us in graphene structures significantly exceeded those obtained in GaAs/AlAs systems, which is probably due to the large scale of cyclotron energies in graphene compared to GaAs, as well as the possible influence of interlayer Coulomb interaction.

Fig.a An optical micrograph of the sample, the top and bottom graphene monolayers are circled in red and blue dashed lines, respectively, and also shows the BN-2 tunnel barrier and the BN-3 gate dielectric. The inset shows the sequence of heterostructure layers and the measurement scheme. Fig.b A sharp peak (red line) on the dependence of the interlayer conductivity on the voltage V_b as a result of effective resonant tunneling, and a dip (marked as ∆ on the blue line) near V_b=0 as a manifestation of the Coulomb correlation gap. The inset shows the Landau levels on Dirac cones of graphene layers and possible tunneling transitions between them with conservation of energy and momentum.

Yu.N.Khanin, E.E.Vdovin, S.V.Morozov, K.S.Novoselov
JETP Letters 118, issue 6 (2023)

Quantum interferometry is a rapidly growing area of research. A promising opportunity for a technological breakthrough in this direction is associated with the discovery of 2D topological insulators, which are materials insulating in the bulk, but exhibiting  conducting   one-dimensional helical edge states (HES)   at the boundaries.  Such HES  are robust to dephasing by  conventional non-magnetic  thermal bath and hence are ideal candidates for building  blocks of quantum sytems based on interference effects.

We study a helical crystal formed by tunnel-coupled  HES existing at the edges of identical antidots periodically situated in a two-dimensional topological insulator placed in a magnetic field.  
The first experimental realizations of  systems of periodically arranged antidots in HgTe/CdTe based structures    have already been reported \cite{Maier2017}.

The  spectrum of the helical crystal  can be controlled by gate electrodes or by changing the magnetic flux through the antidots.  We demonstrate the appearance of  a topologically protected qubit  at the boundary between two regions with different fluxes. The qubit  properties depend on the  value of the flux jump at the boundary  and can be controlled by the gate voltage.  We derive the effective Hamiltonian of such a qubit  and analyze  the dependence of its properties on the main parameters of the superlattice: the tunnel coupling between antidots, and the probability of jumps with  spin flip. We also find that   an ensemble of $N \sim T L/v_{\rm F}$ topologically protected qubits can arise at relatively high temperatures, $T\gg v_{\rm F}/L,$ when the temperature window covers several bands of the crystal (here $L$ is the  size of the antidots)

Thus, we have demonstrated the possibility of creating controllable qubits in the helical crystal. The most interesting applications of the obtained results in the field of quantum computing are expected due to possibilities of purely electrical high-temperature control of qubits.

(a) An example of  experimental implementation of a helical crystal, taken from [1];
(b) One-dimensional chain of helical rings formed by HES (marked in red and blue) connected by tunnel or ballistic contacts (marked in grey) with the boundary between two semi-infinite  arrays of rings with different radii, on which a flux jump occurs, and, as a consequence, a localized qubit appears;
(c) Dispersion of low-lying bands of the helical crystal. The vertical distance between the Dirac points can be controlled by  special configuration of gate electrodes.    The dotted lines show the position of the localized levels that also can be controlled by gates.

1. H. Maier, J. Ziegler, R. Fischer, D. Kozlov, Z. D.Kvon, N. Mikhailov, S. A. Dvoretsky, and D. Weiss, Nat. Commun. 8, 2023 (2017).
 

R. A. Niyazov, D. N. Aristov, V.Yu. Kachorovskii
JETP Letters 118, issue 5 (2023)

It is shown that the effects of p-d covalent mixing of the spin-orbital electron states of divalent manganese and tellurium ions in triple layers Te-Mn-Te in the van der Waals material MnBi₂Te₄ can lead to the formation of nontrivial topology of the energy structure in the presence of long-range magnetic order.

To realize this effect, the combined influence of the crystal field and spin-orbit interaction should lead to such a hierarchy of Kramers doublets of the splitted 3d⁵ electron configuration of Mn²⁺ ions that the states with L_z=2, s_z= 1/2 and L_z=-2, s_z=-1/2 correspond to the half-filled spin-orbit doublet. As in the BHZ model, the states with maximum values of the total orbital moment correspond to the upper spin-orbit doublets, which are formed from 5p⁶ electron configurations of Te ions.

 It is supposed that the intraatomic Coulomb repulsion of electrons in manganese ions is strong. In this case, due to the kinematic interaction of Hubbard fermions, the ferromagnetic state is established in the layer of manganese ions and causes the splitting of spin subbands. This allows realization of conditions when there is energy overlap of the upper subband of Hubbard fermions with p subbands of fermions. Under these conditions Chern number gets the value +1 corresponding to the nontrivial topology.

Fermi excitation spectrum for two phases: a) unsaturated ferromagnetic phase (lines with different colors correspond to the spin-splitted energy branches); b) paramagnetic phase with the energy branches which are degenerated with respect to the spin projection. For ferromagnetic phase the Chern number Q = 1 (the topology of the energy structure is nontrivial) and Q = 0 for paramagnetic state (the topology is trivial).

In the paramagnetic phase the overlap of the bands disappears, and the topology of the energy structure becomes trivial. These factors establish the relationship between the ferromagnetic ordering of magnetic moments of manganese ions in the layer with the topology of the Te-Mn-Te energy structure.

It should be emphasized that, in accordance with the character of the spin orbitals of manganese ions the magnetic moments of these ions in the ordered phase are oriented perpendicular to the layers. In this case the anisotropy is strong, that leads to Ising-like behavior of the magnetic layer of manganese ions. At the same time, the fermion hoppings between such layers lead to the realization of the antiferromagnetic bond between magnetic moments from different layers, according to the Anderson mechanism.

V.V. Val’kov, A.O. Zlotnikov, A. Gamov
JETP Letters 118, issue 5 (2023)

The tunneling approach to the de Sitter stage of the expanding Universe demonstrates the existence of two different thermal processes. The first one is related to the cosmological horizon, and it gives the conventional Gibbons-Hawking temperature $T_{\rm GH}=H/2\pi$, where $H$ is the Hubble parameter.
 The atom in expanding Universe can serve as the detector, which can measure the ionization rate due to absorption of the Hawking photons. However, in addition there is another channel of ionization, which is not related to horizon and is only determined by the de Sitter metric near the atom. The corresponding activation temperature is twice the Gibbons-Hawking temperature, $T=H/\pi$.
This means that the atom feels the de Sitter metric as the thermal bath with $T=H/\pi$, i.e. the de Sitter state has the local temperature, which is not related to horizon. It is not excluded that the atom also feels the thermal bath of the Hawking photons, but anyway the effect of such bath is exponentially suppressed compared to the local bath.
 
If one  assumes that the temperature $T=H/\pi$ determines the local thermodynamics of de Sitter state, one obtains the local entropy density $s_{\rm dS}=(3\pi/4G)T$. Then the total entropy in the volume $V$ inside the cosmological horizon agrees with the Gibbons-Hawking entropy of the horizon, $s_{\rm dS}V=A/4G$, where $A$ is the horizon area.  This entropy is usually interpreted as the entropy of the cosmological horizon, but it comes from the local entropy inside the horizon. It is possible that there is some kind of bulk-surface correspondence.

The local thermodynamics of the de Sitter state includes also the gravitational coupling $K=1/16\pi G$ and the scalar Riemann curvature ${\cal R}$ as the thermodynamically conjugate variables. These variables modify the thermodynamics of the Gibbs-Duhem relation in the de Sitter state. The free energy density is proportional to $-T^2$, which is similar to that in the non-relativistic  Fermi liquids and corresponds to the Sommerfeld law. This is also similar to the relativistic stiff matter introduced by Zel'dovich with equation of state $w=1$.  The modfied thermodynamics is also applied to the Schwarzschild-de Sitter black hole and to black and white holes with the de Sitter cores.
 

G.E.Volovik
JETP Letters 118, issue 4 (2023)
 

Resonant scattering of electromagnetic waves by mesoscale dielectric spherical particles with Mie size parameter in order of 10 is a relative new phenomenon in mesotronics [1]. It has been discovered recently that such weakly dissipating dielectric (from low index [2] to moderate and high index [3]) homogeneous spheres support high order Fano resonances yield magnetic field-intensity enhancement factors on the order of 10⁵–10⁷. In all known works, the Mie size parameter, i.e. external diameter, was chosen from the resonance condition. We show that yet one more novel phenomenon of increasing the intensity of the magnetic field without changing the Mie size parameter of the non-resonant sphere by introducing an air cavity.

In this paper, for the first time, we consider scattering by the mesoscale dielectric cenosphere (from two Greek words “kenos” - hollow and “sphaira” - sphere) and high-order Mie resonances, when the external particle size is not determined from the resonance condition. We show that the maximal field’s intensity enhancement can be controlled by introducing the air cavity into the non-resonant homogeneous sphere and by changing the wall thickness of the cenosphere. It has been show that it is possible to control the interaction between bright and dark modes in a cenosphere by adjusting the air cavity radius. As a result, the intensity of the magnetic and electric field enhancement increase. The results highlight the great potential of the cenosphere to generate the giant magnetic fields intensity in an initially non-resonant dielectric mesoscale sphere.

Figure 1. Magnetic field intensity enhancement distribution for a hollow spherical particle with the Mie size parameter of q=39.75 (8 um diameter), refractive index of n=1.5 in linear (left) and log (right) scale.

References

1. I.V.Minin, O.V. Minin. Photonics 9, 762 (2022).
2. I. V. Minin, O. V. Minin, S. Zhou. JETP Letters, 116(3), 144–148 (2022).
3. Z.Wang, B.S. Luk’yanchuk, L. Yue, et al.  Sci Rep 9, 20293 (2019).

O.V.Minin, S. Zhou, I.V.Minin
JETP Letters 118, issue 3 (2023)

Neutrinos have emerged as a captivating subject within modern physics, stimulating considerable interest and investigation. While the Standard Model initially regarded neutrinos as massless particles, recent experimental observations of neutrino oscillations have provided compelling evidence for their possession of mass. To determine the mass of neutrinos in a model-independent manner, researchers have turned to experiments focused on the analysis of nuclear beta decay and electron capture processes. Presently, the most stringent direct upper limit on the mass of the electron antineutrino stands at approximately 0.8 eV [1], while the most stringent limit on the mass of the electron neutrino is approximately 225 eV [2].

To markedly reduce the laboratory restriction on the mass of the electron neutrino, various collaborations such as ECHo, HOLMES, and NuMECS have proposed an experiment centered on investigating the electron capture process in the isotope Ho-163 using a calorimetric method. These collaborations aspire to diminish the limit on the mass of the electron neutrino to a few eV, rendering it comparable to that of antineutrino. However, to conduct such experiments, it is imperative to ascertain the mass difference between the decay isotopes Ho-163 and Dy-163, also known as the Q value, at the required level of accuracy. Achieving this precision necessitates the utilization of Penning-trap mass spectrometers, exclusively viable for highly charged ions [3]. Recently, the mass difference between Ho-163 and Dy-163 ions was determined for ionization degrees 38, 39, and 40 [4].

The conversion of the mass difference of highly charged ions to that of neutral atoms necessitates the calculation of the binding-energy difference for both atoms and ions, while ensuring an appropriate level of uncertainty. In the present study, the corresponding calculations were conducted employing large-scale relativistic configuration-interaction and relativistic coupled-clusters methods.

References

[1] M. Aker, A. Beglarian, J. Behrens, et al. (KATRIN Collaboration), Nature Physics 18, 160 (2022).
[2] P. T. Springer, C. L. Bennett, and P. A. Baisden, Physical Review A 35, 679 (1987).
[3] P. Filianin, C. Lyu, M. Door, et al., Physical Review Letters 127, 072502 (2021).
[4] S. Eliseev and Y. Novikov, The European Physical Journal A 59 (2023).
 

I.Savelyev, M.Kaygorodov, Yu.Kozhedub, i.Tupitsyn, V.Shabaev
JETP Letters 118, issue 2 (2023)

Rare-earth orthochromites RCrO₃ (R = Y, La – Lu) with distorted perovskite structure are characterized by a high Néel temperature, magnetoelectric effect, and significant magnetocaloric effect at low temperatures. These compounds may be used in magnetic cooling devices, as solid-state fuel cells, thermistors with negative temperature coefficient of electrical resistance, as well as in photovoltaics.

The main intrigue associated with the magnetoelectric effect is that electric polarization cannot arise in the centrosymmetric structure of RCrO₃. Currently, there is an active discussion in the scientific literature about the causes of the magnetoelectric effect in these compounds.

In the present work, a high-resolution spectroscopic study of ErCrO₃ was carried out on crystals grown by advanced technology at the Institute of Solid State Physics, Chinese Academy of Sciences. In addition to the already known phase transitions (antiferromagnetic ordering at T_N = 133 K and Morin-type spin-reorientation transition at T_SR = 10 K), we observed a well-defined anomaly in the temperature dependence of the exchange splitting of erbium spectral lines in ErCrO₃, indicating, possibly, a new phase transition.

A detailed examination of the line shape at low temperatures indicates the presence of additional positions for Er³⁺ ions in ErCrO₃. Presumably, these are positions near uncontrolled impurities entering the crystal during its solution-melt growth and forming regions with distorted structure responsible for the appearance of polarization.

A.Jablunovskis, E.Chukalina, Li-Hua Yin, M.Popova
JETP Letters 118, issue 2 (2023)

Heavy ion collision experiments at RHIC and the LHC led to the discovery of the Quark Gluon Plasma (QGP) formation in $AA$ collisions.
One of the manifestations of the QGP formation in $AA$ collisions is strong suppression of high-$p_T$ hadron spectra (jet quenching).
Jet quenching in $AA$ collisions is due to medium modification of the parton fragmentation functions (FFs) caused by radiative and collisional energy loss of fast partons in the hot QGP.
The dominant contribution to the parton energy loss comes from the radiative mechanism due to induced gluon radiation.
The available data from RHIC and the LHC on the nuclear modification factor $R_{AA}$ of hadron spectra in $AA$ collisions can be described in the pQCD picture of parton energy loss for the QGP formation time $\tau_0\sim 0.5-1$ fm that is roughly consistent with the results of hydrodynamical analyses of experimental data on $AA$ collisions.

It is possible that mini QGP (mQGP) may be produced in $pp$ and $pA$ collisions as well. This possibility is now under active investigation. Experimental data on the strange particle production in $pp/pA$ collisions support the onset of the mQGP regime in $pp$/$pA$ collisions at the charged hadron pseudorapidity multiplicity density $dN_{ch}/d\eta\gtrsim 5$. At the LHC energies in $pp$ jet events we have $dN_{ch}^{ue}/d\eta\sim 10-15$, that seems to be large enough to expect the mQGP formation. The size and the temperature of the mQGP fireball produced in $pA$ jet events should be larger than in $pp$ collisions, since besides one hard
$pN$ interaction the projectile proton typically undergoes several soft interactions with the spectator wounded nucleons. This should result in a stronger medium modification of the FFs in $pA$ collisions. A promising way to probe the jet quenching effects in $pA$ collisions is measurement of the medium modification factor $I_{pA}$ for the photon-tagged FFs for $\gamma$+jet events (see Figure). Experimentally, $I_{pA}$ is defined as the ratio between the away-side associated hadron yields per trigger photon in $pA$ and $pp$ collisions.

We calculate $I_{pA}$ for 5.02 TeV $p$+Pb collisions for conditions of the recent ALICE measurement \cite{ALICE_IpA}. Our calculations show that, for the scenario with the mQGP formation both in $p$+Pb and $pp$ collisions,  jet quenching can lead to a deviation of $I_{pA}$ from unity by $\sim 0.1-0.2$ for $z_T\sim 0.5-0.8$ ($z_T$ is the ratio of the hadron transverse momentum to the photon one). This, within errors, is consistent with ALICE data \cite{ALICE_IpA}. However, a definite conclusion about the presence or absence of jet quenching in $pA$ collisions cannot be drawn due to large experimental errors. Our results demonstrate that this requires a  significantly more accurate measurement of $I_{pA}$ (with errors $\lesssim 0.1-0.2$).

Fig.1 A cartoon of the typical $pA$ collision with $\gamma$+jet production:  side view of the initial state (left) and beam view of   the final state (right)

[1] S. Acharya  et al.  [ALICE Collaboration],   Phys.Rev. C102, 044908 (2020)  [arXiv:2005.14637].

B.G. Zakharov
JETP Letters 118, issue 1 (2023)

The laboratory strategy of searching for axion-like particles (ALPs) implies their production and detection using large electromagnetic fields, and usually called Light-Shining-through-Wall (LSW) experiments.

One of the options of EM fields are applicable to LSW is the radio range setup. It consists of two cavities separated by a non-transparent wall. ALPs are produced in the first cavity by interaction of electromagnetic field components. Generated ALPs can pass through the wall and convert back to photons in the detection cavity. In addition, several proposals with LSW radio cavities appeared in the literature, including superconducting radio frequency (SRF)  cavities.

We compare different LSW setups, including normal conducting and superconducting cavities. Another aspect of our analysis is geometry of the setup, which can be adjusted in order to achieve higher sensitivity to ALPs parameters. We also take into account the technical difficulties of each scheme.

Figure. The sensitivity of normal conducting setup (top panels) and superconducting setup (bottom panels) for coaxial and parallel cavity locations. Left panels: the dependence on the cavities radius-to-length ratio R/L for the fixed volume. Right panels: expected reach as a function of ALPs mass at optimal R/L ratio.

D. Salnikov, P. Satunin, M. Fitkevich, D. V. Kirpichnikov
JETP Letters 117, issue 12 (2023)
 

The electron shell of the daughter atom often appears excited in the double β-decay, which causes a change in the energy taken away by β-electrons. The average value and variance of the excitation energy of the electron shell of the daughter atom are calculated for the double β-decay of germanium in both the Thomas-Fermi model and the relativistic Dirac-Hartree-Fock theory. With a probability lower than one, the parent-atom electron shell evolves into the daughter-ion electron shell in the ground state. The GRASP-2018 software program, which implements the relativistic Dirac-Hartree-Fock approach, is used for constructing the wave functions of the electrons of the germanium atom and the selenium ion to find the corresponding overlap amplitude $K_z = \langle Ge \mid Se III \rangle$,  GRASP-2018-based calculations yield a value of  $K_Z = 0.575$ A two-parametric model of the energy spectrum of β-electrons in the neutrinoless mode is built using the estimates obtained. Figure 1 shows the probability distribution function

$$F(T)=K_Z^2+(1-K_Z^2)\int_T^Qw(1-T'/Q)dT'/Q,$$

which determines the probability of β-electrons to have an energy that differs from the reaction energy, $Q$ , by no more than $Q - T > 0$ . Here,  $ w(x)$ is the probability density of the excitation energy of the electron shell, measured in units of $Q$, and $T = Q(1-x)$. The function  is assumed to be a binomial probability density function with free parameters set by the mean and variance of the electron-shell excitation energy. The shift in total energy of β-electrons is found to be under 50 eV at a 90% confidence level. The average excitation energy, on the other hand, is an order of magnitude greater at  $300 \div 400$ , while the variance is $ \approx (2900 eV)^2$ , which we explain by the dominant contribution of core-level electrons to the energy characteristics of the process. Still, the probability is nearly saturated by electron excitations with a small amount of released energy, which are common at the outer atomic levels. Distortion of the peak shape of the double-β decay must be taken into account when analyzing data from detectors with a resolution of $\approx 100 eV $ or higher.

Fig.1: The probability distribution function of the energy of β-electrons. Lines 1 and 2 correspond to the average excitation energy of the electron shell of 300 and 400 eV, respectively, and the variance $D=(2870 eV)^2$  The numerical values stand for the double β-decay of germanium, with $ Q= 2039.061(7) keV $ representing the reaction energy.

M.I. Krivoruchenko, K.S. Tyrin, F.F. Karpeshin
JETP Letters 117, issue 12 (2023)

In contrast to traditional excitonic insulators, where the Coulomb interaction is responsible for electron-hole coupling and excitons formation, in the case of spin crossover systems, the interaction leading to exciton ordering is due to correlated electron hopping. With the high-time-resolution pump-probe spectroscopy development, of interest are the spin crossover and exciton Bose condensation in nonequilibrium conditions under the action of femtosecond laser pulses. We have elaborated a novel mechanism of excitonic order photoenhancement in strongly correlated spin crossover systems, which is due to the massive mode appearance in the collective excitations spectrum and not associated with a transition to any metastable or excited state (see Fig. 1).

Fig. 1. Collective excitations spectrum in the exciton condensed phase for square lattice (a, b) and exciton order parameter temporal dynamics after laser pulse action (c, d). The calculations were carried out taking into account the diagonal (left) and off-diagonal (right) electron-phonon interaction. The initial thermodynamically equilibrium state is marked by dashed line. The red solid line shows the average value of order parameter time oscillations after turning off the external radiation. Time 𝑡 is given in units of 𝜏₀ = 10⁻¹² sec.

The study of the nonequilibrium dynamics of strongly correlated systems can provide new knowledge in understanding their properties and new ways to control various ordered states.
 

Orlov Yu.S., Nikolaev C.V., Ovchinnikov S.G.
JETP Letters 117, issue 12 (2023)

The interaction between the spin degree of freedom and the orbital motion of the electron plays a key role in modern spin condensed state physics. Indeed, it underlies a number of non-trivial fundamental phenomena, such as spin and anomalous [1] Hall effects, topological insulators [2], Majorana fermions [3]. From an applied point of view, this type of interaction determines the relaxation of nonequilibrium spin polarization and can be used to control the charge carrier spin states. Thus, the study of the spin-orbit interaction in various material systems is an extremely important scientific task.

In the present work a detailed study of the spin-orbit interaction in a series of ZnO/Mg$_{x}$Zn$_{1-x}$O heterojunctions with a wurtzite structure containing a two-dimensional electronic system was carried out. The spin-orbit interaction constants were determined from the analysis of the spin-orbit interaction-induced modification of the single-particle $g$-factor in the quantum Hall effect regime. The $g$-factor value was measured with high accuracy by the electron spin resonance technique in a wide range of magnetic fields and electromagnetic radiation frequencies. The spin-orbit interaction constants were determined for a series of samples with different concentrations of $\text{Mg}$, which allowed the dependence of the spin-orbit interaction constant on the two-dimensional electron density $n$ to be obtained. The measured value of the constant lay in the range $0.5 -0.8$~meV$\times\text{\AA}$ and was rather weakly dependent on $n$. Approximation of the experimental data allowed us to determine the coefficients $\alpha_0=0.5~\text{meV}\times\text{\AA}$ and $\gamma=0.12~\text{eV}\times\text{\AA}^3$, giving linear and cubic by wave vector contributions to the spin-orbit interaction, respectively. These values were correlated with the results obtained by other scientific groups.

Fig. a) Experimentally obtained values of the Rashba coefficient $\alpha$. (a) Dependence of $\alpha$ on the two-dimensional electron density. The blue empty circles are the experimental data obtained in the present work. The red filled circle is the value obtained in [4]. The solid line shows the corresponding theoretical $\alpha$ fit. Inset: red solid and dashed lines are the square of the wave function and the lowest level energy of dimensional quantization, respectively. The black solid and  dashed lines are the profile of the potential well with and without self-consistency. The data are given for the ZnO/MgZnO heterostructure with two-dimensional electron density $n=6.5\times10^{11}$~cm$^{-2}$. (b) Dependence of $\alpha$ on the parameter $\left(b\left\langle \hat{k}_{z}^{2}\right\rangle -2\pi n\right)$. The solid line shows a linear approximation of the dependence. From the slope of the line and its intersection with the ordinate axis, the constants $\alpha_0$ and $\gamma$ shown in the figure are determined.

[1] M. Konig, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L.W. Molenkamp, X.-L. Qi, S.-C. Zhang, Science 318, 766 (2007)
       [2] M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82  3045 (2010)
       [3] S. Nadj-Perge, I.K. Drozdov, J. Li, H. Chen, S. Jeon, J. Seo, A.H. MacDonald, B. A. Bernevig, A. Yazdani, Science 346 602 (2014)
       [4] Y. Kozuka, S. Teraoka, J. Falson, A. Oiwa, A. Tsukazaki, S. Tarucha, and M. Kawasaki, Phys. Rev. B. 87,205411 (2013).
 

A. R. Khisameeva, A. V. Shchepetilnikov, A. A. Dremin, I. V. Kukushkin
JETP Letters 117, issue 9 (2023)

It is known that for the so-called "anomalous" liquids (water, melts of Te, Se-Te, Ga-Te, Ge-Te, etc.), an unusual (often nonmonotonic) behavior of the temperature and pressure dependences of many physical properties is observed. We have shown that these liquids also have anomalous absolute values for a number of physical characteristics. The reason for this is the presence of several types of local structures in these liquids and a change in the mutual concentration of these structures with a change in temperature and (or) pressure (smooth structural transformations). As a result, the heat capacity and compressibility of such liquids are anomalously high, and the speed of sound in them are anomalously low compared to liquids that do not experience structural transformations. For example, water has a compressibility 5 times higher than amorphous modifications of ice. At picosecond and subpicosecond times measurements give "instantaneous" values of the speed of sound and bulk modulus in anomalous liquids, which are much higher than the low-frequency relaxing values. It is this circumstance that leads to anomalous "fast" sound in such liquids. "Fast" sound in ordinary liquids is almost entirely determined by the contribution of shear stiffness at high frequencies. In anomalous liquids, the main contribution to "fast" sound is related to the strong frequency dependence of the bulk modulus (its sharp decrease with decreasing frequency). “Slow” sound, high values of heat capacity and compressibility in anomalous liquids are not directly related to the presence or absence of a first-order phase transition ending in a critical point, and take place in any scenario of structural transformations.

Fig. 1. The temperature dependences of the sound velocity in water and the longitudinal speed of sound for amorphous and crystalline ices are presented. Also the conditional velocity V* = (B/ρ)^1/2 for amorphous ice  is shown (brown color online). The dashed line shows the linear extrapolation of the hydrodynamic sound velocity for water to the region of low temperatures. The asterisk corresponds to the speed of "fast" sound in wate

V.Brazhkin, I.Danilov, O.Tsiok
JETP Letters 117, issue 11 (2023)

The development of an effective multi-qubit optical quantum memory at a telecommunication wavelength (λ~ 1.5 microns) is one of the key tasks in optical quantum technologies largely due to the great interest in creating a quantum repeater based on it for optical quantum communications over long distances. In this work, we experimentally implemented an optical quantum memory protocol based on the revival of silenced echo (ROSE) at a telecommunication wavelength for signal light fields with a small number of photons. To this end, a long-lived (>1 s) absorption line was initialized and the orthogonal geometry of propagation of the signal and rephasing fields was chosen. The recovery efficiency for the orthogonal polarization components of the signal pulse was 17±1% with a storage time of 60 μs. The input pulse contained on average ~38 photons, and the retrieved echo signal ~6 photons with a signal-to-noise ratio of 1.3. Methods for increasing the signal to noise ratio are proposed and discussed in order to implement efficient quantum memory for single-photon light fields at a telecommunication wavelength

Fig.1. The temporal histogram of the photon detection.  Storage of weak coherent input pulse (black histogram at t = 0) with µ~38 photons. Revival of silenced echo signal (red histogram at t=60 μs) contained µ = 6  in the detection window of 4 μs . Retrieval efficiency of input pulse was 15.9%.  Optical noise level from spontaneous emission within the echo temporal mode was 4.5 photons.

M.Minnengaliev, K.Gerasimov, S.Moiseev
JETPL Letters 117, issue 11 (2023)

Approximate formulas for the potentials for protons and hydrogen atoms in a metal are proposed. It is shown that taking into account the effects of screening the charge of an incident particle makes it possible to explain the difference between the interatomic interaction potentials obtained in the framework of the density functional theory for the gas phase and the potentials obtained by the authors when processing experimental data on the scattering of atomic particles from the surface of a solid body. The effect of screening in the potential on the angular distributions of atomic particles after passing through thin films of matter and on nuclear stopping power is established.

Fig. 1. Interaction potential versus the interatomic distance for H-Au system. The DFT potential for the gas phase is given. Dots show the data, in which the potential values were obtained by processing the experimental data on the scattering of particles on a surface or passage through thin films. Lines with dots calculation by proposed formulas.

P.Yu. Babenko, V.S. Mikhailov, A.N. Zinoviev
JETP Letters 117 issue 10, (2023)

We consider formation of a spatially-separated Fermi-Bose mixture in the bismuthates BaKBiO3 (BaKPbBiO3). We remind that the superconductivity in bismuth oxides is governed by the tunneling of the local electron pair from one SC (bosonic) cluster to the neighboring one via the normal (non-superconducting) fermionic barrier in the two-well structure of the effective ionic potential.

We analyze the disordered thin films of the granular SC on the basis of the 2D attractive-U Hubbard model in the presence of random potential describing the scattering of electrons on impurities and defects in the dirty film. In the framework of the Bogoliubov-De Gennes approach, we observe in this model an appearance of inhomogeneous states of spatially separated Fermi-Bose mixture of Cooper pairs and unpaired electrons with the formation of bosonic droplets of different size in the matrix of the unpaired normal states for large values of Hubbard attraction and diagonal disorder.

We discuss briefly the possibility of the formation of the metallic hydrogen droplets in the insulating matrix close to the first-order phase boundary on the phase diagram between  liquid and crystalline metallic and molecular hydrogen .

Fig.1. Two-dimensional distribution of electron density (left column), electron-hole mixing (middle column) and order parameter (right column) for the averaged electron density n = 0.15 per site on 24 × 24 square   lattice with the amplitude of diagonal disorder: V / t = 10.0., where t is the nearest neighbor hopping integral.

M.Yu.Kagan et al.,
JETP Letters 117, issue 10 (2023)

In the TeV range of energies, it becomes difficult and very costly to control particle trajectories using electromagnets to obtain extracted beams at accelerators. For these purposes, high-gradient devices based on curved crystals are more suitable. These crystals can work as ultra-strong lenses with a focal length of less than 1 m, with an equivalent magnetic field of 1000 Tesla. In this work, we implemented a scheme for the formation of a divergent beam with an energy of 50 GeV by two successive focusing crystals to create an axially symmetric beam with a small divergence of 30 μrad in both the horizontal and vertical planes (see Fig. 1).

Figure 1. a – two-crystal  optical scheme for the formation of an axially symmetric beam. b – two-dimensional image of the beam profiles measured behind the crystals : 1 - undeflected 50 GeV proton beam, 2 - horizontally deflected beam by the first crystal due to channeling, 3 - vertically deflected beam by the second crystal, but not captured by the first crystal into channeling, 4 - axially symmetric beam with small divergence (Lindhard angle, 30 mrad), which passed through two crystals in the channeling mode.

       In this experiment, the bent crystals simultaneously deflect and focus the beam due to the bevelled front end face. The use of such a scheme with an internal target and two crystals will make it possible to implement a new method for the formation of neutrino beams at large accelerators, which is significantly simpler than the schemes used now.

II.G.Britvich et al.,
JETP Letters 117, issue 9 (2023)

Controlling the spin structure in graphene is one of the most important problems of material science today. To use graphene in spintronics, especially for the realization of dissipation-free transport, it is necessary to be able to control the spin splitting of its electronic states and the topologically nontrivial band gap at the Dirac point.

This work aims to investigate the influence of the size of misfit dislocation loops on the sublattice ferrimagnetism in graphene. It is shown that graphene and the underlying gold layer with different sizes of Au-Co dislocation loops are characterized by ferrimagnetic ordering within atomic layers. The presence of additional Au adatoms under graphene enhances the induced Rashba interaction in graphene, but does not destroy the ferrimagnetic order in graphene. Since gold clusters can be present in the system after intercalation of gold, both on the surface of graphene and under graphene, control of the number and size of clusters as a result of intercalation can be used to enhance the induced Rashba interaction and obtain a topological phase in graphene.

Fig. 1. (a) Relaxed unit cell of Gr/Au/Co structure with misfit dislocation loop. Arrow's sizes are proportional to atomic magnetic moment values on carbon atoms. (b) STM image of periodic dislocation loops under graphene. (c) ARPES intensity map for the π band as the second derivative of intensity with respect to binding energy. The magnetic band gap E_g of about 80 meV is indicated.

A.G.Rybkin et al.,
JETP Letters 117, issue 8 (2023)

Integrable systems in classical mechanics can be subdivided into two large classes. The first one consists of many-body systems and their spin generalizations. The second includes integrable tops, Gaudin models and spin chains. In statistical mechanics these two classes are known as IRF (interaction-round-a-face) models and Vertex models respectively. A pair of statistical models of different types are (sometimes) related by the so-called IRF-Vertex correspondence, which transforms their quantum R-matrices into each other. Similar phenomenon in classical mechanics provides gauge transformation relating Lax pairs of two models. For example, the Calogero-Moser model is many-body system with inverse square potential. There exists a gauge transformation, which transforms it into the top like model of Euler-Arnold type. Two-body Calogero-Moser is gauge equivalent to some special integrable top in 3-dimensional space, and $N$-body system is transformed into  ultidimensional matrix top.

In this paper we describe gauge equivalence at the level of 1+1 field generalizations of the above mentioned models. The field analogue of Calogero-Moser model is given by quite complicated system of soliton equations. At the same time the 1+1 field generalization of the integrable top is given by a certain Landau-Lifshitz type model, describing behaviour of multidimensional magnetization vector on a line (or circle). We show that two models are indeed gauge equivalent at the level of U-V pairs satisfying the Zakharov-Shabat equation. As a result explicit change of variables is obtained.

K.R. Atalikov, A.V. Zotov
JETP Letters 117, issue 8 (2023)

Based on Akama-Diakonov (AD) theory of quantum gravity it was suggested that one can introduce two Planck constants, which are the parameters of the corresponding components

of Minkowski metric, $g^{\mu\nu}_{\rm Mink} = {\rm diag}(-\hbar^2,\hslash^2,\hslash^2,\hslash^2)$. In the AD theory, the interval $ds$ is dimensionless, as all the diffeomorphism invariant quantities (we call this "the dimenionless physics"). The metric elements and thus the Planck constants are not diffeomprphism invariant and have nonzero dimensions. The Planck constant $\hbar$ has dimension of time, and the second Planck constant $\hslash$ has dimension of length. It is natural to compare $\hslash$ with the Planck length $l_{\rm P}$. However, this connection remains an open question, because the microscopic (trans-Planckian) physics of the quantum vacuum is not known.

Dimensionless physics emerges also in some other approaches. This includes the $BF$-theories of gravity, the model of superplastic vacuum described in terms of the so-called elasticity tetrads, and also the acoustic gravity experienced by phonons in Bose condensates. In the Bose liquids, such as superfluid $^4$He, the microscopic physics is well known: it is atomic physics. The atomic physics demonstrates that the corresponding acoustic Planck constant $\hslash_{\rm ac}$ is on the order of the interatomic distance $a$. This suggests that in the relativistic quantum vacuum, the Planck constant

$\hslash$ is on the order of the Planck length $l_{\rm P}$. Then the Planck mass, which enters the Einstein–Hilbert action and which is dimensionless as all the masses in the AD quantum gravity, is on the order of unity, $M_{\rm P}=\sqrt{\hslash /G}\sim 1$. That is why the Planck mass becomes the natural choice for the unit of mass.

In liquid helium the application of pressure changes the interatomic distance $a$ and thus modifies the acoustic Planck constants. In relativistic quantum vacuum, the non-zero vacuum pressure corresponds to the expanding de Sitter Universe. This suggests that in the de Sitter vacuum the Planck constants deviate from their Minkowski values. The relative change is

$\Delta \hbar/ \hbar \sim \Delta \hslash/\hslash \sim \hslash^2 H^2 \ll 1$, where $H$ is the Hubble parameter.

G.E. Volovik
JETP Letters 117, issue 7 (2023)

Discovered more than 100 years ago liquid crystals are nevertheless much younger than other equilibrium states of matter known from ancient times. Hence, liquid crystals are far from being exhausted as a topic of research. Due to their already existing and potential applications, special attention has been attracted to chiral liquid crystals. Chiral nematics or cholesterics are formed by spatial orientational ordering of elongated molecules and are characterized by helical structure.

In this work we study the behavior of cholesteric near the temperature of the transition to the isotropic phase T_C. Near T_C depending on the pitch of cholesteric helix a remarkable sequence of structures is formed: three-dimensional (3D, so-called Blue Phases BPIII, BPII, BPI), two-dimensional (2D) and one-dimensional (1D) in the plane of the sample:

The transition from 3D to 2D and 1D occurs near T_C with decrease of chirality.

This work mainly discusses the 2D periodic structures forming near T_C (Figure 1). The reason of their appearance can be related to frustration which could be relieved by formation of topological defects and focal conic domains. We expect that our results will motivate further investigations of various modulated textures in chiral liquid crystals.

Figure 1. (a) Periodic two-dimensional (2D) structures formed by chiral nematic; photographs in reflected and transmitted light. The horizontal size of the images is 60 micron (a) and 80 micron (b)

K.D. Baklanova, V.K. Dolganov, E.I. Kats, P.V. Dolganov
JETP Letters 117, issue 7 (2023)
 

Physical phenomena such as echo arise due to the coherence of atomic states, which is induced in a medium by exposing it to pulses of various physical nature. In the case of a photon echo, we are talking about laser pulses in the visible and infrared ranges [1, 2]. In the case of a phonon echo in paramagnetic crystals, the carrier frequencies of probing acoustic pulses lie in the far ultrasonic range [3, 4].

Echo-signals demonstrate the memory of the prehistory of exposure on the various media. Therefore, echo-effects can find applications in information storage and processing systems.

After actions on a two-level medium by two resonant pulses, separated from each other by a time interval $\tau$, the primary echo-signal appears at the instants of time $2\tau$.

Atomic coherent states are destroyed under the action of irreversible phase relaxation. For example, in two-level atoms, phase relaxation leads to an obvious decrease in the intensity of echo responses. In multilevel media, phase relaxation processes can be supplemented by quantum intra-atomic interference of various quantum transitions. Therefore, here one should expect nontrivial phenomena related to the effect of phase relaxation on the properties of echo-signals after exposure to the medium by coherent resonant pulses.

Figure. The appearance of two echo signals at the instants of time $2\tau$ and $3\tau$ after the actions on the paramagnet of two transverse ultrasonic pulses separated by a time interval $\tau$. Pulses are characterized by envelope $\psi$ and durations $\tau_1$ and $\tau_2$. Generation of $3\tau$- echo is possible only if the irreversible phase relaxation times for allowed quantum transitions different from each other.

The study carried out here demonstrates the fundamental possibility of generating two coherent echo signals at times $2\tau$ and $3\tau$ (see figure) in an equidistant three-level system with a cascade scheme of allowed transitions. Moreover, the second echo signal is due to irreversible phase relaxation. The disappearance of phase relaxation entails the disappearance of the echo signal. The mechanism of this effect lies in the destructive interference of two allowed quantum transitions emitting in anti-phase. The difference in phase relaxation times at these transitions leads to incomplete suppression of the resulting coherence. It is for this reason that a signal is generated the $3\tau$- echo. As a physical implementation, an ultrasonic echo on a system of paramagnetic ions embedded in a cubic crystal is considered. Thus, the incoherent processes occurring in the medium are the main reason for the occurrence of one of the coherent responses of the medium to an external resonant action. In a two-level system, such an effect is impossible, since it is the result of destructive interference of two quantum transitions emitting in anti-phase.

1. U.Kh. Kopvillem and V.R. Nagibarov, Fiz. Metallov i Metalloved. 15, 313 (1963).
2. N.A. Kurnit, I.D. Abella, and S.R. Hartmann, Phys. Rev. Lett. 6, 567 (1964).
3. V.R. Nagibarov and U.Kh. Kopvillem, Sov. Phys. JETP 25, 618 (1967).
4. N.S. Shiren and I.G. Kazyaka, Phys. Rev. Lett. 28, 1304 (1972).
   

   S.V. Sazonov
   JETP Letters 117, issue 7 (2023)

Among carbon allotropes, one of the mostly discussed and largely controversial candidate is the T12 carbon phase, the representation of which as a monolayer made it possible to propose a hypothetical material - penta-graphene (PG) [1], a single-layer carbon allotrope consisting of five-membered rings. Its atomic structure and various properties have been studied in detail using the computational methods. Studies show a wide range of potential applications for penta-graphene, however, it should be noted that there are a number of works that investigate the stability of penta-graphene. The results allow us to conclude that penta-graphene is not mechanically stable, undergoing bending and twisting deformations of the atomic structure in the periodic and limited representations.
In this work, we study the stability of different types of two-dimensional structures based on penta-graphene and show its possible formation and stability. In addition, optical and electronical properties for different types of considered structures have been demonstrated.

1. S. Zhang, J. Zhou, Q. Wang, X. Chen, Y. Kawazoe, P. Jena, PNAS 112, 2372–2377 (2015).

A.N. Toksumakov, V.S. Baidyshev, D.G. Kvashnin, Z.I. Popov
JETP Letters 117, issue 6 (2023)

The interatomic dipole-dipole interaction is commonly thought to be the main physical reason for spectroscopic effects, which are nonlinear in atomic density. However, we have found that the free motion of atoms can lead to other effects that are nonlinear in atomic density due to the damping of the running wave in a gas of resonant atoms. As a result, from the viewpoint of an atom moving at a velocity v, the wave not only changes the frequency by the value kv (Doppler frequency shift), but the field amplitude becomes time dependent: it increases when the atom moves contrary to the wave propagation and decreases when the atom moves along the wave propagation. Correct taking into account of this effect in the framework of the self-consistent solution of the Maxwell-Bloch equations leads to the deformation (shift and asymmetry) of the Doppler lineshape of the absorption resonance. For example, the frequency shift of the field-linear contribution to the transmission signal is more than an order of magnitude greater than the shift due to the interatomic dipole-dipole interaction, and the first nonlinear correction has an even stronger deformation, which exceeds the influence of the interatomic interaction by three orders of magnitude. Thus, the found effects caused by the free motion of atoms require a significant revision of the existing picture of spectroscopic effects, which depend on the atomic density in a gas.

V.I. Yudin et al.
JETP Letters 117, issue 6 (2023)

The presence of dust clouds, formed as a result of carbon dioxide condensation, with a dust particle characteristic size of about 100 nm at altitudes approximately equal to 100 km is an important feature of the Martian mesosphere. The existence of such clouds was discovered by the Mars Express mission measurements using the SPICAM infrared spectrometer. In March, 2021, the rover Mars Science Laboratory Curiosity took photographs of Martian clouds that appeared to be formed of solid carbon dioxide particles.

The natural assumption is that, analogously to the noctilucent clouds in the Earth’s atmosphere, these mesospheric clouds are the dusty plasma structures in the ionosphere of Mars. This assumption is consistent with the concepts of dusty plasmas, according to which one of the main features distinguishing dusty plasmas from ordinary one (not containing charged dust particles) is the possibility of self-organization, leading to the formation of macroscopic structures such as dusty plasma clouds, drops, crystals, etc.

The purpose of this letter is to refine the model describing the dusty plasma structures in the Earth’s ionosphere, as well as to determine (on the basis of the updated model) the altitude distribution of particles constituting the Martian mesospheric clouds. The model for the Martian atmosphere takes into account the following features in comparison with the Earth’s atmosphere:

(1) The main gas component of the Martian atmosphere is carbon dioxide (about 95%), therefore only solid carbon dioxide particles constitute the Martian mesospheric clouds. In turn, water vapor, forming composite icy particles of noctilucent clouds in the Earth’s ionosphere, contains only 0.5% of the mass of atmospheric gas.

(2) Under conditions of the Earth’s atmosphere the density of water vapor is negligible compared to the density of nitrogen and oxygen, so that during the entire time of sedimentation the main inhibiting factor is viscous friction, while for the Martian mesosphere the situation is more complicated. In the condensation zone, the inhibition factor of a dust particle due to the collision of condensate molecules to it (analogous to the reactive force) is significant because of the large number density of desublimating carbon dioxide, as well as non-zero relative velocity of CO₂ molecules. At the same time, the viscous friction force is caused by only 5% of gases admixed to the carbon dioxide of the atmosphere of Mars. In the sublimation zone, all the gas of the Martian atmosphere creates a viscous friction force, because the relative velocity of the evaporating carbon dioxide molecules is equal to zero in this case. Physically, this means that the particles of the evaporated CO₂ detached from the dust particle are decelerated not due to the acceleration of the particle, but due to the molecules of the atmosphere.

(3) As in the case of Earth, the atmosphere of Mars does not transmit ultraviolet radiation with sufficiently low wavelengths. Thus, the transmission coefficients of the Martian atmosphere at an altitude of about 100 km, calculated on the basis of experimental data obtained by the SPICAM spectrometer, for wavelengths less than 165 nm (which corresponds to photon energies exceeding 7.5 eV) are approximately equal to zero, and for higher wavelengths are approximately equal to one. The work function of CO₂ in the solid phase is equal approximately to 11.5 eV. Thus, it can be assumed that at the observed altitudes the photoelectric effect is negligible for the dust particle charging process. Furthermore, the charges of dry ice (CO₂) particles are negative because the electron mobility is greater than the ion one.

Based on the developed model, the altitude distribution of dust particles in the Martian mesospheric clouds has been obtained. It turns out that an important factor affecting the formation of dusty plasma clouds, which should be taken into account, is the Rayleigh-Taylor instability. This instability leads to the fact that the dusty plasma clouds can exist only with sufficiently small sizes of their constituent dust particles. Furthermore, there is an upper limit on the thickness of the dusty plasma clouds.

Figure. (left) Temporary evolution of the dust particle altitude distribution in Martian mesospheric clouds formed as a result of sedimentation of a cloud of seeds, which constitutes initially a model rectangular profile of number densities at altitudes of 110-120 km. (right) The dependence of the characteristic development time of Rayleigh-Taylor instability and the sedimentation time versus dust particle sizes at the altitude of 90 km.

Yu. S. Reznichenko, A. Yu. Dubinskii, and S. I. Popel
JETP Letters 117, issue 6 (2023)

KMnO$_4$, a compound containing highly oxidized Mn$^{+7}$, appears to be in conflict with the extremely high ionization energy of approximately a hundred eV required to create such an ion. This value far exceeds the typical chemical bonding energy of a few eV. To gain further insight into this phenomenon, we employ the Wannier functions formalism to examine the distribution of Mn-3d electrons and O-2p electrons in the MnO$_4^-$ complex for empty electronic states.  Our results indicate that the $d^0$ configuration for the manganese ion in this compound is indeed not entirely representative of the system. Specifically, only approximately half of the hole density attributed to this configuration by the Wannier functions corresponds to d-electrons, while the remaining half is distributed among the surrounding oxygen atoms (see Figure). Consequently, the actual charge of Mn atoms is closer to +2, as the calculated total number of d-electrons is equal to 5.25.

Moreover, we suggest a method for dividing the bonding energy into covalent and ionic contributions within the Wannier functions formalism. Our analysis clearly indicates that the MnO$_4^-$ complex exhibits a nearly perfect covalent type of chemical bonding, with a smaller ionic component.

In other words, in Mn(VII) state only about two electrons are transferred to oxygen atoms, while the remaining five electrons are engaged in covalent bonding.

Anisimov V.I., Oganov A.R., Mazannikova M.A., Novoselov D.Y., Korotin Dm.M.
JETP Letters 117, issue 5 (2023)

Transverse periodic modulation of the refractive index in arrays of waveguides has a stabilizing effect and makes it possible to avoid spatiotemporal  collapse, in contrast to a homogeneous cubic non-linear medium.
               In this letter we have demonstrated strong spatiotemporal compression of IR radiation in the weak anomalous group velocity dispersion region, in arrays of waveguides fabricated by femtosecond laser writing inside fused silica. With pulse shortening by more than an order of magnitude without additional dispersive post-compression, the pulses reach a duration of several periods of the light field at wavelengths of the telecommunication range.
               These results open up wide opportunities for the development of waveguide arrays for spectral transformation and temporal compression of subpicosecond pulses with μJ energies, further experimental studies of the dynamics of ultrashort pulses in topological switching devices and, in particular, the excitation and propagation of stable topological light bullets in systems with complex spatial structures, e.g. dynamic waveguide arrays.

Cross-correlation measurements with a reference pulse, depending on the input energy of IR pulses. Linear mode (left), localization threshold (middle) and maximum localization (right). The bottom row shows the corresponding IR images of the output profiles.

A.A. Arkhipova et al.
JETP Letters 117, issue 5 (2023)

The atomic Bose condensate is a unique macroscopic quantum object. Its use in quantum computing has long been discussed. The use of magnon Bose condensate (mBEC) for this purpose has a number of advantages. In a film of yttrium iron garnet (YIG), magnons reach the concentration required for Bose condensation with a dynamic deviation of the precessing magnetization by an angle of about 3°. In this case, the magnon density can reach 10¹⁶ per cm³. Averaging over such a large number of identical particles makes it possible to carry out quantum operations up to room temperature. Typically, mBEC is formed at the repulsion of magnons. In this case, a positive frequency shift occurs, called the "foldover" resonance. In this article, for the first time, the coherent state of magnons is obtained at their attraction. A negative frequency shift was obtained, called the inverse "foldover" resonance. In this case, the magnon Bose condensate should also appear. The stability of the condensate is achieved by external RF pumping. Promising are the further studies of the dynamic properties of the resulting Bose condensate with an attractive potential, which have already been studied for an atomic condensate.

Fig. 1. Angle of precessing magnetization deflection for in-plane (2,4) and out-of-plane (1,3) magnetization as a function of the pump energy. At angles larger than 3°, magnons should form mBEC.

Yu.Bunkov, P.Vetoshko, T.Safin, M.Tagirov
JETP Letters 117, issue 4 (2023)

This work is devoted to theoretical studies of methods for obtaining and experimental identification of superhard hexagonal (2H) diamond (Fig. 1a). Calculations showed that the most probable way to obtain 2H diamond is to treat cubic (3C) diamond with [211](111) shear stress exceeding 102.9 GPa at an average pressure of ~ 37.7 GPa (Fig. 1b). We also calculated spectral characteristics of hexagonal diamond and other diamond polytypes. It is established that hexagonal diamond can be unambiguously identified if there are no other diamond polytypes with non-zero hexagonality in the system under study. In addition, Raman and electron energy loss spectroscopy data were analyzed for the presence of 2H diamond polytype in carbon compounds of artificial or natural origin. The analysis showed that pure hexagonal diamond has not yet been obtained, and the structure of the synthesized compounds is close to the structure of polytypes with a large lattice period or random layer packing.

Figure 1. (a) Crystal structures of 3C and 2H diamond polytypes. (b) Pressure versus shear stress during the phase transition of cubic diamond to hexagonal diamond.

V.Greshnyakov
JETP Letters 117, issue 4 (2023)

Erbium-doped crystals are widely studied with the aim of using them in quantum telecommunications. The lifetime of coherence of electronic states is important here. Analyses of the time dependence of the photon echo intensity provides a direct method of measuring this time.
   The article presents results of studying the external magnetic field effect on the intensity of photon echo in LuYF₄ and YLiF₄ single crystals with erbium impurity ions. It was found that the intensity of echo signals critically depends on the direction of the magnetic field H changes and on the sign of the angle between H and the C axis of the crystal. Moreover, this dependence exhibits a butterfly-shaped hysteresis.

To explain the observed effects, it is assumed that they are caused by the interference of magnetic dipole and electric dipole resonance  transitions excited simultaneously by optical resonance pulses. The effects of such interference are present in materials with a magnetoelectric effect, when external magnetic field creates electric polarization, and electric field creates magnetization. Usually such effects are observed in multiferroics, materials in which spontaneous polarization and magnetization can coexist. We believe our paper reports the first observation of the magnetoelectric effect in crystals with low-concentration of paramagnetic impurity centers. The results obtained may be important  for the development of fundamentally new methods for controlling optical properties of impurity ions in crystals by  the external magnetic field.

 A.M.Shegeda, S.L.Korableva, O.A.Morozov, V.N.Lisin, N.K.Solovarov, V.F.Tarasov
JETP Letters 117, issue 4 (2023)

This work is aimed at theoretical studies of artificial graphene created by lateral triangular electrostatic modulation (superlattice) of two-dimensional electron gas in GaAs heterostructure. The period of the superlattice is about 100nm. Experiments on this system are in progress. The system is interesting for two major reasons that are related to the large lattice spacing. (i) The magnetic field 25 mT is equivalent to 6000 T in natural graphene, so this is the study of graphene at extremely high magnetic field. (ii) Electron-electron correlations are strongly enhanced compared to that in natural graphene.
The Hall resistance at the energy slightly below the first Dirac point is shown in the figure. The red line represents the device without disorder. As expected, there are quantum Hall plateaus at $B\approx30$ mT. What is unexpected and what is the major result of the present work is the reduction of the quantum Hall plateaus resistance due to long-range disorder. The green and the blue lines show the Hall resistance for devices with progressively increasing disorder.

O. A. Tkachenko, V. A. Tkachenko, D. G. Baksheev,  O. P. Sushkov
JETP Letters 117, issue 3 (2023)

A method of ghost fiber-optic 3D endoscopy is proposed, in which, spatial and temporal correlations of light beams formed in a bundle of single-mode fibers illuminated by femtosecond laser pulses are used to obtain volumetric images of objects. An original algorithm, using both the properties of femtosecond radiation and the features of light propagation in an inhomogeneous scattering medium, makes it possible to achieve spatial depth resolution in the process of ghost image restoraton. To confirm the effectiveness of the proposed method, numerical simulation of the restoration of a  3D ghost image of an object in the form of an octahedron with a layered structure was carried out (Fig. 1).

Fig.1. (a) the original profile of a layered 3D object in the form of an octahedron; (b) numerical result of reconstructing the three-dimensional profile of its scattering using the ghost  3D algorithm

The obtained results are important for the development of the fundamentals of ghost fiber  optics, which is at the intersection of  fiber, statistical and quantum optics, ghost image method and intelligent computer vision systems.

                                                                       A.V.Belinsky, P.P.Gostev, S.A.Magnitskiy, A.S.Chirkin,
                                                                       JEPT Letters 117, issue 3 (2023)

Isotropic diffuse gamma-ray flux in the PeV energy band is an important tool for multimessenger tests of models of the origin of high-energy astrophysical neutrinos and for new-physics searches. So far, this flux has not yet been observed. Carpet-2 is an air-shower experiment at the Baksan Neutrino Observatory of INR RAS capable of detecting astrophysical gamma rays with energies above 0.1 PeV. Photon-induced air showers can be distinguished from the cosmic-ray background by their low muon content, and Carpet-2 uses its 175 square-meter muon detector for this purpose. Here we report the upper limits on the isotropic gamma-ray flux from Carpet-2 data obtained in 1999-2011 and 2018-2022. To minimize the effect of uncertainties of modelling of hadronic air showers on the result, we developed a new statistical method based on the shape of the entire muon-number distribution. With this method we obtained upper limits on the isotropic flux shown as open and filled circles in the plot (the gray symbols represent the limits from other experiments).

D.D.Dzhappuev et al.
JETP Letters 117, issue 3 (2023)

In Diakonov theory of quantum gravity, the gravitational tetrads emerge as the bilinear combinations of the fermionic fields. According to this theory, such tetrads have dimension of inverse length, $1/[L]$, and thus the metric in general relativity may have dimension $1/[L]^2$. Several other approaches to quantum gravity, including the model of superplastic vacuum and BF-theories of gravity, support this suggestion. Even the acoustic metric emerging in condensed matter systems has dimension $1/[L]^2$. The important consequence of such unusual dimension of the metric is that all the diffeomorphism invariant physical quantities are dimensionless. These include the action $S$, interval $ds$, cosmological constant $\Lambda$, scalar curvature $R$, scalar field $\Phi$, etc., Dimensionless physics: Planck constant as an element of Minkowski metrici.e. $[S]=[ds]=[\Lambda]=[R]=[\Phi]=[1]$. The consequences of Diakonov theory suggest that metric describes the dynamics, quantum mechanics and thermodynamics, rather than the geometry.

In this paper we are trying to further exploit the Diakonov idea and consider the dimension of the Planck constant $\hbar$. The application of the Diakonov theory suggests that the Planck constant $\hbar$ is the parameter of the Minkowski metric and has the dimension of length, $[\hbar]=[L]$. Moreover, the Newton constant $G$ also has the dimension of length, $[G]=[L]$, which provides the correct dimension of the Planck length $[l_P]^2=[\hbar G] =[L]^2$. Whether the Planck constant $\hbar$ equals the Planck length $l_P$ is an open question.

In principle it is not excluded that there can be different Minkowski vacua, with cosmological phase transitions between these vacua, see the paper by F.R. Klinkhamer, Extension of unimodular gravity and the cosmological constant, Phys. Rev. D 106, 124015 (2022). Then each vacuum may have its own value of the parameter $\hbar$. In this case the thermal contact between two Minkowski vacua obeys the Tolman law, i.e., in thermal equilibrium their temperatures are connected in the following way: $\hbar_1/T_1=\hbar_2/T_2$.

G.E.Volovik
JETP Letters 117, issue 3 (2023)

Magnetic and electronic states of iron in the hexagonal close-packed (hcp) ε-Fe phase were studied by synchrotron Mössbauer spectroscopy on Fe-57 nuclei by the nuclear forward scattering (NFS) method. The measurements were performed at ultrahigh pressures up to 241 GPa (2,410 MBar) in the temperature range from 4 to 300 K, as well as in external magnetic fields up to 5 Tesla. It has been found that Fe atoms are in a non-magnetic state (Fig. 1c) in the entire P-T region. The  theoretically proposed magnetic instability and quantum spin fluctuations, which can be stabilized by external magnetic field, are not confirmed by our measurements of NFS spectra in an external magnetic field. It has been found that the dependence of the isomer shift on pressure IS(P) is non-linear (Fig. 1a), and at the maximum pressure of 241 GPa, the value of IS reaches an extremely high negative value ≈ – 0.8 mm/s, indicating a very high electron density at the iron nuclei. At 100–240 GPa, sharp changes in the electron density on the iron nuclei were found in the 100–200 K temperature range (Fig.1b). This indicates the occurrence of phase transitions with a change in the electronic structure, that may be associated with a sharp increase in conductivity or even with the appearance of superconductivity.

Figure 1. (a) Pressure dependence of the isomer shift in ε-Fe iron for various temperatures. The solid lines are the third-degree polynomial approximation. (b) Temperature dependences of the isomer shift for various pressures. The isomeric shift values are given relative to α-Fe at room temperature and ambient pressure. (c) P-T phase diagram of iron: triangular symbols mark the P-T points where the NFS spectra were measured in our experiment.  All points indicate the non-magnetic state of iron.

A. Gavriliuk,  V. Struzhkin, S. Aksenov, A. Mironovich, A. Ivanova, I. Troyan, I. Lyubutin
JETP Letters 117, issue 2 (2023)

Mesocavities support simultaneous interactions of exciton to few cavity modes. Such situation occurs when strength of exciton-photon interaction (Rabi splitting) and energy interval between cavity modes are comparable. Recently, non-monotonic dependence of the occupancy of polariton states on the pumping intensity has been observed.

Figure. Dependence of the population of polariton modes on pumping. For polariton modes with energies below the exciton energy, anomalous hysteresis loops are observed with a nonmonotonic dependence of the population on pumping.

A. V. Belonovskii, V. V. Nikolaev, E. I. Girshova
JETP Letters 117, issue 2 (2023)
 

The Fröhlich charge transfer mode was initially erroneously proposed as an explanation for superconductivity. It turned out later that the described collective conductivity mechanism is indeed realized in quasi-one-dimensional conductors with charge density waves (CDWs), but the CDW conductivity is finite. Moreover, in the limit of a strong electric field E, the CDW conductivity, $\sigma_{\rm CDW}(\it E)$, approaches the conductivity of the electrons condensed in it in the normal (metallic) state, but never exceeds it. No universal explanation for this regularity has been proposed by now.

In this work, this regularity is probed on the NbS₃ monoclinic phase. NbS₃ compound is unique in that three CDWs are formed in it, and all three can slide in the presence of  electric field. The authors have suggested a way of mobility estimation, applicable both to the CDWs and to the quasiparticles forming them. It turned out that the difference between the mobilities of different CDWs reaches almost two orders of magnitude. At the same time, the mobility of each of them is close to the normal-state mobility of the quasiparticles forming it. Moreover, there is a correlation between the temperature dependences of CDW and quasiparticle mobilities. For example, both the CDW-0 state and its constituent quasiparticles exhibit a dielectric behavior. In this case, the mobility value, 0.04–0.05 cm²/Vs, evidences for the hopping origin of conduction. The results of the work actualize questions about the mechanism of limiting conductivity of charge density waves.

Fragments of temperature dependences of conductivity of NbS₃ samples in the regions of the three CDW transitions: T_P0 (left), T_P1 (middle) and T_P2 (right). The vertical red lines show the “projections” of the $\sigma (\it E)$ dependences measured up to the high fields. The lines are placed at the temperatures, at which $\sigma (\it E)$ was measured. The length of each line gives the estimate of $\sigma_{\rm CDW}(\infty)$. One can see that this value is comparable with the value of s step, $\delta \sigma$, at the corresponding CDW transition (the left panel illustrates the method of $\delta \sigma$ estimation).

S. Zybtsev, V.Ya. Pokrovskii, S. Nikonov, A. Mayzlakh, S. Zaitsev-Zotov 
JETP Letters 117, issue 2 (2023)

The neutrino masses are at least six orders of magnitude smaller than the masses of all other charged fermions of the Standard Model. The exchange of weakly interacting particles of low mass creates an interaction potential with a high interaction radius, which can affect the structure of neutron stars. Since neutrinos are fermions, they can participate in long-range two-body interactions through the exchange of neutrino pairs. The neutrino-pair exchange potential is similar to the van der Waals potential resulting from the exchange of two photons.
The infrared instability of long-range multiparticle neutrino interactions in neutron stars has been the subject of discussion for a long time [1-3]. For regularization of neutrino-induced interactions in the infrared range, it was proposed to limit neutrino masses from below to a value of the order of one electron volt, which is remarkably close to the current neutrino mass constraints derived from tritium β-decay experiments and cosmological models.
In this paper, it is demonstrated that the infrared divergences discussed so far in the literature are absent in each individual term of the decomposition of the thermodynamic potential by powers of neutron matter density. Moreover, for both massless and massive neutrinos, all the terms vanish except for the interaction of two neutrons, which is negligible. As a result, long-range multiparticle neutrino interactions have no observable effect on the structure and stability of neutron stars.

[1] E. Fischbach, Long-Range Forces and Neutrino Mass, Ann. Phys. (N.Y.) 247, 213 (1996).
      [2] As. Abada, M.B. Gavela, O. Pinea, To rescue a star, Phys. Lett. B 387, 315-319 (1996).
      [3] E. Fischbach, D.E. Krause, Quan Le Thien and C. Scarlett, Implications of Recent KATRIN Results for Lower-Limits on Neutrino Masses, arXiv:2208.03790v1 [hep-ph] 7 Aug 2022.

M.I. Krivoruchenko
JETP Letters 117, issue 2 (2023)

The intrinsic antiferromagnetic topological insulator MnBi₂Te₄ provides a very attractive platform for the realization of various magnetic and topological states. In the ground state, the MnBi₂Te₄ thin films with an even number of septuple-layer blocks are axion insulators, but with increasing external magnetic field, they show a transition to quantum anomalous Hall regime, which is accompanied by conversion between collinear and non-collinear magnetization textures.
In this letter we present theoretical investigation of such topological transition. In the continuum approach, we model an effective two-dimensional Hamiltonian for the thin film of a topological insulator with non-collinear magnetization, on the basis of which we obtain the energy spectrum and the Berry curvature. The analysis of topological indices makes it possible to construct a topological phase diagram depending on the parameters of the system and the canting angle. For topologically different regions of the diagram, we describe the edge electronic states on the film side face. In addition, we investigate the spectrum of one-dimensional states on the domain wall separating domains with the opposite canting angles (see the figure). We also discuss the experimental situation in the MnBi₂Te₄ thin films.
The obtained results significantly deepen the understanding of the relationship between band topology and magnetic ordering.

Spectrum of electronic states in a thin film of antiferromagnetic topological insulator containing a domain wall.

V. N. Men’shov & E. V. Chulkov
JETP Letters 117, issue 2 (2023)

Optical coherence tomography (OCT) is a non-invasive imaging approach, expending the diagnostic possibilities in a wide range of tasks. An ability to resolve two closely located reflectors characterizes longitudinal spatial resolution, which is one of the most important characteristics of the OCT system. However, chromatic dispersion of the sample deteriorates the spatial resolution. Quantum OCT, based on the biphoton interferometery (general scheme is shown in figure 1, on the left), is widely considered as a means to cancel the dispersion effect.
The current Letter reports on a novel quantum OCT approach, based on interference of biphotons, that have different frequencies of the photons. It is shown that when the spectral separation between the photons is changed, the probability of coincident detection of the photons has an oscillating shape (an example of a spectral-domain biphoton interference signal is shown in figure 1 on the right).
The proposed spectral-domain quantum OCT approach was compared with traditional time-domain quantum OCT and classical OCT in terms of the longitudinal spatial resolution. It was analytically shown that when both the parasitic interference components and dispersion influence are taken into account, spatial resolutions of both time-domain quantum OCT and classical OCT are nearly the same, while the proposed spectral-domain quantum OCT can provide about 1.5-times better spatial resolution.

N. Ushakov, T. Makovetskaya,.A.Markvart, L.Liokumovich
JETP Letters 117, issue 1 (2023)

Within the self-consistent nuclear many-body theory and the Green function method, the task of calculation probabilities of the E1- transition between the first $2^+ and 3^-$  -excited levels in nuclei with pairing is considered. For the first time, calculations were performed for a long chain of even-even tin isotopes. For the characteristics of both phonons and E1- transitions between excited states, the well-known Fayans energy density functional was used. A good description of the available experimental data has been obtained for the reduced probabilities of E1 transitions between the first one-phonon states for isotopes ^116-124Sn, rather than for isotopes ¹¹²Sn and ¹¹⁴Sn. Possible causes of this discrepancy are discussed, the most probable of which is the appearance of deformation in the ground or excited states. It is shown that for the explanation of E1-transition experiments in ^116−124Sn it is necessary  to take into account new (i.e. dynamic three-quasiparticle) ground state correlations (GSC), Fig.1. Therefore, a self-consistent theoretical analysis of transitions between excited states is very promising for low-energy physics.

Fig.1. The reduced probabilities of E1-transition between one-phonon states B(E1)($3^-_1 \rightarrow 2^+_1$), e²fm².
           The results of the calculation with and without dynamic ground state correlations are given. Experimental data [1, 2]

[1] R. Wirowski, M. Shimmer, L. Eser, S. Alberos, K.O. Zell and P. von Brentano, Nucl. Phys. A 586, 427 (1995).
       [2] L. I. Govor, A. M. Demidov, O. K. Zhuravlev, I. V. Mikhajlov and E. Y. Shkuratova, Sov. J. Nucl. Phys. 54, 196 (1991).

M. I. Shitov, S. P. Kamerdzhiev, S. V. Tolokonnikov
JETP Letters 117, issue 1 (2023)
 

The Mott (metal-insulator) transition occurs in d-metal compounds owing to strong Coulomb interaction (electron correlations). More often, this transition occurs in antiferromagnetic phase (so-called Slater scenario), but the situation changes for magnetically frustrated systems: only paramagnetic metallic and insulator states are involved, a spin liquid being formed. The transition into such insulator state is related to correlation-induced Hubbard splitting (the Mott scenario). In the Mott state the gap in the spectrum is essentially the charge gap determined by boson excitation branch. Therefore the electrons become fractionalized: the spin degrees of freedoms are determined by neutral fermions (spinons), and charge ones by bosons. The corresponding slave-boson representation was first introduced by Anderson.

In fact, bosons and fermions are coupled by a gauge field, so that the problem of confinement occurs. The transition into the metallic confinement state is described as a Bose condensation, the electron Green's function acquiring finite residue. On the other hand, in the deconfinement insulator state the bosons have a gap, so that the spectrum is incoherent (the full electron Green's function is a convolution of boson and fermion ones) and includes Hubbard's bands.

New theoretical developments provided a topological point of view for the Mott transition, since spin liquid possesses topological order. Phase transitions in frustrated systems can be treated in terms of topological excitations (instantons, monopoles, visons, vortices) which play a crucial role for confinement.

To describe the Mott transition we use the Kotliar-Ruckenstein slave-boson representation which provides explicitly the spectrum of both Hubbard bands. In the absence of considerable quasimomentum dependence of spinon distribution function (a localized spin phase without fermion hopping), the corresponding self-energy tends to zero. However, for a spin liquid we have a sharp Fermi surface. Thus for the Mott insulators the spinon Fermi surface is expected to be preserved even in the insulating phase, so that the Luttinger theorem (conservation of the volume under the Fermi surface) remains valid. However, this Fermi surface is strongly temperature dependent since a characteristic scale of spinon energies is small in comparison with that of electron ones. Thus the spectrum picture in the insulating state is considerably influenced by the spinon spin-liquid spectrum and hidden Fermi surface.

V.Yu  Irkhin
JETP Letter 117, issue 1 (2023)

In an imbalanced bilayer electron system formed in a single wide (60 nm) GaAs quantum well, we have observed an unexpected drastic transformation of the sequence of quantum Hall effect (QHE) states when tilting the magnetic field from the normal to the  plane of the bilayer system. The collective integer QHE states at total filling $\nu$ one and two are replaced by a set of fractional QHE states. Depending on the total electron density and its distribution between the two layers, controlled by the top- and back-gate voltages, the $\nu_F=4/3$, 6/5, 10/7 and 5/4 fractional quantum Hall states with both odd and even denominators have been observed. They typically come in pairs with two different fractions for a single field sweep. With a dual gate capacitive technique [1, 2], these fractional states have been identified as a combination of the integer QHE state at filling factor one in the layer with higher electron density (layer A) and fractional states at filling factors $\nu_F-1$ in the lower density layer (layer B). The observation of a pair of fractional states implies a redistribution of the electrons among both layers as the magnetic field is swept. This allows maintaining filling factor one in layer A, while facilitating a change to the other fractional filling factor in layer B. This is a new feature of co-existing QHE states in bilayer systems. Both the striking influence of tilting the magnetic field as well as the emergence of the 5/4 fractional quantum Hall state with 1/4 filling of layer B, deserve thorough theoretical analysis. Phenomenologically, the magnetic field component parallel to the layers impairs the coupling between them. We also note, that in our imbalanced samples the nearest neighbours for electrons in the lower density layer B are electrons of layer A, which can fundamentally change the manifestation of the electron-electron interaction. This may be responsible for the appearance of the even denominator 1/4 state in layer B. In general, the electron configuration studied here is promising for the quest for novel many body effects.

The magnetoresistance $R_{xx}$ (right scale) and Hall resistance $R_{xy}$ (left scale) versus normal component $B_n$ of magnetic field for two angles between the field and normal to the quantum well: $\Theta=0^{\circ}$ (blue lines) and $\Theta=48^{\circ}$ (black solid lines). Blue $R_{xy}$ line is shifted downwards by 0.05 for clarity. Vertical dashed lines show positions of total filling factors $\nu$ and $\nu_F$. The electron densities in the lower density layer $n_B$ (measured at low magnetic field) and in total electron system $n_t$ are given in units of $10^{10}$~cm$^{-2}$. Temperature $T=0.5$~K.

[1] S.I. Dorozhkin, A.A. Kapustin, I.B. Fedorov, V. Umansky, K. von Klitzing, and J.H. Smet, J. Appl. Phys. 123, 084301 (2018).
       [2] S.I. Dorozhkin, A.A. Kapustin, I.B. Fedorov, V. Umansky, and J.H. Smet, Phys. Rev. B 102, 235307 (2020).


 

S. I. Dorozhkin, A. A. Kapustin, and I. B. Fedorov, V. Umansky, J.H. Smet
JETP Letters 117, issue 1 (2023)

The Figure below shows the Fermi surfaces for InCo2As2 (panel (a)) and KInCo4As4 (panel (b)) obtained in LDA. For InCo2As2, all large sheets of the Fermi surface are concentrated around the corners of the Brillouin zone. For InCo2As2, all Fermi surface sheets have a pronounced kz-dependence. In the KInCo4As4 system, where the K- and In- layers of the crystal structure are interchanged, the Fermi surface becomes practically quasi-two-dimensional (panel (b)). It can also be seen in the band structure in the G-M and M-A directions near the Fermi level are almost identical (Panel (b)) in contrast to InCo2As2 (panel (а)). The Fermi surface for KInCo4As4 is similar to that of iron-containing superconductors, but the shape of the Fermi surface sheets near the G-point is closer to a rectangular prism than to a cylinder. This shape of the Fermi surface sheets may facilitate nesting. Experimental synthesis and study of the KInCo4As4 samples is interesting for testing the occurence of superconductivity.

DFT/LDA calculated Fermi surfaces for InCo2As2 (panel (a)) and KInCo4As4 (panel (b)).

N.Pavlov, I.Shein, K.Pervakov, I.Nekrasov
JETP Letters 117, issue 1 (2023)

One of the most important directions in modern methods of micro-fabrication is stereographic two-photon polymerization lithography (TPP). This method enables creating three-dimensional polymer structures with a high accuracy, and is also very flexible for any production tasks.
Here we show how the TPP method can be useful for printing the basic elements of three-dimensional integrated optics. We fabricated polymer waveguides with attached prism adapters, as well as microresonators of various shapes and sizes. The waveguides suspended above a glass substrate with input/output prisms (Fig.1(a)) showed good efficiency in low-mode regime. The advantages of the proposed prism coupler are small size, wide spectral range and low losses (no more than 1.25dB). Another important feature of this work is the demonstration of printing of an active optical system using a polymer doped with various laser dyes. We also demonstrate  combined systems consisting of active microresonators and passive waveguides on a single substrate (Fig.(c)). The future development of such integrated optical system is very promising for creation of three-dimensional optical logic and sensor devices.

Figure 1. a) 3D model of a suspended waveguide with prism adapters, the blue line shows path of the optical beam, b) SEM image of the printed structure, c) optical image of the printed structure under illumination with white light and UV radiation, the blue ring is the luminescence of the dye in the cylinder.

A.Maydykovskiy, D.Apostolov, E.Mamonov, D.Kopylov, S.Dagesyan, T.Murzina
JETP Letters 117, issue 1 (2023)

In the transition metal compounds the Mott metal-insulator transitions driven by strong electron correlation effects are often accompanied by complex phase transformations associated with long-range ordering of the spin, charge, and orbital states. It results in the formation of complex phases and rich phase diagrams, which makes these compounds highly attractive for technological applications. A specific orbital ordering often yields a spin-singlet orbital-assisted Peierls state at low temperatures. In this view, quasi-one-dimensional vanadate V$_6$O$_{13}$, a member of the Wadsley phases V$_{m}$O$_{2m+1}$, reveals a highly unusual %coexistence of long-range magnetic and nonmagnetic spin-singlet states experimentally observed
magnetic state in its low-temperature insulating phase. In fact, being a mixed-valent oxide containing both 4+ and 5+ V ions (in the nominal $3d^1$ and $3d^0$ electronic state, respectively) with a corresponding ratio 2-to-1, below $\sim$150 K V$_6$O$_{13}$ undergoes a metal-insulator transition, accompanied by a remarkable decrease of magnetic susceptibility. Here, using the DFT+$U$ method we show that the phase transition at $\sim$150 K is associated with charge ordering at which the half of V$^{4+}$ ions form spin-singlet pairs, while the remaining V$^{4+}$ ions in the double V-V layers order antiferromagnetically below $\sim$55 K. Based on this we propose that the metal-insulator transition and low-temperature magnetic properties of V$_6$O$_{13}$ involve the spin-Peierls transition assisted by orbital ordering and concomitant distortions of the crystal structure.

 

(a) Lattice structure of the low-temperature (LT) spin-Peierls insulating phase of V$_6$O$_{13}$ projected on the (100) plane. (b) The crystal structure of V$_6$O$_{13}$ projected on the (110) plane. (c) Charge and orbital ordering of LT V$_6$O$_{13}$ projected on the (100) plane. The double layers with $x=\pm\frac{a}{4}$ which include zigzag chains running along the $b$-axis containing both 4+ and 5+ V ions, and a single layer ($x=0$) which is formed by V$^{4+}$ (with $3d^1$ state) ions, are shown. The size of orbital corresponds to its occupancy.  Red and blue colors correspond to the majority and minority spin states, respectively.

I. V. Leonov
JETP Letters 116, issue 12 (2022)

Quasi-one-dimensional (1D) linear-chain ternary iron chalcogenides AFeX₂ (A = K, Rb; X = S, Se) have recently begun attracting attention due to their wide range of potential applications. One of the most interesting application is antiferromagnetic spintronics due to the great speeds and frequencies of magnons in these crystals. Tuning of an anticipated spin Hamiltonian and corresponding approximations to accurately describe a certain magnetic subsystem of a compound can be derived by comparing the experimental magnetic specific-heat data with the theoretical predictions derived from the model. The magnetic specific heat of a compound can be obtained as a difference between total specific heat and all the other contributions, exclude the magnetic one. However, the crystal lattice specific heat inevitably should be taken into account.
In this work, we have performed ab-initio calculations of vibrational properties of KFeSe₂ compound using the density functional theory (DFT) without Hubbard correction as first approach to this task. Total and element specific phonon densities of states (PDOS) were calculated within a direct approach of harmonic approximation (Fig. 1 inset). Calculated PDOS shows numerous high-frequency vibrational modes of Fe and Se atoms, which strongly restrict application of the Debye model for fine analysis of thermodynamic properties of KFeSe₂ such as lattice specific heat.
We used the obtained PDOS to calculate lattice contribution to the specific heat directly by using quasi-harmonic approximation. The calculated lattice contribution to the specific heat is presented in Fig. 1. The lattice specific heat reaches 96 JK^-1mol^-1 at 300 K and does not exceed Dulong-Petit law’s limit (about 99 JK^-1mol^-1). The lattice specific heat could be used in a future detailed analysis of magnetic properties of KFeSe₂ such as magnetic specific heat and entropy of magnetic subsystem.

Figure 1. Temperature dependence of the lattice specific heat of KFeSe₂; the inset shows the calculated phonon density of states in KFeSe₂: element-specific (K, Fe and Se atoms, from bottom to top) and the total PDOS (at the bottom).

M.D. Kuznetsov, A. G. Kiiamov, D.A. Tayurskii
JETP Letters 116, issue 12 (2023)

Emergent Majorana zero modes in topological materials are extensively studied due to their exotic properties. Due to their nontrivial exchange statistics, braiding of Majorana modes allows for topologically protected quantum logic gates and their use for topological quantum-state manipulations.

In particular, hybrid superconductor-topological insulator structures were discussed. Fu and Kane analyzed a topological Josephson junction between superconducting films on top of a topological insulator and demonstrated the appearance of Majorana edge states. We consider a junction in an external magnetic field perpendicular to the surface where Majorana zero states are point-like structures bound to Josephson vortices. Similar setups can be used as a platform for topological quantum computations.

We observe that the tunnel coupling between the Majorana zero modes vanishes at zero chemical potential. This indicates protection of these modes and needs to be accounted for in relevant experiments. Moreover, variation of the chemical potential provides a method to couple Majorana modes and perform quantum operations, equivalent to braiding.

Figure. Superconductor-Topological Insulator-Superconductor Josephson junction in a transverse magnetic field along z. Blue and orange spots indicate location of Majorana bound states.

Backens S., Shnirman A., Makhlin Yu.
JETP Letters 116, issue 12 (2022)

Wе report the first experimental observation of quasi two-dimensional (q2D) plasma crystal in (3+1) dimensions: we resolved every single particle over a long time with unprecedented accuracy in both the spatial 3D and time domains, which allowed us to observe fine details of melting and recrystallization of the q2D structure confined in rf discharge. A new instrument based on optical tomography (optical stereo vision) was developed and implemented. We observed, in particular, a buckling transition from a nearly planar plasma crystal (with hexagonal lattice) to a two-layer system with square lattice vertically shifted relative to each other. We have found that the splitting of the planar system into two layers (or the structural instability of the crystal with the transition 1△ → 2□) occurs in the central part of the crystal and the phenomenon is caused by horizontal parabolic-like confinement, which leads to heterogeneity of the crystal in the radial direction. The conditions for the instability onset are met in the center of the plasma crystal due to maximal density of microparticles, while the crystal remains planar with a triangular lattice at the periphery. Molecular dynamics (MD) simulations of the simple Yukawa system reproduce remarkably well the observed structural instability.

(a) The central part of the plasma crystal observed in the experiment. The splitting of the planar crystal and formation of two layers with shifted square lattice can be clearly seen.
(b)   MD simulations of the Yukawa system in horizontal parabolic confinement with parameters close to the experimental ones reveal very similar features. The particles are color-coded according to their vertical position on both panels (a) and (b). The insets show side view of the systems.

R.A. Syrovatka, A.M. Lipaev, V.N. Naumkin and B.A. Klumov
JETP Letters, vol. 116, issue 12 (2022)

This paper reports on the observation of generation of coherent terahertz (THz) radiation from a-Si:H/a-SiC:H/c-Si p-n heterostructures  when they are photoexcited by laser pulses with a pulse duration of 15 fs and a wavelength of 800 nm. Such structures were designed as solar cells (SC) that capture a significant part of the solar spectrum and have sufficiently high quantum efficiency [1].

The THz generation is observed at a reverse bias voltage across the structure. As the bias voltage increases, the THz radiation pulse changes polarity and increases significantly in amplitude. The properties of the observed THz radiation can be explained by the fact that the contribution to the formation of THz radiation is made by two fast photocurrents generated in the structure by femtosecond laser pumping, which have the opposite directions and change in magnitude with increasing bias voltage. Investigations of THz generation processes can be used to study the dynamics of nonequilibrium charge carriers at subpicosecond times in complex structures of heterojunction solar cells. With a certain optimization of the structure of SCs, based on a-Si:H/a-SiC:H/c-Si, they can be used as emitters of coherent THz radiation.

(a) Waveform of THz radiation generated in the SC structure at a reverse bias of 9 V. The arrows indicate the positions of the peaks of the pulses of the observed THz radiation: the first pulse (solid arrow) and subsequent “echo” pulses (dashed arrows) due to the multiple reflection of the THz radiation from the upper and lower indium-tin-oxide layers of the structure, i.e. the Fabry-Perot effect. The inset shows the amplitude spectrum of THz radiation at a voltage of 9 V. The spectrum shows a THz frequency comb corresponding to Fabry-Perot resonances. (b) Dependence of the amplitude of the main (first in time) THz radiation pulse on the reverse bias voltage on the SC structure based on a-Si:H/a-SiC:H/c-Si.

[1] A. S. Abramov, D. A. Andronikov, S. N. Abolmasov and E. I. Terukov, Silicon Heterojunction Technology: A Key to High Efficiency Solar Cells at Low Cost.  In:  V. Petrova-Koch, R. Hezel, A. Goetzberger (eds),
    High-Efficient Low-Cost Photovoltaics (Springer Nature Switzerland AG, 2020), Ch. 7, p.113-132.

                                                                               A.V. Andrianov, A.N. Aleshin, S.N. Abolmasov, E.I. Terukov, E.V. Beregulin   
JETP Letters 116, issue 12 (2022)

Within the framework of the atomic representation, it is shown that ultracold atoms in an optical lattice with strong interaction at one site are described by an ensemble of colored Hubbard bosons (CBC). The chromaticity of such a boson is determined by the number of the induced transition between single-site states differing by one in the number of atoms. The ordinary boson is represented by a coherent superposition of CBH.

An essential property of the CBH ensemble is associated with the kinematic Dyson interaction due to the commutation relations of dynamic variables corresponding to the Lie algebra. This interaction in a strongly correlated mode affects both the Bose-Einstein condensation and the excitation spectrum of the CBC ensemble.

For small but finite values of the ratio of the kinetic energy to the repulsion energy of atoms at the site, in addition to the kinematic interaction, an important role is played by the effective intersite attraction and correlated jumps of the CBC. The use of the Dyson method with the introduction of the indefinite metric makes it possible to pass to new bosons and obtain equations describing the Bose condensation and the excitation spectrum of the CBC ensemble. The figure shows the increasing influence of the noted interactions on the excitation spectrum with an increase in the concentration n of bosons in the system. The concentration of condensate particles is denoted by n₀.

Excitation spectrum in an ensemble of colored Hubbard bosons in the strong correlation regime. Red dotted line: n=0.25, n₀=0.22; Green dashed line: n=0.6, n­₀=0.4; Blue solid line: n=0.98, n₀=0.46. As n increases, when the interaction between bosons effectively increases, a singularity appears in the dependence of the excitation energy on the quasimomentum, which corresponds to the roton part of the spectrum.

V.V. Val’kov    
JETP Letters 116, issue 12 (2022)

One of the most important achievements of the weak turbulence theory is the exact solutions to the kinetic equations for the wave energy spectrum found by Zakharov with co-authors in 1970-80. These distributions called now as the Kolmogorov-Zakharov spectra describe constant fluxes of energy or another integrals to small- or large-scale regions. To date, the weak turbulence theory has been very well confirmed for waves with notable dispersion.

            The situation is essentially different for acoustic type waves propagating without dispersion or with weak dispersion. The spectrum of weak acoustic turbulence was obtained in 1970 by Zakharov and Sagdeev. This theory assumes weak nonlinearity relative to the wave dispersion. In the limit of zero dispersion, the behavior of acoustic waves becomes strongly nonlinear resulting in formation of discontinuities. According to Kadomtsev and Petviashvili (1973), acoustic turbulence in this regime is considered as an ensemble of  shock waves. Thus, two types of spectra are known for acoustic turbulence: the weakly nonlinear Zakharov-Sagdeev spectrum and the strongly nonlinear Kadomtsev-Petviashvili (KP) spectrum. Despite the rather long history of the acoustic turbulence study, it has not yet been precisely clarified which of the turbulence spectra is realized in three-dimensional geometry.

            In this work, we have carried out direct numerical simulation of three-dimensional acoustic turbulence based on the model with quadratic nonlinearity and weak positive dispersion. The simulation was carried out using very accurate spectral methods. The results show that the system quickly enough passes into the developed turbulence regime with such a pumping so that nonlinear effects are weak compared with dispersion. In the turbulence energy distribution in the region of small wave numbers there appear jets in the form of cones which expand with increasing $k$, see Figs. 1a, 1b. The emergence of such structures has a very pronounced nonlinear origin. The turbulence spectrum, presented in Fig. 1c, has two different behavior at large and small scales. In small $k$, the energy distribution $\epsilon_k$ is anisotropic with visible deviations in the power-law spectrum. In the second region, $\epsilon_k$ becomes more isotropic and the turbulence spectrum $E(k)$ approaches the Zakharov-Sagdeev spectrum.

Fig. 1. (a) Isosurface of $\epsilon_k$ in the $k$ space; (b) $\epsilon_k$ at $k_z=0$;  (c) Energy spectrum $E(k)$,  the Zakharov-Sagdeev spectrum (black dashed line), and the KP spectrum (red  line).

E.Kochurin, E.A.Kuznetsov           
JETP Letters 116, issue 12 (2022)

Lithium rare-earth fluorides LiREF$_4$ is a family of magnetic materials with dominant dipolar interactions. Their magnetic properties can be significantly influenced by a single-ion anisotropy and exchange interactions between magnetic rare-earth ions. This influence is especially notable in the most isotropic member of the family, LiGdF$_4$, which exhibits no magnetic ordering down to a few hundred mK range. A lack of ordering signifies a delicate compensation between principal terms in the magnetic Hamiltonian. Such a ``hidden'' magnetic frustration may lead to a complex behavior, exotic states and multiple phase transitions as well as become a prerequisite for an enhanced magnetocaloric effect down to low temperatures.

Precise determination of the microscopic interactions is an essential task in exploring and understanding fundamental magnetic properties of LiGdF$_4$. We performed a comprehensive electron paramagnetic resonance (EPR) study of LiY$_{1-x}$Gd$_x$F$_4$ single-crystal samples with different concentrations of Gd ions ($x=0.005$ and 0.05). Modelling the EPR-spectra from individual Gd ions present in both samples gives an accurate determination of the single-ion anisotropy. Additional weak resonance lines observed only in the $x=0.05$ sample  (see upper panel in Figure) can be nicely reproduced by a model of Gd pairs coupled by dipolar and exchange interactions. Corresponding simulations (lower panel) give reasonable values of the two exchange interaction constants, which are further tested by comparing a strongly anisotropic Curie-Weiss temperature obtained for concentrated LiGdF$_4$ sample in our static magnetization measurements with theoretically computed values. A fine balance between the strongest interactions is indeed confirmed making this system quite promising for fundamental research and practical applications.

Left: The unit cell of diluted LiY$_{1-x}$Gd$_x$F$_4$ (only RE-sites are shown). Right top: Resonance absorption spectrum with basic single-ion lines (experimental and simulated) along with minor peaks (marked as ``a'', ``b'' and ``c'') originated from coupled pairs; Right bottom: simulated positions of minor resonance lines vs nearest-neighbor exchange constant $J_{\rm NN}$ compared to the absorption peak values.

S. S. Sosin, A. F. Iafarova, I.V.Romanova, O.A.Morozov,
S. L.Korableva, R.G.Batulin, M. Zhitomirsky, V.N.Glazkov
JETP Letters 116, issue 11 (2022)

Recently, signatures of Majorana zero modes were revealed in the monolayer FeSe compound.  On the theoretical side, it was predicted that a topological phase indeed emerges in the monolayer FeSe material in the normal state through considering an intrinsic spin-orbital coupling, while in the superconducting state, it was indicated that the nontrivial topology only appear for the odd parity pairing. Therefore, actually it is still not clear whether the superconducting monolayer FeSe material is topologically trivial.

In this Letter, we start from a two-orbital model which can describe qualitatively the superconducting properties of the monolayer FeSe superconductor. The edge states and the zero modes in the vortex core emerge when an additional spin-orbital coupling term is considered. Our main results are indicated in Fig.1. As is seen in Fig.1(a), when the open boundary condition is considered, the edge states indeed emerge. The low energy eigenvalues of the Hamiltonian in the presence of the two vortices are presented in Fig.1(b). As is seen, four zero energy eigenvalues exist. This can explain qualitatively the experimental signatures of the Majorana zero modes in this material. However, based on the calculation of the topological invariant and the Wilson loop technique, our results indicate that this system is still a topologically trivial system. We provide a possible explanation for the emergence of the zero modes in the monolayer FeSe material.

(a) The energy bands as a function of the momentum $k_y$ with the spin-orbital interaction with considering the open boundary condition along the $x$-direction. (b) The low energy eigenvalues of the Hamiltonian with two vortices.

F.Miao and T.Zhou                          
JETP Letters 116, issue 11 (2022)

On October 9, 2022, astrophysical instruments all over the world detected the record-breaking cosmic gamma-ray burst (GRB) 221009A. It was the brightest GRB ever observed, and it was accompanied by gamma rays of the energy never seen from a GRB. In particular, photons up to 18 TeV were observed by LHAASO and a photon-like air shower of 251 TeV was detected by Carpet-2. These energetic gamma rays cannot reach us from the claimed distance of the source (redshift z=0.151) because of the pair production on cosmic background radiation. If the identification and redshift measurements are correct, one would require new physics to explain the data. One possibility invokes axion-like particles (ALPs) which mix with photons but do not attenuate on the background radiation. Here we explore the ALP parameter space and find that the ALP--photon mixing in the Milky Way, and not in the intergalactic space, may help to explain the observations. However, given the low Galactic latitude of the event, misidentification with a Galactic transient remains an undiscarded explanation.

S.Troitskiy                                         
JETP Letters 116, issue 11 (2022)

Nowadays, the intrinsic magnetic topological insulator MnBi2Te4 [1] is the most promising platform for realizing a number of quantum effects caused by a combination of magnetic and topological properties in a material. Recently, the modification of the stoichiometry of this material by substituting Bi atoms for Sb atoms has been actively studied. Previously, an antiferromagnetic phase was demonstrated for the Mn(Bi_1-xSb_x)₂Te₄ x=[0, 0.5] material [2]. In this article, we have studied a number of samples Mn(Bi_1-xSb_x)₂Te₄ and discovered the existence of another magnetic phase in which both ferromagnetism (FM) and antiferromagnetism (AFM) are present at the same time. This is an important point, since the combination of FM and AFM in topological insulators is very interesting for realizing quantum effects and, therefore, for applications in devices.

In this work, SQUID magnetometry was used to investigate the magnetic properties. A feature of the work is that the samples Mn(Bi_1-xSb_x)₂Te₄ were studied by the ferromagnetic resonance (FMR) method for the first time. The field dependences of the magnetization measured by the SQUID method for all Mn(Bi_1-xSb_x)₂Te₄ x=[0, 0.5] samples clearly show both a hysteresis loop (characteristic of FM ordering) and a kink in the spin-flop transition (characteristic of AFM ordering) . Although the saturation magnetization of the hysteresis loop and the slope of the curve at fields above the spin-flop field differ significantly from sample to sample, other important characteristics, such as the spin-flop field and coercive force, show stability. In addition, the general regularity of the decrease in the field of the spin-flop transition, the Neel temperature, and the effective magnetization with an increase in the concentration of Sb x atoms is retained.

Figure: a) FMR data for Mn(Bi_1-xSb_x)₂Te₄ x=0.2 b) SQIUD data for Mn(Bi_1-xSb_x)₂Te₄ x = 0.2, gray dotted lines mark the kink of the spin-flop transition, H_C is the coercive force.

[1] M. M. Otrokov, I. I. Klimovskikh, H. Bentmann, and collaboration, Nature, 576 416 (2019)
[2] B. Chen, F. Fei, D. Zhang, and collaboration, Nat. Communications, 10 4469 (2019)

D.Glazkova еt al.                            
JETP Letters 116, issue 11 (2022)

The authors of the presented work develop a new direction for solving the problem of exciton Bose-condensation by proposing to condense magnetoexcitons - excitations in two-dimensional electron systems placed in an external quantizing magnetic field. Recently, the idea appeared to ​​condense cyclotron magnetoexcitons, in which the electron and hole are at different Landau levels in the conduction band. From this point of view, triplet cyclotron magnetoexcitons (or spin-flip excitons) in a quantum-Hall dielectric (electron filling factor n = 2) turned out to be the most promising. They are formed by an electron vacancy (Fermi-hole) at the completely filled zero Landau level and an excited spin-flipped electron at the empty first Landau level. Spin-flip excitons are the lowest-energy excitations in the system. In addition, they are long-lived composite bosons with spin S = 1, whose lifetime reaches milliseconds. At temperatures T < 1 K and concentrations n_ex ~ (1-10)% of the density of magnetic flux quanta in this Fermi system a new phase is formed, named magnetofermionic condensate. A distinctive feature of this condensate is its ability to spread from the region of photoexcitation into the volume of a quantum-Hall insulator over macroscopic distances - hundreds of microns and even millimeters.

It is found in this work that the ability to propagate in a non-diffusive way over macroscopic distances is inherent not only to excitons in the roton minimum, with a generalized momentum on the order of the reciprocal magnetic length, $q\sim 1/l_B$, which form a coherent magnetoexciton condensate, but also to excitons with momenta close to zero, $q\sim 0$. Therefore, it can be presumed that at small momenta, the spin-flip exciton transport also has a collective nature.

A.Gorbunov, A.Larionov, L.Kulik, V.Timofeev
JETP Letters 116, issue 11 (2022)

Spin defects in semiconductors are widely used for magnetic field sensing at the nanoscale. The most prominent example is the nitrogen-vacancy (NV) center in diamond, which is already being commercialized for a variety of applications. The sensing principle is based on the optically-detected magnetic resonance (ODMR) spectroscopy and requires application of resonant microwave (MW) fields with simultaneous measurement of the fluorescence intensity. Very recently, intrinsic defects in silicon carbide (SiC) emerged as serious candidates for sensing applications beyond diamond. SiC hosts spin centers (V_Si), particularly silicon vacancies and divacancies, which can be coherently controlled at room temperature, possess a long coherence time in the ms range, reveal single-photon emission with a spectrally narrow zero-phonon line, and show integrability into electronic and photonic circuits. Further, these spin centers in SiC permit all-optical, MW-free magnetometry (effect of level anticrossing). In particular, a MW-free approach allows measuring in electrically conducting environments, such as integrated circuits (IC’s) or biological solutions, because photoluminescence of V_Si in the 900 nm region, transparent to most biological materials.

In this article, we propose an alternative quantum magnetometer based on SiC. We demonstrate the use of SiC nanoparticles with vacancy spin centers in combination with commercial AFM cantilevers. We have developed a fabrication protocol for quantum sensors compatible with modern scanning microscopes. For this purpose, we have fabricated nanoparticles with V_Si. Such crystals have been characterized and successfully attached to AFM probes.

Figure. Capture of a single 6H-SiC nanoparticle with $V_{Si}$ at the tip of a commercial AFM cantilever (a) AFM-topography of the Si wafer section with helium ion-irradiated 6H-SiC nanoparticles. (b) Confocal image of the PL signal (at 900 nm, with 532 nm excitation) of the same section. (c) The fabrication of an AFM probe capturing of a single SiC nanoparticle with V_Si. (d) Control SEM images of the modified nano-SiC AFM probe

K.V.Likhachev et al.,                       
JETP Letters 116, issue 11 (2022)

Under conditions of high pressures up to 157 GPa (1,57Mbar) and high temperatures up to 2000 K, seven different iron-hydrogen FeHx compounds with completely different electronic and magnetic properties were synthesized. It was found that one of these compounds -  FeH2 has a tetragonal crystal structure I4/mmm and at a pressure of 82 GPa is magnetic up to a temperature of about 174 K (Fig. 1a). Another surprising result is the discovery of one of the FeHx phases, of unknown composition, that at a pressure of 128 GPa remains magnetically ordered in the temperature range from 4 to 300 K, and the extrapolated value of the Neel temperature can reach ~ 2100 K! (Fig.1b). The existence of magnetic phases of iron compounds at such a record high pressure is unique and has not been observed to date. It should be noted that such high pressures are characteristic of the region located on the boundary between the lower mantle and the outer core of the Earth, in which iron predominates. Therefore, the obtained experimental data on the magnetic state and electronic properties of iron phases are very important both from the fundamental point of view of the physics of metals and their magnetism, and also from the point of view of the physics of the Earth and terrestrial magnetism.

Figure 1. Temperature dependence of the magnetic hyperfine field B_hf at Fe-57 nuclei in the FeH₂ phase at a pressure of 82 GPa; estimated Néel temperature is ~174 K (a); and in the FeHx(I) phase at a pressure of 128 GPa. Extrapolated value of the Neel temperature is  ~ 2100 K (b).

A.Gavriliuk et al.                              
JETP Letters 116, issue 11 (2022)

At the beginning of the nonlinear optics era, promoted by the invention of the laser, the higher-order nonlinearities were considered as the limiting factor for the nonlinear conversion processes. Since that time, such an intriguing research area appeared on the scientific horizon and the optical harmonic generation became the subject of intensive investigation. The extension of generated harmonics spectra to extreme ultraviolet (EUV) and X-ray spectral regions due to the process of high-order harmonics (HHG) generation paves the way to the generation of coherent electromagnetic pulses with the duration of attosecond level ($\sim 10^{18}$), that can be used to study the dynamics of matter on the time scale of electron motion. Nowadays, only HHG sources can provide the completely coherent radiation in these spectral regions, but its moderate photon flux is a drawback . Thus, the development of methods aimed at the increase of harmonic generation efficiency is a key task on the way to the construction of EUV and X-ray sources.

One of these methods is to control the macroscopic response of the medium, that is a collective response of the atoms constituting this medium. In the present work the macroscopic response of the medium is studied while registering the low-order (5, 7, 9, 11 – Fig.1) harmonics generated by femtosecond radiation of the Fe:ZnSe laser system (wavelength is $4.5 \mu m$ , pulse duration is 160 fs by the level of FWHM) in the argon gas jet. In order to optimize the regime of laser-matter interaction and to enhance the optical harmonic generation efficiency the gas jet length and the pressure were tuned. The experimental results were supported by analytical and numerical calculations. It is demonstrated that the increase of the jet length up to the confocal parameter size boosts the generation efficiency by more than one order of magnitude. Moreover, change of the jet length also leads to the change of the phase matching conditions that causes the modification of dependence of the generation efficiency on pressure. The latter fact indicates that propagation effects are important in such interaction regimes.

Fig.1. Experimental spectrum of harmonics generated by the mid-infrared $4.5 \mu m$, 160 fs pulse.

B. Rumiantsev et al.
JETP Letters 116, issue 10 (2022)
 

Recently it has been shown that new 2D diamond-like films - hydrogenated and fluorinated graphene bilayers twisted near 30^o angles with forming interlayer bonding between the carbon atoms can have ultra-wide band gaps. These films named moiré diamanes have superlattice atonic structures close amorphous diamond.   To evaluate applications of the diamanes, for example, in optoelectronics and straintronics, the study of their mechanic properties is of great importance.

Herein mechanic properties of such type of diamanes have been explored by ab-initio molecular dynamics simulations. It is shown that for moiré diamanes the elastic constants differ noticeably from similar constants of the untwisted diamanes, and their break in plane occurs at larger strains than for the latter. Breakthrough under the action of the tip for the membrane Dn29.4 with twisted 29.4o angle occurs at greatest “critical” force value. Thus, the Dn29.4 diamane (an approximant of the quasicrystal) turned out to be more stiffed than the other diamanes.

Dn27.8 and Dn29.4 membranes (diameter 7 nm) bent without damage up to critical depths δ_c=11 Å and 9.4 Å, respectively. In this case, the “critical” force F applied to the Dn29.4 membrane turns out to be 4% higher than that for the Dn27.8 membrane.

Artyukh A.A., Chernozatonskii L.A.
JETP Letters 116. issue 10  (2022)

The behavior of 2D systems in the vicinity of melting is one of the important problem of condensed matter physics. Here, we focus on the kinetics of defects and clusters of defects during the melting of 2D Yukawa system (which is well known closely packed system with hexagonal lattice at crystalline state). In particular, we have shown that concentration of defects is a nice universal measure, sharply depending on the temperature at melting and characterizing the solid-liquid transition in two dimensions. Additionally, we obtained a spectrum of clusters of defects versus its mass; the spectrum also reveals quasiuniversal behaviour. Some metrics are proposed to use to quantify “solid-liquid’’ transition of 2D closely packed systems.    

Two-dimensional Yukawa system in the vicinity of melting: concentration of defects n_d versus reduced temperature (here, T_m is the temperature of melting) taken at two different screening parameters κκ {\displaystyle \kappa } : (κ=2 (blue) and κ=4 (red)). Universality (i.e. the parameter n_d  is κ-independent) of this measure is clearly seen. Insets show how the defects (clusters consisting of blue and red particles) look like for the different phases: solid-like (a), hexatic (b) and melt (c). Most abundant defects (dislocations of mass 2 and 4) and point disclinations are also indicated. Green color corresponds to crystalline particles, blue and red particles have 5 and 7 nearest neighbors, respectively. As seen, the value of n_d  can be used to unambiguously determine the phase state of the system.

B.A. Klumov                                  
JETP Letters 116, issue 10 (2022)

Nematic aerogel immersed into the superfluid 3He significantly changes its properties. Since the strands in nematic aerogel are directed along one axis (the anisotropy axis of aerogel) it makes possible to observe the Polar phase of superfluid 3He in such a system. The Polar phase has some unique features that differs it from other superfluid phases of 3He: it has topologically protected Dirac nodal line in the quasiparticle energy spectrum, stable half-quantum vortices in the system, etc.

In this letter we present another unique property of the system concerning its sound spectrum. In hydrodynamic regime two types of sound are possible in the superfluid system: the first sound – oscillations of pressure and density, and the second sound - oscillations of temperature and entropy. Due to interaction between impurities and 3He the combined system has four oscillation modes in the superfluid regime, including transverse oscillations of aerogel. Considering sound spectrum of the system we use another feature of the system -- the big difference between the values of elastic coefficients of aerogel and 3He, i.e. the speed of the first sound in 3He is much greater than any speed of sound in aerogel. In real experiments aerogel is surrounded by superfluid 3He and considering low-frequency modes of aerogel and 3He inside of it the liquid outside of aerogel can be assumed as incompressible. That is the reason for the existence of pure shear mode in the system where only oscillations of the form of aerogel are occurring while the volume of the system is fixed. The coupling between shear mode of aerogel and the second sound of superfluid liquid arises from anisotropy properties of aerogel. The found oscillation mode can explain the temperature dependence of frequency for one of resonances observed in experiments on oscillations of nematic aerogel in superfluid 3He. The given temperature dependence has two regimes: it is the same as in the fourth sound of the system in the vicinity of Tc, and further it follows the dependence of the shear mode of aerogel.  

E.Surovtsev                                 
JETP Letters 116, issue10 (2022)

Layered Ba(Fe,Ni)₂As₂ pnictides of the Ba-122 family remain still attracting due to their anisotropic superconducting properties, and possible interplay between superconducting, nematic, and magnetic subsystems. Unfortunately, the superconducting properties of underdoped BaFe_1.92Ni_0.08As₂ crystals have not been studied yet, whereas the available data on the Ba(Fe,Ni)₂As₂ family are scattered and contradictory.

Here, for the first time we present a powerful complementary study of the superconducting order parameter symmetry in compounds with anisotropic superconducting properties in the crystallographic ab-planes. Using incoherent multiple Andreev reflection effect (IMARE) spectroscopy and the measurements of the lower critical field H_c1(T) of BaFe_1.92Ni_0.08As₂ single crystals, we show at least two-gap superconductivity, directly determine amplitudes of the superconducting order parameters at T << T_c and their temperature dependences. We revealed a substantial in-plane anisotropy of both superconducting gaps, i.e. the dependence of the Cooper pair coupling energy on the k_xk_y-momentum direction. A strong anisotropy of the small superconducting gap (up to 100% with nodes), as compared to that in optimally doped and overdoped Ba-122 pnictides studied by us earlier, could result from an influence of the antiferromagnetic phase which manifests in Ba(Fe,Ni)₂As₂ pnictides of underdoped composition.

A. Sadakov, A.Maratov, S.Kuzmichev et al.
JETP Letter 116, issue 10 (2022)

Twisted bilayer graphene is intensively studied nowadays. This material consists of two graphene layers; one of them is rotated with respect to another one by some twist angle q. Twisting produces the superstructure in the system. The band structure of twisted bilayer graphene depends substantially on q. At the so called first magic angle q_c≈1^o, it has 4 almost flat almost degenerate bands separated by energy gaps from lower and higher dispersive bands. This makes the electron liquid very susceptible to interactions. Magic angle twisted bilayer graphene shows unique properties including Mott insulating states and superconductivity.

In this Letter we study the spin density wave as possible ground state of the magic angle twisted bilayer graphene, existing on the background of non-uniformly distributed electron density. We showed that doping reduced the symmetry of the spin density wave order parameter from C₆ down to C₂ indicating the appearance of the nematic state. For doped system, the local density of states at Fermi level also shows nematic properties. This is confirmed by experiments. The spin texture changes from collinear to almost coplanar with doping. We also showed that in energy units the on-site magnetization is larger than variation of the charge density when doping is less than 3 extra electrons or holes per supercell.

Fig. 1. The spatial distribution of the absolute value of the on-site spin density wave order parameter calculated at half-filling (two extra holes per supercell). The profile is stretched in some direction indicating the appearance of the nematic state.

A.Sboychakov, A.Rozhkov, A.Rakhmanov
JETP Letters 116, issue 10 (2022)

This paper analyses the  behaviour of semiconductor based artificial graphene (SAG) in magnetic field. The SAG is created by patterning of the  honeycomb lattice on top of two-dimensional electron gas. Why  can one be interested in SAG when there is a very high quality natural graphene? The major difference is that SAG is tunable and hence can be driven to the regime of strong electron correlations that is impossible in natural graphene.  Therefore, SAG is an avenue to study exotic many-body electronic states. Another difference is in the magnitude of the magnetic field. We predict the  Wannier diagram shown in the figure. To observe such  Wannier diagram in natural graphene  one needs magnetic field about 200 thousand Tesla. Unless  an experimentalist has a laboratory in the vicinity of a neutron star, such experiment is unrealistic.  In SAG the predicted Wannier diagrams can be  observed in  usual laboratory magnetic fields.

We simulated one-particle quantum transport through $2\times 2\mu m^2$ square sample with a hexagonal lattice and a short-range disorder. Maps of the density of states DoS were calculated as a function of  magnetic field $B$ and electron density $n$ (Wannier diagrams) for several amplitudes of periodical potential comparable to or significantly greater than the Fermi energy. The figure shows the Wannier diagram for a dimensionless modulation $w=1$. Calculations of the four-terminal resistances show that the sign and magnitude of the dark ray slopes of DoS correspond to the plateaus of quantized Hall resistances $R_{xy}$.

Figure. Top panel - the  DoS$(n, B)$ map  calculated for the lattice with total modulation of the periodic potential $6.2$meV (dimensionless modulation $w=1$) and  $80$nm period.  The amplitude of shortwave disorder is $V_r=2$meV. Values $n_{1D}=3.6\cdot 10^{10}/$cm$^2$ and $n_{2D}=14.5\cdot 10^{10}/$cm$^2$ at $B=0$ mark the positions of the first and the second Dirac points. Bottom panel - Hall resistance $R_{xy}(B)$  for modulations $w=0.25$, $0.5$, $1.5$, calculated at fixed density $n=6\cdot10^{10}$cm$^{-2}$ and disorder $V_r=2$meV. Dashed arrows show a correspondence between points on dark rays of DoS and centers of quantized plateaus $R_{xy}$.

O. A. Tkachenko, V. A. Tkachenko, D. G. Baksheev,  O. P. Sushkov
JETP Letters 116, issue 9 (2022)

 

Currently, there is an increased interest in graphene-like group-IV materials such as silicene, germanene that are considered as perspective materials for the implementation of next-generation electronic devices. To control electronic properties one needs to apply a perpendicular electric field, therefore the insulating layer (or substrate) not destroying the two-dimensional nature of these materials is required. The most promising candidate is CaF₂, having the closest lattice constant to the Si one and forming a quasi van der Waals interface with this material. In this work, we have grown the two-dimensional Si layers  embedded in a CaF₂ dielectric matrix by molecular beam epitaxy and studied their properties by a variety of experimental methods. Studies using Raman spectroscopy, transmission electron microscopy, photoluminescence (PL) spectroscopy and electron paramagnetic resonance (EPR) method confirm the formation of two-dimensional Si layer areas in epitaxial structures obtained by the deposition of one, two and three biatomic Si layers (BLs) on the CaF₂/Si(111) substrate at temperature of 550°C. In the Raman spectra of these structures, a narrow peak at 418 cm^–1 was found (Fig. 1), which is due to light scattering on vibrations of Si atoms in the plane of a two-dimensional calcium-intercalated Si layer. In the EPR spectra of multilayer structures with areas of two-dimensional Si layers embedded  in CaF₂, an isotropic EPR signal with an asymmetric Dyson shape and g = 1.9992 was observed under illumination. These characteristic properties make it possible to attribute this signal to photo-induced conduction electrons in extended two-dimensional Si islands. The results of the photoluminescence study demonstrating the PL peak at 685 nm can be considered as an additional evidence in favor of the formation of two-dimensional Si islands. The peak position corresponds to a bandgap width of 1.78 eV, that is in a good correspondence with the theoretical value obtained for bilayer silicene passivated with fluorine (e.g., when embedding in CaF₂). The results obtained can be useful for understanding the mechanisms of two-dimensional material formation on CaF₂/Si(111) substrates.

Figure 1. Raman spectra from multilayer structures with 9 Si layers, each of which was obtained by deposition of 1 BL (curves 3 and 4), 2 BLs (curve 2) and 3 BLs (curve 1). The spectrum from the structure with one Si layer  obtained by deposition of 1 Si BL (curve 5). For comparison the Raman spectra from the original Si(111) substrate (curve 7) and the CaF₂ film (curve 6) with a thickness of 40 nm grown on the Si(111) substrate at 550°C are presented.

V. A. Zinovyev, A. F. Zinovieva, V. A. Volodin, A. K. Gutakovskii, A. S. Deryabin, A.Yu. Krupin,
L. V. Kulik,  V. D. Zhivulko, A. V. Mudry, A. V. Dvurechenskii

JETP Letters 116, issue 9 (2022)

Liouville gravity was invented by Polyakov as an alternative approach to superstring theory. The Liouville Minimal Gravity (MLG), which is a special  exactly solvable  class of Liouville  gravity, was partly exactly solved by Knizhnik, Polyakov and A. Zamolodchikov in 1987.
Namely, explicit expressions were found for the gravitational dimensions of physical observables,  as well as for two-point correlation functions. Then due to results of A. Zamolodchikov and Al. Zamolodchikov in 2-dimensional Liouville field theory  the explicit expression of 3-point correlators in MLF was found. The next important step, finding of 4-point correlators, was done in 2005 in the work of Al. Zamolodchikov and of one of the authors of this paper using the found earlier by Al. Zamolodchikov  the so-called Higher Equatios of Motion (HEM).
After that, the process of finding all ршпрук correlations stopped. The reason was a lack of understanding of what to do with the so-called quasi-exact Q-terms. In this paper, we consider $N$-point correlators in Liouville's minimal gravity and  show how to solve the above problem and explicitly calculate the correlators for $N>1$. We explicitly demonstrate our approach for the $N=5$ case.

A.Artem'ev and A.Belavin
JETP Letters 116, issue 9 (2022)

         We discuss the connection between the Schwinger particle creation in the constant electric field and the particle production in the Unruh and Hawking effects. For that we consider the combined effects, which involve simultaneously the Schwinger particle production and the other effects.
One example is the combined Schwinger + Unruh process, in which both the charged and neutral particles are formed in the electric field. In this process, the charged particle is created by the Schwinger effect and moves with the acceleration in electric field. In the accelerated reference frame, the moving massive particle plays the role of the detector in the Unruh vacuum. This detector experiences the emission of a neutral particles – the Unruh radiation.
Another example is the combined Schwinger + Unruh + Hawking process, in which the pair of charged black holes is created in the electric field. It represents the triple cotunneling – the coherent sequence of three tunneling events.
The coherent combinations of the several processes are similar to the phenomenon of cotunneling in the electronic systems, where electron experiences the coherent sequence of tunneling events. These combined processes demonstrate that the entropy and temperature can be associated not only with the event horizons, as it was suggested by Gary Gibbons and Stephen Hawking, but can also be extended to the Schwinger effect. Schwinger pair creation obeys the same thermodynamic laws as in the black hole thermodynamics.

G.E. Volovik,                                     
JETP Letters 116, № 9 (2022)      

Superconductors with non-trivial pairing attract significant attention due to their rich physics. In this review, we discuss theoretical progress toward doped topological insulators that is the candidate for the spin-triplet superconductor. At low temperatures, nematic superconductivity in doped topological insulators of the family Bi2Se3 emerges. The experiment reveals that under the transition of these materials to the superconducting state, a spontaneous violation of rotational symmetry occurs in them. Such superconductivity is usually called nematic. It is well described by a vector spin-triplet order parameter. The review presents the main provisions of the microscopic theory and the phenomenological theory of Ginzburg-Landau (GL) for nematic superconductivity. Strong spin-orbit coupling inherent for Bi2Se3 and two electronic bands at the Fermi surface give rise to a competition between superconducting states with different spin and orbital structures. It turns out that taking into account the hexagonal crystal symmetry of Bi2Se3 (which manifests itself in the hexagonal warping of the Fermi surface) is necessary for the realization of the experimentally observed spin-triplet nematic phase. The dominance of the interorbital electron-electron pairing over the intraorbital one is another necessary condition for the existence of nematic superconductivity. In contrast to singlet superconductors, the critical temperature of the nematic superconductivity is partially sensitive to the non-magnetic disorder. The effect of Lifshitz transition from close to open Fermi surface under doping and the surface Andreev states are also discussed. The derivation of the GL theory with a two-component vector order parameter from the microscopic theory is presented. The GL approach shows that the ground state of the doped superconducting Bi2Se3 is either a nematic phase with the real order parameter and spontaneous strain or a “chiral” phase with the complex order parameter and spontaneous magnetization. The vector structure of the order parameter causes an unusual relationship between the superconductivity and the strain or magnetization. In particular, it gives rise to a strong anisotropy of the upper critical field (see Figure), a peculiar Pauli paramagnetism of triplet Cooper pairs, and the possible existence of the spin vortices with Majorana-Kramers fermion pairs located near their cores.

Figure description: Figure. A solid line shows in the polar coordinates the experimentally observed dependence of the upper critical magnetic field $H_{c2}$ on the angle $\theta$ between the direction of the applied field and the strain axis for two single crystals of Sr$_x$Bi$_2$Se$_3$ (A. Yu. Kuntsevich et al, Phys. Rev. B {\textbf 100} 224509 (2019)); (а) the sample is stretched, (b) the sample is compressed. Ginzburg-Landau's theory of nematic superconductivity fits the experiment well.

Khokhlov D.A., Akzyanov R.S., Rakhmanov A.L.
JETP Letters 116, issue 10 (2022)
 

One of the trends in the development of physical acoustics is the search for and prediction of phenomena similar to those discovered or predicted in nonlinear optics [1]. To a large extent, this concerns nonlinear phenomena associated with soliton dynamics. The temporal durations of the investigated acoustic solitons lie in a wide range of values ​​from micro- to subpicoseconds. In this case, carrier frequencies fill the far ultrasonic range from units to hundreds of gigahertz. The trend noted above also takes place in the study of optical and acoustic solitons containing about one and even half of the oscillation period of the corresponding physical nature. The studies of dissipative optical solitons should be singled out as a separate line [2]. Here the properties of both quasi-monochromatic and unipolar solitons are studied. Acoustic analogs of optical dissipative solitons are considered in accordance with the above-mentioned trend [3].
In this work, we study the possibility of the formation of unipolar localized acoustic objects due to two-phonon transitions in a system of nonequilibrium populated Stark and Zeeman sublevels of impurity paramagnetic ions. It is shown that a nanosecond unipolar soliton-like pulse of the type of a localized shear deformation autowave propagating perpendicular to the magnetic field can form in a cubic paramagnetic crystal subjected to longitudinal static deformation in the direction of an external magnetic field. The influx of the energy stored in paramagnetic ions into the pulse due to the nonequilibrium initial population of their stationary quantum states is compensated by irreversible losses caused by pulse damping due to its interaction with thermal vibrations of the crystal lattice, defects, and microinhomogeneities.

MnBi₂Te₄ is the most promising platform for realizing non-trivial quantum effects, such as the quantum anomalous Hall effect and the topological quantum magnetoelectric effect. Recently, modifications of the stoichiometry of this material have been actively studied. In this work the electronic and spin structure of the topological surface states (TSS) of layered materials (MnBi₂Te₄)(Bi₂Te₃)_m, m=1, 2 was studied.
This work presents calculations of the features of the electronic and spin structure of TSS, carried out by the density functional theory (DFT) method for samples with different surface terminations - magnetic MnBi₂Te₄ or non-magnetic Bi₂Te₃. Comparison with the results of experimental studies carried out by the method of angle-resolved photoelectron spectroscopy (ARPES) showed a correlation between the results of calculations and experimental measurements.
The effect of variation in the van der Waals distance between layers on the surface was theoretically studied and it was shown that with a variation of the surface van der Waals interval within ±4% for both systems, the possible change in the size of the gap at the Dirac point is within 30-50 meV. The application of an out-of-plane electric field to the surface leads to a different energy shift of the cone of Dirac states and the states of the valence and conduction bands. In this case, the applied electric field changes the size of the gap at the Dirac point, and at an electric field strength of –0.34 V/Å, the gap at the Dirac point almost closes, which can be used to modulate the magnetic and physicochemical properties of these magnetic topological insulators.

Electronic and spin structure with in-plane and out-of-plane spin orientation for MnBi₄Te₇ and MnBi₆Te₁₀ surfaces terminated by a magnetic septuple layer, and their change when an electric field (-0.34 eV/Å) is applied perpendicular to the surface. The circles show the change in the localization of the Dirac point and the Dirac gap size.

A.Shikin et al.
JETP Letters 116, issue 8 (2022)

HgTe/CdHgTe quantum wells (QWs) are one of the most interesting objects of modern condensed matter physics due to a number of unique properties Among them is the possibility of a topological phase transition induced not only by changing parameters of the HgTe QW, but also by varying pressure, temperature, or degree of disorder. For double HgTe/CdHgTe QWs there is another possibility, namely the degree of structure inversion asymmetry of the system caused by the electric field.
In this Letter, we have established the origin of this structural asymmetry in HgTe/CdHgTe double QWs and determined the contributions due to the built-in electric field, the difference in QW widths, and the order of their arrangement in the structure. In particular, we have shown that the states of the CdTe cap layer make the dominant contribution to the nonzero hole concentration in the QWs.

Figure illustrating the main charge distribution and electric field orientation in the double HgTe/CdHgTe p-type QW.

A.V.Ikonnikov et al.
JETP Letters 116, issue 8 (2022)

The observations at RHIC and the LHC in $AA$ collisions of the transverse flow effects and the strong suppression of high-$p_T$ hadron spectra (jet quenching) give evidence of the quark-gluon plasma (QGP) formation in $AA$ collisions. It is possible that a small QGP fireball can be formed in $pp$ collisions as well. The mini QGP formation in $pp$ collisions should lead to some jet modification. But since the effect should be small, it is practically impossible to detect it via the medium modification of the hadron spectra as compared to predictions of the standard perturbative QCD calculations. A promising observable for quenching effects in $pp$ collisions is the variation with the soft (underlying event (UE)) hadron multiplicity of the medium modification  factor $I_{pp}$ for the hadron-tagged jet fragmentation functions.
We calculate $I_{pp}$ for conditions of the recent preliminary ALICE measurement for 5.02 TeV $pp$ collisions. We find that the theoretical predictions with no free parameters for the multiplicity dependence of the ratio $I_{pp}/\langle I_{pp}\rangle$ are in reasonable agreement with the drop of this ratio with the UE multiplicity obtained by the ALICE Collaboration (see figure). The  escription of the data becomes better for the scenario with an incomplete thermalization of the matter at $dN_{ch}/d\eta < 10$. Our results show that the drop of the ratio $I_{pp}/\langle I_{pp}\rangle$ with the UE multiplicity, if confirmed by further measurements, may be viewed as the first direct evidence for the jet quenching in $pp$ collisions.

The ratio $I_{pp}/\langle I_{pp}\rangle$ vs the charged multiplicity   density $dN_{ch}/d\eta$  for $pp$ collisions at $\sqrt{s}=5.02$ TeV.   The solid curve is obtained assuming the QGP formation in the whole range   of the UE multiplicity, and the dotted line   corresponds to the scenario with a smooth transition from production   of free streaming particle   to formation of the thermalized QGP in the range $dN_{ch}/d\eta \sim 5-10$.

B.G.Zakharov
JETP Letters 116, issue 6 (2022)

The Lieb lattice is included as a sublattice in a very wide class of compounds with a perovskite type lattice, which have a wide variety of physical properties: high-temperature superconductors, ferroelectrics, ferromagnets and multiferroic.

In this paper we show that for two-dimensional Lieb lattice the energy of electron system decreases as a result of displacements of edge atoms from the centers along the edges. A decrease in the electronic energy leads to the appearance of soft phonon modes, anharmonic phonons, and to lattice instability. Under certain conditions, as a result, in the case of strong instability (i) a partially ordered sublattice of edge atoms arises with the doubled number of equilibrium positions for them, and (ii) quantum tunneling of edge atoms between equilibrium positions leads to the appearance of quantum tunneling modes.

The results of the work can be used in the study of a very wide range of phenomena: from high temperature superconductivity to fast proton transport in confined water, and quantum properties of a hydrogen bond.

M.I. Ryzhkin, A.A. Levchenko, I.A. Ryzhkin
JETP Letters 116, issue 5 (2022)

Ferroelectric domain reversal (engineering) is indispensable for nonlinear optics and highly promising for nanoscale memory devices. One of important features of the ferroelectric polarization reversal is that the necessary applied electric fields are typically orders of magnitude smaller than the depolarizing fields arising during this process. Thus, a strong compensation of arising polarization fields and charges is necessary. Very low bulk conductivity of ferroelectrics prevents such a compensation.

In this letter, we argue that two-dimensional conduction of arising domain walls can be the necessary effective mechanism of the charge compensation. This implies a revision of the basics of the ferroelectric domain reversal process. The expected involvement of the domain wall conduction follows the recent discovery and investigations of this phenomenon in many ferroelectric materials including lithium niobate crystals.

One of crucial ingredients of the reversal process is domain nucleation controlled by the value of the domain formation energy $W$. In the absence of the charge compensation this energy is excessively high ($W \gg 1$eV) making the reversal process practically forbidden. We have found that account for the domain wall conduction substantially lowers the domain formation energy and makes it sufficient for initiation of the domain reversal.  

 

a) The domain formation energy $W$ (in eV) at the applied field $E_0 = 4$kV/mm versus the transverse ($l_{a}$) and longitudinal ($l_c$) sizes of a half-spheroidal domain nucleus in the presence of the domain wall conductivity.
b) The energy $W$ (in eV) at $l_a = 1$~nm versus the applied field $E_0$ and $l_c$.
      

Sturman B., Podivilov E.,
JETP Letters 116, issue 4 (2022)

A complete understanding of soft matter rheology (including also elastic turbulence, or drag reduction) is still lacking. According to Newton response of a material (shear stress $\sigma (t) $) is proportional to the the applied shear strain $\gamma (t)$. However in many cases when shear strain ${\dot {\bar \gamma }}$ is suddenly withdrawn, the stress decays exponentially with a certain relaxation time in a contrast to the instantaneous dissipation in a Newtonian liquid. The following nomenclature of types of viscoelastic flows (non-linear viscoelasticity) are used to describe observations in soft matter materials

• Dilatants or shear thickening (e.g., observed in a starch
• Pseudo-elastic or shear thinning (observed in a blood or paint flows).
• Bingham rheology, typical for materials like toothpaste or ketchup.
• Thixotropy - viscosity depends on the time duration, and not on the rate of the applied shear. All thixotropic  materials are shear-thinning.

For such complex soft matter materials qualitative interpretation of non-Newtonian rheology are more-or less clear. For example shear thinning  behavior observed in polymer melts and solutions, is caused by the disentanglement of polymer chains during flow. This leads to less molecular/particle interaction and a larger amount of free space, decreasing the viscosity. Dilatancy (shear thickening), often occurs due to aggregation into flock.  Material jams when it is stirred vigorously, and flows when stirred gently.

Surprisingly enough almost all mentioned above types of the behaviors were observed recently in less exotic for physics material, so-called twist-bend nematic liquid crystal ($N_{TB}$). In this work I present a simple model to describe shear rheological behavior of the $N_{TB}$ liquid crystals. Using coarse-grained description of the $N_{TB}$ phase I find that at relatively low shear rate (${\dot \gamma } \leq {\dot \gamma}_{c1}$) the stress tensor $\sigma $ created by this shear strain, scales as $\sigma \propto {\dot \gamma }^{1/2}$. Thus the effective viscosity decreases with the shear rate ($\eta \propto {\dot \gamma }^{-1/2}$) manifesting so-called shear-thinning phenomenon. At intermediate shear rate ${\dot \gamma }_{c1} \leq {\dot \gamma} \leq {\dot \gamma }_{c2}$, $\sigma $ is almost independent of ${\dot \gamma }$ (a sort of plateau), and at large shear rate (${\dot \gamma } \geq {\dot \gamma}_{c2}$), $\sigma \propto {\dot \gamma }$, and it looks like as Newtonian rheology. Within our theory the critical values of the shear rate scales as ${\dot \gamma }_{c1}\propto ({\tilde {\eta }_2^0}/{\tilde {\eta }_3^0})^2$, and ${\dot \gamma}_{c2} \propto ({\tilde {\eta }_2^0}/{\tilde {\eta }_3^0})^4$ respectively. Here ${\tilde \eta }_2^0$ and ${\tilde \eta }_3^0$ are bare coarse grained shear viscosity coefficients of the effective smectics equivalent to the $N_{TB}$ phase at large scales.

E. I. Kats
JETP Letters 116, issue 4 (2022)
 

Under certain conditions a whole group of resonant centers (atoms, molecules, quantum dots etc) can emit radiation with parameters completely different from what a single resonant center would produce. This occurs due to either the emission-mediated interaction between resonant centers or certain constructive interference effects. Such collective emission phenomena when multiple dipole oscillators radiate in-phase are often referred as the superradiance and can result in generation of ultra-short intense light pulses.

In this Letter we demonstrate an unusual example of such collective radiation phenomena upon the excitation of an optically thick layer of a two-level medium by a pair of driving subcycle attosecond pulses, such that the delay between them equals half of the period of the medium resonant transition.

We find that in such a system the optical response represents a pair of two unipolar half-cycle pulses of opposite sign separated by a temporal gap proportional to the layer thickness. Such response results from the constructive interference of the emission of two-level centers distributed over the whole layer thickness. Alternatively, one can represent the layer’s response as the radiation of the half-cycle pulse of the induced medium polarization sandwiched in between two excitation pulses and propagating along with them.

Unipolar pulses are of significant interest themselves as they possess constant sign of the electric field and are thus able to efficiently transfer momentum to charged particles both in free space and in the medium. The paper finding can be therefore not only of fundamental interest but also outline a novel way for producing unipolar subcycle pulses of controllable shape in resonant media.

An example of the electric field reflected from a 10-μm-thick layer of a two-level medium

A. Pakhomov,  M. Arkhipov,  N. Rosanov, R.Arkhipov
JETP Letters 116, issue 3 (2022)
 

One of the most crucial challenges for implementing a trapped ion quantum computer is temperature control. The fidelity of quantum gates, especially involving multiple qubits, dramatically reduces if the ions are not cooled to a low enough level. Hence, the problem of determining the temperature of ion chains in the Lamb-Dicke regime has to be solved efficiently in a practical sense. For the purpose of simplifying the measurement process, this letter addresses the usage of a phenomenon referred to as Rabi oscillation dephasing.
When a laser field, which is resonant with a certain narrow electronic transition, is applied to a specific ion in the chain, Rabi oscillations occur between relevant electronic states. The Rabi frequency is dependent on the motional state of the ion, which in the general case consists of several normal modes. Since the motional state population is distributed among the modes, Rabi oscillations would decay due to dephasing between oscillations with different Rabi frequencies. The rate of this decay is determined by the modes’ mean motional quantum numbers, which, in turn, correspond to the temperature of the chain.
In this letter we propose a method of measuring the temperature of an ion chain by studying the aforementioned dephasing. We derive an analytical expression for the population of the excited ion state, assuming the Lamb-Dicke regime, and test it experimentally. We use this method to determine the heating rate of a single ion in a trap, as well as measure the temperature of a 5-ion linear chain.
Our proposed method yields adequate results for mean motional quantum numbers on the order of 50, and it doesn’t require any additional laser sources besides those which are already used for spectroscopy or quantum computing with the ions.

Rabi oscillation dephasing in the first ion of a 5-ion chain. The mean motional quantum number is approximately equal to 75, which corresponds to the temperature of 1.7 mK.

N.Semenin et al.
JETP Letters 116, issue 2 (2022)

Giant photoconductance of a quantum point contact (QPC) has been discovered experimentally and studied numerically in [1-3]. The effect occurred in the tunneling mode, under irradiation by terahertz radiation with photon energy ħw₀ = 2.85 meV, close to the difference between the top of the potential barrier and the Fermi energy ħw₀ = U₀ - E_F (Fig. a). The effect was explained by the photon-stimulated transport (PST) of electrons due to the absorption of photons. However, a counter-intuitive disappearance of the photoconductance observed in [1] for a higher photon energy ħw₁ = 6.74 meV, has not received a clear qualitative explanation, although it agrees with the results of the numerical calculations [1,2]. Here we propose such an explanation based on semiclassical considerations of the momentum conservation at PST.

The explanation is illustrated in Fig. b, which shows the electron dispersion laws near the stopping point and near the top of the barrier, as well as optical transitions with photon energies ħw₀ и ħw₁. It can be seen that for the "resonant" photon energy ħw₀ = U₀ - E_F, the optical transition from the bottom of the lower parabola to the bottom of the upper parabola is vertical and does not require additional scattering in momentum; therefore, the probability of such a transition is high. On the contrary, for ħw₁ > ħw₀, the transition to a state with a high kinetic energy of an electron over the top of the barrier requires simultaneous scattering in momentum (the dashed line in Fig. b), so the probability of such a transition is small due to the small probability of acquiring a large momentum under transfer through a smooth barrier.

We calculated PST spectra according to the perturbation theory, as the product of the optical transition probability W and the electron transfer probability D through the potential barrier in the final state. The calculated spectra contain peaks corresponding to the optical transitions from the Fermi level to the top of the potential barrier, in accordance with the numerical results [2] and with the explanation proposed here. On the other hand, our calculations restrict this explanation, which is based on the assumption that the optical transitions at the stopping points yield the major contribution to the PST. In reality, a relatively broad region, which includes a smooth foot of the barrier, yields a considerable contribution to the matrix element of the optical transitions.

In a direct drive ICF plasma with strong temperature gradients appearing in the absorption domain a mean free path of electrons can be comparable to the temperature space scale. A significant contribution to heat flux is made by the electrons with energy few times greater the thermal one. These electrons runaway the region of strong gradient that provide the energy flux nonlocality. The Fourier law states that the flux in a given point is proportional to the electron temperature gradient with heat conductivity coefficient at this point. In the nonlocal regime the electron energy flux is dependent on plasma parameters in a nearby region. In turn, absorption efficiency and target dynamics depends on heat transfer. Self-consistent simulation of the nonlocal effect requires collisional kinetic model. The Fokker-Planck simulation has been used to simulate electron dynamics of laser heated plasma. Such a model is limited to rather short temporal and spatial scales (several hundreds of electron-ions collision times and free path length) and can't be directly used in global ICF simulations. However, kinetic model makes it possible to test a number of kernel-based nonlocal models, which could be incorporated in ICF hydrocodes. In Fig. 1 the comparison of heat wave dynamics is presented with several models included: FP — the Fokker-Planck kinetic simulation, f=0.15 — the flux limited Spitzer-Harm model, Psi_BB — our nonlocal model with integral form heat flux. The latter is applied to simulations of direct drive ICF target. The nonlocal effects lead to shell smoothing and modified dynamics during target compression, that has an impact on the ignition.

S.Glazyrin, V. Lykov, S.Karpov, N.Karlykhanov, D.Gryaznykh, V. Bychenkov
JETP Letters 116, issue 2 (2022)

Implementation of the next generation of supercomputers will not be possible without energy-efficient digital and storage technologies “beyond-CMOS”. In the published paper "Magnetic memory effect in planar ferromagnet/superconductor/ferromagnet micro-bridges", a possible design of a novel superconducting element of magnetic memory is proposed. The element functioning is based on an experimentally observed effect of storing the low-resistive state of the ferromagnet/superconductor/ferromagnet trilayers. The power consumption in the resistive state is only 15 pW, which is 3000 times less than one obtained earlier on similar structures and 2-4 orders of magnitude less than the power consumption of modern CMOS memory elements

L.N.Karelina et al.
JETP Letters 116, issue 2 (2022)

The only way to solve problem of the knee in the HECR spectrum is to determine the composition of CRs. The conclusions of this work are based on the analysis of the characteristics of EAS cores obtained using X-ray emulsion chambers. According to these data, a number of anomalous effects are observed in the knee region, such as an increase in the absorption length of hadron showers, a scaling violation in the spectra of secondary hadrons, an excess of muons in EAS with gamma families, a violation of isotopic invariance, the appearance of halos and the alignment of energy centers along a straight line. At the same energies equivalent to 1-100 PeV, laboratory system colliders show scaling behavior. So analysis of the data on the EAS cores suggests that the knee in their spectrum is formed by a component of cosmic rays of a non-nuclear nature, possibly consisting of stable (quasi-stable) particles of hypothetical strange quark matter. In this case, cosmic rays up to the fracture energy at 3 PeV consist of nuclei from protons to iron, and at high energies in the knee region from strangelets with electric charges Z = 30-1000.

Fig.1. The spectrum of cosmic rays.

S.B.Shaulov , V.A.Ryabov, A.L.Shepetov, S.E.Pyatovsky, V.V.Zhukov, K.A.Kupriyanova, E.N.Gudkova
JETP Letters 116, issue 1 (2022)

Plasma turbulence developing in intense high-frequency fields have been studied for more than 60 years. Such interest is connected with the problems of plasma heating in thermonuclear fusion devices, and to explain the features of the propagation of high-power radio waves in near-Earth plasmas. In particular, high-power ground-based and space-borne transmitters are capable of inducing artificial ionospheric turbulence (AIT). This AIT can modify the properties of radio waves’ propagation significantly, and affect the operation of radio communication and radio sounding systems.

In laboratory experiments performed on large-scale KROT device the turbulence was studied arising in a magnetoplasma when it was heated by intense high-frequency pump pulse. Large-scale cold quasi-uniform and magnetized plasma column (4 m in length and about 1 m in diameter) makes it possible to simulate ionospheric phenomena in a so-called “boundary-free” approximation. The pump pulse was applied to the loop antenna at frequencies both lower than electron gyrofrequency, and above it. The turbulence manifests itself in excitation of plasma density perturbations, generation of low-frequency electric currents, strong pump pulse self-modulation, and the modulation of test electromagnetic waves propagating through the perturbed plasma area. Turbulent density irregularities were studied by a set of microwave resonator probe (MRP) operated simultaneously. Correlation analysis of MRP data revealed the properties of space-time density dynamics. The density disturbances are field aligned and narrow (about 1 cm across the magnetic field). The electric currents pulsate in a direction mainly parallel to ambient magnetic field, and correlate with density disturbances. The turbulence occurred in a magnetoplasma transparent to the pump wave only, i.e. at frequencies below the electron gyrofrequency; at higher frequencies the turbulence was not observed. The measurements of turbulence decay characteristic time after the pump switching off, on the one hand, and estimates based on electron and ion transport velocities, on the other, suggest the fast unipolar regime of density disturbances’ evolution.

The turbulence (AIT) similar to those studied in a paper can arise in active ionospheric experiments with powerful satellite-based transmitters used to emit whistler waves at frequencies below the local gyrofrequency. Particularly, self-modulation effects observed can lead to noise-like signal distortions, and impose the limitations on radio pulse duration and amplitude.

(a) – laboratory experiment layout; (b) – pump pulse envelope waveforms received in plasma at various pump power levels

I.Yu.Zudin  et al.
JETP Letters 116, issue 1 (2022)

The idea of a metric with changing signature attracts a lot of attention in quantum cosmology, quantum gravity and condensed matter physics. Whereas all experiments and observations do not question the fact that the classical metric of the Universe has Lorentzian signature, we can consider the problems with signature changing in quantum gravity, cosmological models of the initial moments of the Universe. From the mathematical point of view the existence of a special signature is not evident. Therefore, one might ask two simple questions. The first one is about the generalization of Riemannian geometry, which allows the coexisting of different signatures of metric. The second question is why this is the Lorentzian signature that is observed in practice. One of the possibilities for the generalization of Riemannian geometry is  complexification of space – time manifold, and the appearance of complex geometry with holomorphic functions introduced instead of the real functions. In this theory there is a problem of the reduction of 4D complex manifold to the observed 4D real world. In the present approach the problem is considered differently.

We start from Riemann-Cartan gravity instead of conventional general relativity. This theory is easily generalized to the case of varying  signature. In order to introduce arbitrary signature of space – time the nontrivial metric is introduced in tangential space. It is given by real symmetric matrix O_ab, which is our new  dynamical variable (considered in addition to vierbein and spin connection). Now, depending on O_ab the general signature of metric can be arbitrary. There are several different forms of O_ab, to which it can be reduced. Minkowski signature corresponds to O=diag(-1,1,1,1) and O=diag(1,-1,-1,-1). Euclidean signature corresponds to  O=diag(1,1,1,1) and O=diag(-1,-1,-1,-1).  The cases O=diag(-1,-1,1,1) and O=diag(1,1,-1,-1) represent the signature, which is typically not considered in the framework of conventional quantum field theory. For these canonical forms of the O,  the vierbein belongs to representation of one of the three groups SO(4), SO(3,1), SO(2,2). The local gauge theory would contain the gauge field of one of the three Lie algebras. The group, which contains SO(4), SO(3,1), SO(2,2) must be introduced. The SL(4,R) group is taken as an example.

Therefore, we have a theory, which simultaneously describes geometry with different signatures allowed. One of the possibilities must be chosen dynamically through the corresponding Lagrangian for the O field and for the modified Riemann-Cartan gravity. We consider the general form of the Lagrangian, which describes dynamics of the field O. It appears that Lorentzian signature is preferred dynamically for a certain choice of such a Lagrangian. As an example of the possible application of the proposed approach we consider separation of space-time to the pieces with different signatures. An analogue of the black hole configuration, in which the interior has Euclidean signature is discussed. In this set-up the radial dynamics of a particle was shortly considered.  

To conclude, we propose the theory, which allows to the signature of metric to be changed dynamically.  This theory, in principle, allows investigation of various aspects of quantum gravity, and the early Universe cosmology. There is also an interesting mathematics behind.

S.Bondarenko, M.Zubkov
JETP Letters 116, issue 1 (2022)

The transition to superconducting digital circuits utilizing only Josephson junctions as functional elements promises a drastically increased integration density while maintaining high speed and energy efficiency. For this purpose, it was proposed to represent information in the form of the superconducting order parameter phase changes on bistable Josephson junctions. However, the practical fabrication of such Josephson heterostructures with parameters suitable for large-scale-integration density circuits doesn't yet seem possible. In this paper, we propose the concept of phase logic based on standard Josephson $\pi $-junctions having a single minimum of potential energy at the superconducting order parameter phase difference value equal to $\pi $. A complete set of $\pi $-phase logical elements necessary for the operation of digital devices is presented.

A.A.Maksimovskaya et al.
JETP Letters 115, issue 12 (2022)

Active development of optical quantum technologies including optical quantum computing and long-range quantum communications stimulates the creation of quantum memory (QM). The creation of highly-efficient QM will not only significantly expand the capabilities of these technologies, but will also contribute to the creation of new directions in their development. In this work a quantum memory protocol based on the revival of silenced echo (ROSE) signal in a ¹⁶⁷Er³⁺:Y₂SiO₅ crystal at a telecommunications wavelength has been experimentally implemented for input light fields with a small number of photons. A storage efficiency of 44% with a storage time of 40 µs was achieved. The input pulse contained on average ~340 photons, and the reconstructed echo signal ~150 photons, at a signal-to-noise ratio of 4. The main source of noise is the spontaneous emission of atoms remaining in the excited state due to the imperfection of rephasing pulses. Methods for increasing the signal to noise ratio are proposed and discussed in order to implement efficient quantum memory for single-photon light fields.

Fig.1. Storage of weak coherent input pulse (black curve at t = 0) with ~340 photons. Revival of silenced echo signal (blue curve at t=40 μs) contained ~150 photons in average. Retrieval efficiency of input pulse was 40%.  Optical noise level from spontaneous emission within the echo temporal mode was ~40 photons.

M.M.Minnegaliev et al.
JETP Letters 115, issue 12 (2022)

     Recent discovery of the first intrinsic antiferromagnetic topological insulator, layered MnBi₂Te₄ with Neel temperature of 25.4K and a magnetic gap in the electronic topological surface states as a prerequisite for the realization of anomalous quantum Hall state [1] has triggered the beginning of studying a series of quantum materials which MnBi₂Te₄ belongs to and which are known today as MnBi₂Te₄·n(Bi₂Te₃), where an integer index n shows the number of the quintuple Te-Bi-Te-Bi-Te atomic layer blocks (QLs) inserted between the neighboring magnetic septuple  Te-Bi-Te-Mn-Bi-Te atomic layer blocks (SLs) [2]. Remining topologically non-trivial at room temperature, the bulk crystals of MnBi₂Te₄·n(Bi₂Te₃) can also be considered as MnBi₂Te₄/n(Bi₂Te₃) heterostructures with n running from 0 to ∞ [3]
  The present work reports the results of the room temperature experimental studies of Raman-active modes of MnBi₂Te₄·n(Bi₂Te₃) with n =0,1,2,3,4,5,6, and ∞, along with the results of DFT-based calculations of the phonons in one, three, four and five free-standing QLs of Bi₂Te₃, as well as in bulk Bi₂Te₃ and MnBi₂Te₄.
  Lattice dynamics of the MnBi₂Te₄·n(Bi₂Te₃) for n>0 turns out to be described by lattice dynamics of the n number of QLs of Bi₂Te_3. Accordingly, lattice modes, the number of which is fixed to 4, due to their strong degeneracy, represent cooperative atomic displacements in QLs under practically immobile atoms of SLs. 
  A good illustration (Figure 1) reflecting such unusual lattice dynamics is brought about by very close correspondence between the Raman spectra (and their n-dependence) of MnBi₂Te₄·n(Bi₂Te₃) with n>0 and n QLs of Bi₂Te₃ deposited on SiO₂/Si substrate [4].

Fig.1 Normalized Raman spectra of MnBi₂Te₄·n(Bi₂Te₃) with n >0 (solid curves) and n QL of Bi₂Te₃ (open circles [4]).

[1] M. M. Otrokov et. al., Nature 576, 416 (2019).
       [2] Z. S. Aliyev et.al., J. Alloys and Compounds. 789, 443 (2019).
       [3] I. I. Klimovskikh et.al., npj Quantum Materials. 5, 54 (2020).
       [4] Y. Zhao et. al., Phys. Rev. B 90, 245428 (2014).

N. A.Abdullaev et al.
JETP Letters 115, issue12 (2022)

We present 2D frequency-resolved measurements of terahertz emission from a single-color femtosecond filament. In the low-frequency spectral range from 0.1 to 0.5 THz the conical shape of the THz fluence is observed, with the cone angle decreasing with growing frequency. This shape complies with the models of THz emission proposed in the literature. However, at higher frequency of ~1 THz, the two-lobe shape of THz fluence is measured. In the transverse plane, the axis containing the THz emission maxima is orthogonal to the linear polarization of the pump laser pulse. For the elliptical pump polarization, the cone shape of emission pattern is restored.

The observed THz directional diagram is found to be essentially sensitive to the laser pulse polarization direction. The majority of theoretical works propose a THz pattern to be conical regardless of the THz frequency or pump laser pulse polarization. Some of the models propose the modulation of the cone, which nevertheless is not enough to split the cone into the two lobes. The experimental data on both spectral and spatial characteristics of THz emission gathered in our work pave the way to comprehension of the physics underlying the THz emission from a single-color filament.

Normalized angular distributions of radiation at frequency of 1 THz, obtained for horizontal (a) vertical (b) and elliptical (c) polarization of the laser pump pulse

Rizaev G.E., Mokrousova D.V., PushkarevD.V.  et al.
JETP Letters 115, issue 11 (2022)

Peccei-Quinn axions, suggested as a solution to the strong CP-problem, are viewed as one of the most credible candidates for the dark matter. Spin of particles couples to the oscillating pseudomagnetic field  caused through Weinberg's derivative interaction  by their motion in the dark halo of our galaxy. Close to the speed of light velocity of particles in storage rings makes the Weinberg interaction the dominant source of the axion signal and strongly enhances the performance of the particle spin as a NMR-like axion antenna. The current searches for the resonant spin rotation in storage rings use the JEDI collaboration developed technique of the buildup of the vertical polarization from the  in-plane one. In the case of protons the showstopper for the JEDI approach is a short spin coherence time. Based on our analytic treatment of the impact of the spin coherence time on the frequency scanning search for  the axion signal, we suggest the alternative scheme of a rotation of the initially vertical spin onto the horizontal plane. This scheme is free of the axion field phase ambiguity, does not need radiofrequency spin flippers and can readily be implemented with polarized protons stored in the Nuclotron, NICA and PTR storage rings as an axion antenna. Of particular interest is PTR with concurrent electric and magnetic bending. We suggest to run PTR off of the frozen spin mode, varying  the electric and magnetic fields in sync  to retain the injection energy. This would make PTR a unique broaband axion antenna covering the axion field oscillation frequencies below 0.5 MHz.
 

N.N.Nikolaev
JETP Letters 115, issue 11 (2022)

The negative differential resistance (NDR) in the current driven regime is rarely met in superconductors being in resistive state, in contrast to NDR which appears in  the voltage driven regime. Known examples are underdamped Josephson junction (JJ) in the presence of microwave radiation and superconducting thin film with periodic array of ariticial defects placed in perpendicular magnetic field just above the first matching field (at this field all defects are occupied by vorticies). From physical point of view this effect is unusual because despite of increase of dc driving force (dc current) the 'particle' (vortex in thin film or the 'effective partcile' in case of JJ) moves with smaller average velocity. It is known that in both systems NDR appears when chaotic dynamics of superconducting phase (JJ) or chaotic motion of vortices (thin film) is realized.

In our work we have observed similar NDR in superconducting MoN strips with a slit near one edge and in the presence of high-power microwave radiation. On the I–V characteristic, the section with NDR is adjacent to steps (well visible at low power of microwave radiation) similar to the Shapiro steps in the Josephson junction. An analysis within the framework of the time-dependent Ginzburg-Landau equation and the heat balance equation for electron temperature showed that a possible cause of NDR is the disordered (chaotic) motion of vortices across the strip near the slit, which appears at high enough microwave radiation power.

Our findings give another example of superconducting system which reveals NDR in the current-driven regime and the origin of this effect is again connected with chaotic motion of vortices.

 

S. S. Ustavschikov, M. Yu. Levichev, I. Yu. Pashenkin, N. S. Gusev, S. A. Gusev, D. Yu. Vodolazov

JETP Letters 115, issue 10 (2022)

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Quantum interference of electrons travelling along the closed diffusive trajectories yields the correction to the conductivity of the electron system [1, 2]. In case of constructive interference the electrons become more "localized" and the net resistivity rises. Presence of spin-orbit interaction facilitates the spin rotation of electrons moving in closed loops and promotes the destructive interference of electron waves leading to the decrease of the resistivity. This effect is traditionally referred to as "weak antilocalization". Thus, studying the resistance of the 2D electron system in the presence of weak antilocalization can be used both to judge the parameters of electron wave coherence and to extract the strength of the spin-orbit interaction - one of the key fundamental interactions governing the semiconductor physics of spin.

In the present work, the weak antilocalization effect was discovered for the first time in a narrow AlAs quantum well containing a two-dimensional electron system. This structure features both strong spin-orbit interaction of the Dresselhaus type [3] and large effective mass [4]. Large mass ensures the significant role of the manybody physics in this system, as the kinetic energy is small compared to the characteristic energy of the Coulomb interactions.

Analysis of the experimentally observed quantum corrections was performed following  [5] and allowed us to estimate the constant $\beta=10.1$~meV$\times{\AA}$ of the spin-orbit interaction. Independently, this constant $\beta=7.6$~meV$\times{\AA}$ was determined by studying the modification of the single particle spin splitting probed by electron spin resonance. Obtained constants turned out to be rather close and the remnant discrepancy may be attributed to the effects of the electron-electron interactions.

                      Quantum corrections to the conductivity of the two-dimensional electron system enclosed in a 4 nm AlAs-quantum well. The blue circles denote experimental data, and the black line is approximation according to the work [5]

 

[1] Hikami S., Larkin A. I., Nagaoka Y. Progress of Theoretical Physics. 63, 707-710 (1980)
       [2] G. Bergmann, Physics Reports 107, 1 (1984)
       [3] A. V. Shchepetilnikov, D. D. Frolov, Yu. A. Nefyodov, I. V. Kukushkin, L. Tiemann, C. Reichl, W. Dietsche, and W. Wegscheider Phys. Rev. B 98, 241302(R) (2018)
       [4] A. R. Khisameeva, A. V. Shchepetilnikov, V. M. Muravev, S. I. Gubarev, D. D. Frolov, Yu. A. Nefyodov, I. V. Kukushkin, C. Reichl, W. Dietsche, and W. Wegscheider Journal of Applied Physics 125, 154501 (2019)
       [5] A. Punnoose, Appl. Phys. Lett. 88, 252113 (2006)

A. V. Shchepetilnikov, A. R. Khisameeva, A. A. Dremin, I. V. Kukushkin
JETP Letters 115, issue 9 (2022)
 

A new method of hardening industrial products by laser generation of a powerful shock wave (SW) melting the metal is proposed. A laser pulse of 0.1-1 picosecond duration with maximum intensity determined by the optical breakdown of air is used. In metals with low reflection coefficient (e.g., titanium considered here) the absorbed energy is tens of J/square cm. In this case, due to poor thermal conductivity of titanium, the initial pressures reach values of the order of 10¹² Pascal. The SW melts the metal as long as the pressures at the front exceed the values of 10¹¹ Pa. As a result, the thickness of the melt layer is an order of magnitude greater than in melting due to thermal conductivity alone.

The specifics of the SW transition from melting (mode M) to non-melting (mode S) propagation are important. During crystallization of the melt layer, the connection with the crystalline ordering of the parent monocrystal, which represented the titanium target before the laser exposure, is lost. The point is that a rather wide transition zone (up to 100 nm) of "mechanical" melting occurs during the M-S transition [1]. This zone is filled with randomly oriented particles of nanocrystallites inside the melt [1]. The solidification of the liquid layer due to heat conduction into the volume through the M-S transition zone leads to crystallization starting from these nanocrystallites. As a result, after solidification, the melt layer is transformed into a layer filled with randomly oriented crystallites. This layer is qualitatively different from the underlying single crystal. The non-melting SW that has escaped into the underlying monocrystal leaves a dislocation trace in the monocrystal. The concentration of dislocations gradually decreases as they move away from the boundary of the layer that has gone through melting and crystallization. This is due to the weakening of the SW.

Figure shows the Q6 order parameter profiles in M mode (43.2 ps) and in S mode (52.8-81.6 ps). The values of Q6 below the dashed horizontal line refer to the liquid phase. The M-S transition region is clearly visible on the upper panel and on the S profiles. The spatial coordinate x in Figure is from the initial position of the titanium-air boundary.

[1] Budzevich et al., Evolution of Shock-Induced Orientation-Dependent Metastable States in Crystalline Aluminum, Phys. Rev. Lett. vol. 109, 125505 (2012)

V.A. Khokhlov, V.V. Zhakhovsky, N.A. Inogamov, S.I. Ashitkov, D.S. Sitnikov, K.V. Khishchenko, Y.V. Petrov, S.S. Manokhin, I.V. Nelasov, Y.R. Kolobov, V.V. Shepelev
JETP Letters 115, issue 9  (2022)

Cooling and trapping atoms near the atom chip need high local concentration of atoms. It increases the sensitivity of quantum sensors based on atom chip through the increasing of the cold atoms in the trap cooled for the smallest time. A method for increasing the loading rate of atoms into a U-shaped magneto-optical trap of atoms near an atomic chip is considered in this paper. The approach is based on focusing a low-velocity atomic beam into the localization region of atoms on an atomic chip. The mode of focusing with excessive damping is considered. In this case, the focal length does not depend on the initial transverse velocity of the atoms. It is shown that due to the focusing of the atomic beam, it is possible to increase the loading rate by a factor of 160 in the localization region with a diameter of 250 μm.

A.E. Afanasiev et.al
JETP Letters 115, issue 9 (2022)

An approach that makes it possible to calculate the coherence and interference characteristics of macroscopic quantum systems is proposed. A general method based on the Schmidt decomposition for the analysis of two-particle quantum systems is presented. This method makes it possible to investigate the quantum entanglement between the system and the environment, as well as the coherence of interfering alternatives. Simple formulas expressing the relationship between coherence, interference visibility, and the Schmidt number are obtained. As an illustration, the characteristics of coherence and interference for the multimode quantum Schrödinger cat state were studied. It was shown that the phenomenon of decoherence of multimode states is clearly manifested under conditions where there are many modes, with the average number of photons per mode is much less than unity. Hypothetically, macroscopically distinguishable interfering alternatives in the multimode Schrödinger cat state can be characterized by arbitrarily high values of the total energy and the total number of photons. However, such macroscopically distinguishable superpositions are almost completely destroyed already when observing a limited number of environmental modes, which contain totally about one photon. Thus, the fate of the legendary Schrödinger's cat does not depend on a macroscopic observer, but on microscopic processes affecting a limited number of environmental modes and constituting a negligible fraction of the initial multimode state itself.

The figure shows the dependence of the probability of "survival" for a multimode Schrödinger cat depending from the number of measured environment modes m. It can be seen that, starting approximately from $m = 15 \cdot \ 10^3$ (corresponds to a $m \alpha^2 = 1.5$  photon), the superposition of the states of a “live” and “dead” cat is almost completely destroyed.

The dependence of the probability of "survival" of the Schrödinger cat from the number of reduced modes. The amplitude of each mode $\alpha = 0.01$, the total number of modes $n = 1 000 000. 30 $ numerical experiments were performed.

Yu. I. Bogdanov, N. A. Bogdanova, D. V. Fastovets, V. F. Lukichev
JETP Letters 115, 8 (2022)

The notion of the Planckian dissipation is extended to the system of the Caroli-de Gennes-Matricon energy levels in the vortex core of superconductors and fermionic superfluids. In this approach, the Planck dissipation takes place when the inverse scattering time is comparable with the distance between the levels (the minigap). This type of Planck dissipation determines the transition to the regime, when the effect of the axial anomaly becomes important. The anomalous spectral flow of the energy levels along the chiral branch of the Caroli-de Gennes-Matricon states takes place in the super-Planckian regime. Also, the Planck dissipation separates the laminar flow of the superfluid liquid and the vortex turbulence, see dashed vertical line in the phase diagram.

The phase diagram is determined by two Reynolds numbers, related to two types of Planckian dissipation. It has three regions. The laminar flow takes place in the super-Planckian regime with the spectral flow. In the sub-Planckian regime the spectral flow   is suppressed, which leads to quantum turbulence. The grey line marks the crossover between two regimes of quantum turbulence: the classical-like Kolmogorov cascade, and the Vinen-type turbulence with the single length scale – the distance between vortices.

G.E. Volovik                                  
JETP Letters 115, № 8 (2022)      

The essence of the optical diode effect is as follows: the intensity of light transmitted through a plate of material in one direction is several times higher than the intensity of light transmitted in the opposite direction. Fig. 1a. shows cases in which the polarization of the electric component $E^{\omega }$ does not change with the reversal of the wave vector. Consequently, the magnetic component of light $H^{\omega}$  flips the direction. This leads to the change of sign in the sum of operators of electric and magnetic dipole transitions: $dE^{\omega } + \mu H^{\omega }$.

For materials where both space and time inversion symmetry is broken (FeZnMo₃O₈ is an example), the net probability of transition $W_{\psi _1 \psi_z} \sim | \langle \psi _1 | dE^{\omega }+ \mu H^{\omega } | \psi _2 \rangle |^2$ contains additional terms linear  in magnetic and electric components of the light wave $E^{\omega } _{\alpha} H^{\omega } _{\beta }$. Due to  these terms, the absorption intensity changes with the change of sign of one of the components.

In this work we contribute to the microscopic theory of  interaction of  electromagnetic waves with the dipole and magnetic moments of Fe²⁺ ions in the FeZnMo₃O₈ crystal. The energy levels, wave functions and transition probabilities between the states of the ⁵D term are calculated. For free Fe²⁺ ion electric dipole transitions within the states of 3dⁿ electronic configuration are forbidden by the parity conservation law, and the electric quadrupole transitions are weak. Thus, the mechanism of magnetic dipole transitions becomes dominant. In FeZnMo₃O₈ the Fe²⁺ ion occupies the positions with no inversion symmetry. The states of the 3d⁶ electronic configuration mix with the configuration of opposite parity 3d⁵4p, as well as with the states in which electrons from the nearest oxygen ions can be transferred to the 3d shell. The mixing process induces electric dipole transitions within the states of the 3d⁶ configuration. According to our calculations in FeZnMo₃O₈, the contributions of magnetic and electric dipole transitions in the terahertz region of the absorption spectrum turned out to be of the same order of magnitude. This circumstance explains the basic feature of the optical diode effect. Some of the results of our calculations are shown in Fig. 1b, 1c.

Fig. 1. (a) The illustration of the optical diode effect. The width of the cylinders reflects the intensity of light. (b) Experimental (symbols from Ref [1]) and calculated (solid lines) magnetic field dependence of the absorption frequencies. (c) Magnetic field dependence of the absorption coefficients calculated in this work.

[1] Shukai Yu, Bin Gao, Jae Wook Kim, Sang-Wook Cheong, Michael K. L. Man, Julien Madeo, Keshav M. Dani, Diyar Talbayev, Phys. Rev. Lett., 120, 037601 (2018)

K. V. Vasin, M. V. Eremin and A. R. Nurmukhametov
JETP Letters 115, issue 7 (2022)

In recent years much interest was attracted to experimental studies of Hall effect at low temperatures in the normal state of high -- temperature superconductors (cuprates), which is achieved in very strong external magnetic fields [1]. The observed anomalies of Hall effect in these experiments were usually attributed to Fermi surface reconstruction due to formation of (antiferromagnetic) pseudogap and corresponding quantum critical point [2].

Commonly accepted view is that cuprates are strongly correlated systems and their metallic (superconducting) state is realized as a result of doping of a parent Mott insulator usually described within Hubbard model. However, there are almost no works devoted to systematic studies of doping dependence of Hall effect in this model. Central question here is the sign of Hall coefficient and critical doping for its change.

Deeply in hole doped Mott insulator the Hall coefficient is in fact determined by filling of the lower Hubbard band. For the model with electron - hole symmetry a qualitatively estimate the band -- filling corresponding to sign change of Hall coefficient can be done as follows. Consider paramagnetic phase with $n_{\uparrow}=n_{\downarrow}=n$, so that $n$ denotes electron density per single spin projection, while the total electron density is $2n$. It is natural to assume that the sign change of Hall coefficient takes place around half - filling of the lower Hubbard band corresponding
to $n_0\approx 1/2$. The total number of states in the lower Hubbard band is $1-n_{\downarrow}=1-n$. Then the actual band - filling is given by $n=n_{\uparrow}=n_0(1-n)\approx 1/2(1-n)$. Solving this equation gives $n_c\approx 1/3$,
or $\delta_c=1-2n_c\approx 1/3$ for corresponding hole concentration, for the critical doping at which the Hall coefficient changes its sign.

In this work extensive DMFT [3] calculations of Hall effect were performed for two - dimensional Hubbard model with tight - binding electronic spectrum, keeping in mind the comparison with experimental data on YBCO. In general case (without electron -- hole symmetry) the value of $n_c$ ($\delta_c$) depends on parameters of the model (transfer integrals ratios and correlation strength, as well as on temperature). In  Fig. 1  the comparison of calculated  Hall number (Hall concentration) $n_H=\frac{a^2}{|eR_H|}$ is shown for typical model parameters with experimental data for YBCO from Ref. [1].  Almost quantitative agreement with experiment was obtained. Thus it is quite possible that the interpretation of Hall effect in cuprates based on a simple picture of doping of the lower Hubbard band, not related to more sophisticated factors, such as change of topology of Fermi surface or quantum critical points.

Fig.1 Dependence of Hall number $n_H$ on doping - comparison with experiment [1] on YBCO, $\delta=1-2n$ - hole concentration, stars - theory (for typical spectrum parameters for YBCO and relatively strong correlations), circles - experiment.

[1] S. Badoux, W. Tabis, F. Laliberte, B. Vignolle, D. Vignolles, J. Beard, D.A. Bonn, W.N. Hardy, R. Liang, N. Doiron-Leyraud, L. Taillefer, C. Proust. Nature 531, 210 (2016)
[2] C. Proust, L. Taillefer. Annu. Rev. Condens. Matter Phys. 10, 409 (2019)
[3] Th. Pruschke, M. Jarrell, J. K. Freericks. Adv. Phys.  44, 187 (1995)

E.Z. Kuchinskii, N.A. Kuleeva, D.I. Khomskii, M.V. Sadovskii.
JETP Letters 115, issue 7 (2022)

 

A review of research on geodesic acoustic modes and Alfvén Eigenmodes (AE), and their relations to other types of turbulence and plasma confinement in tokamaks and stellarators is presented. The main experiments were carried out at the T-10 tokamak (Russia) with powerful electron cyclotron heating (ECH) of the plasma and at the TJ-II stellarator (Spain), where the plasma was created and heated by ECH and neutral beam injection (NBI). With NBI, AEs are excited in the plasma, the AE frequency is varied with the plasma density n according to the Alfvén scaling (f_AE~n^-1/2). In addition to AE with a continuous frequency change, chirped AE modes with a sharp change in frequency can occur. Alfvén modes can worsen the confinement of energetic particles. When the additional ECH is supplied, AEs are weakened, so it is proposed to use ECH to suppress Alfvén modes in future fusion reactors.

Evolution of the Alfvén mode from continuous to chirped and back in the TJ-II stellarator with neutral beam injection (NBI) and variation in the power of electron-cyclotron heating (ECH). Top - spectrum of magnetic fluctuations. White line is the Alfvén scaling on the density (f_AE~n-^1/2); Bottom – weakening and suppression of AE by ECH.

A.V. Melnikov, V.A. Vershkov, S.A. Grashin, M.A. Drabinskiy, L.G. Eliseev, I.A. Zemtsov, V.A. Krupin, V.P. Lakhin, S.E. Lysenko, A.R. Nemets, M.R. Nurgaliev, N.K. Kharchev, P.O. Khabanov and D.A. Shelukhin
JETP Letters 115, issue 6 (2022)

The creation of quantum memory is of growing interest due to the importance of its use in solving problems of practical quantum information science. It has recently been shown that a system of high-Q resonators with a periodic structure of resonant frequencies opens up real possibilities for working with broadband signals [Scientific Reports, 8, 3982 (2018)]. However, a significant increase in the lifetime requires the integration of long-lived quantum information carriers into the multi-resonator quantum memory circuit.

In this letter [1], we propose a quantum memory based on a system of few resonators containing one atom in each resonator, where the resonators are connected to an external waveguide through a common resonator. Principle scheme is shown in Fig., where storage (retrieval) of the signals A_in,out(t) from an external waveguide on long-lived atomic coherences s_n(t) through the common resonator and  minicavities  modes (x_n(t) and a(t)). Using the properties of the reversible dynamics and optimization methods, the parameters of resonators and atoms interacting with them are found, at which an effective transfer of a single-photon wave packet from an external waveguide to a long-lived coherence of atoms is possible. It is also shown that the proposed scheme provides the operation with a broadband photon wave packet with Gaussian temporal mode.

Finally, we also discuss the possible experimental implementations including using three-level quantum dots as artificial resonant atoms providing sufficiently strong coupling with a photon in high-Q micro- and nanophotonic resonators. In this case, the considered quantum memory protocol is implemented by using off-resonant Raman interaction of a photon with three-level quantum dots with effective integration of resonators into external devices.

[1] S.A. Moiseev, N.S. Perminov, and A.M. Zheltikov. JETP Letters 115, № 6 (2022).

S.A. Moiseev, N.S. Perminov, and A.M. Zheltikov
JETP Letters 115, issue 6 (2022).

The sensitivity of the system to the small changes of the initial condition was noted by  H. Poincaré. He discovered it during the study of the three-body problem. Then, this problem was studied by A. Lyapunov. The notion "butterfly effect"\~ was suggested by E. Lorenz, who discovered similar instability during the study of the atmospheric processes. Due to this effect, the distance between close trajectories of the system increases exponentially in time i.e. $\frac{\partial q(t)}{\partial q(0)}\sim e^{\lambda_L t}$. The parameter $\lambda_L$ is called the Lyapunov exponent.

One should observe the out-of-time ordered correlation function (OTOC) to study this effect in the quantum system. It was pointed out in the work  [1]. The Google Quantum Ai group did the experimental study of the OTOC, and the result was published in the work   [2]. They used the quantum processor to simulate the motion backward in time.
 

For the big class of the quantum systems, the Lyapunov exponent is bounded: $\lambda_L \le \frac{ 2\pi T}{\hbar}$ where $T$ is a temperature of the system, and $\hbar$ is the  Planck constant, it was shown in the work  [3]. The Sachdev-Ye-Kitaev (SYK) (see. [4] model is an example with maximal Lyapunov exponent.  

In the present paper, we propose the generalization of the SYK model with a non-zero spatial dimension. The OTOC shows the following behavior. For short times it changes with the maximal Lyapunov exponent. Here short means less than the so-called Ehrenfest time. We see the chaotic behavior of the system for such times, but it is not yet developed. When  Ehrenfest time comes, chaos is locally well developed, and it starts to spreads through the system with constant speed as a front. A similar scenario was described in the work  [5] for the Fermi-liquid-like system, whereas our model is not of such class.

Our result is fully analytical, and the technique could be applied to any  SYK-like model. We also present the first calculation of the front speed in this work. It is interesting to note that for sufficiently low temperature, the speed  of front depends only on the temperature $T$ and the typical
 length scale of the problem $a$ i.e. $v\approx\frac{ 2\pi T}{\hbar}a\times 1.6$
[1] A.I. Larkin, Yu. N. Ovchinnikov, Sov Phys JETP,  28, issue 6 (1969)
[2] X. Mi, P. Roushan, C. Quintana (Collaboration) arXiv preprint arXiv:2101.08870
[3] J. Maldacena, S.H.  Shenker, D. Stanford,Journal of High Energy Physics 2016 8 (2016)
[4] A. Kitaev, S.J. Suh, Journal of High Energy Physics, 2018 5 (2018)
[5] I.L. Aleiner, L. Faoro, L.B. Ioffe, Annals of Physics, 375 (2016)
 

A.V.Lunkin
JETP Letters 115 issue 5 (2022)

Fabrication of fluorescent integrated optical elements is a challenging task. One of the most perspective methods for the growth of such structures is the two-photon laser lithography from dye-doped polymers, which can provide desirable geometrical parameters as well as high fluorescence quantum yield.

In this letter we demonstrate the composition of microresonators using OrmoCopm polymer with Coumarin-1 dye and mixture of Rhodamine-640 and Rhodamine-590. We demonstrate the formation of microresonators of various shape such as cylinders, pentagons etc. of the characteristic dimensions of 10-15 micrometers. Homogeneity of the dye distribution within the structure and bright fluorescence of dyes after the polymerization was shown by means of two-photon fluorescence microscopy. We also demonstrate that Coumarin-1 acts as a photoinitiator as well as an active dopant that diminishes by two orders of magnitude the laser fluence required for the polymerization.

Captured scattered fluorescence patterns proved excitation of different types of resonator modes: whispering gallery and bow tie modes, that was supported by FDTD simulations.

A. Maydykovskiy, E. Mamonov, N. Mitetelo, S.Soria, T.Murzina
JETP Letters 115, issue 5 (2022)
 

The interplay between topology and magnetism in magnetic topological insulators (TI) provides particularly rich playground for realization of new exotic physics. These unusual properties make magnetic TIs extremely attractive for applications in novel electronics, especially in the trendy 2D and antiferromagnetic spintronics and quantum computations. To date, the most promising platform for realizing such effects is the recently discovered MnBi2Te4 antiferromagnetic TI, which inspired a lot of research activity as it holds promise of the high-temperature quantized anomalous Hall and axion insulator states, Majorana hinge modes and other effects. Nevertheless, originally MnBi2Te4 is highly n-doped, while for any practical purpose there must be a charge neutral state. A known way to change the doping level for MnBi2Te4 is to replace Bi atoms with Sb atoms. Here we study in detail the change of the electronic structure in the Dirac cone region and core levels depending on the concentration of Sb atoms in Mn(Bi1-xSbx)2Te4 in wide region of x. The photoelectron spectra of valence and conducting bands are presented, that clearly show the change in the doping level (see fig). Besides, in the paper a detailed dependence of the doping level on the concentration of Sb atoms at a particular measured point is plotted. This dependence is approximated by a root function, that corresponds to a linear increase in the density of charge carriers. Our results provide an important step towards the applications of new magnetic TIs in post-silicon electronic devices.

D.A. Glazkova et al.
JETP Letters 115, issue 5(2022)

       Now the most interesting topics in the condensed matter physics are related to topological materials: topological insulators, topological superconductors, Dirac and Weyl topological semimetals, etc. Superfluid phases of liquid 3He are the best representatives of the topological matter. Each phase has its unique topological property. Recently the new topological phase of superfluid 3He has been discovered - the beta phase, where only single spin component of the liquid is superfluid. The beta-phase is obtained by strong polarization of the nematic polar phase. Here we consider half-quantum vortices (HQVs), which are formed in rotating cryostat with polar phase, and discuss theoretically the evolution of the vortex lattice in the process of the transition from the polar phase to the beta-phase via the spin-polarized polar phase.

In the pure polar phase, the elementary cell of the vortex lattice in Fig.a contains two HQVs: the spin-up and spin-down HQVs. When the polar phase is spin-polarized by magnetic field, the balance between spin-up and spin-down vortices is violated. The lattice as before contains two sublattices in Fig.b, where HQVs in the spin-down component have smaller amplitude. Finally, the spin-down sublattice fades away at the transition to the beta-phase in Fig.c, and only the vortices in the spin-up component remain. In this scenario, the HQV in the spin-up component in the polar phase continuously transforms to the single quantum vortex in the beta phase.

G.E. Volovik
JETP Letters 115, issue 5 (2022)      

Layer-by-layer thinning transition of free standing smectic nanofilms are one of the most spectacular discoveries in the physics of liquid crystals in the latest decades. The essence of the effect is that smectic nanofims do not melt on heating, melting is replaced by a series of transitions with a decrease of the film thickness by one or several molecular layers. This phenomenon was recognized (observed and theoretically described) quite some time ago. Therefore it might be thought that its mechanism would be completely understood. Our investigation shows that it is not the case. In this work, we have discovered a new mechanism of nanofilm thinning, which was not previously observed in experimental studies and was not theoretically predicted.  Namely we found a significant change in the shape of the meniscus near the thinning transition, the formation of a thin film section in it, and an increase in the size of the meniscus itself which leads to a thinning of the entire film. We do believe that our work opens a new avenue of research of the smectic films. The phenomenon of film thinning turns out to be much more complex and rich than previously thought.  Further experimental and theoretical studies are required.

Process of thinning of a smectic free-standing film (from (a) to (f)) starting near the meniscus-film boundary. (a) – T=59.5°C; (b) – T=60.15°C; (c) – T=60.26°C; (d) – T=60.29°C; (e) – T=60.31°C; (f) – T=60.34°C.

P.V. Dolganov, V.K. Dolganov, E.I. Kats

JETP Letters 115, Issue 4 (2022)

Current optical manipulation techniques make it possible to localize, move, and sort micro- and nanoparticles in compact microfluidic devices. In contrast to conventional optical tweezers, newly emerging techniques usually employ the near field of planar optical elements. This allows one to integrate the entire optical circuit inside the device. Unfortunately, manipulating particles using optical near-field is typically accompanied by increased viscous friction and adhesion probability. To overcome these difficulties, researchers have been looking for optical systems with the potential energy minimum located at a distance from the structure.

Previously, a similar problem was solved for optical trapping of atoms. To hold them at a distance from the waveguide structures, it has been proposed to use light of two different wavelengths. Since the polarizability of atoms changes sign near the transition frequency, it is possible to choose wavelengths so that the optical forces have opposite directions and balance each other at a finite distance from the surface. Such an approach can be useful not only for trapping atoms but also for manipulating high-refractive-index micro- and nanoparticles, whose polarizability changes sign near Mie scattering resonances. However, its applicability to this case has not been previously explored.

In this work, near-field optical manipulation of Mie-resonant silicon particles in water is modeled. To localize particles at a controlled distance from the surface, Bloch surface waves of two optical frequencies are used. The forces acting on the particles are calculated as a function of particle size, wavelength, and distance from the surface. The range of the equilibrium position adjustment is estimated for typical experimental parameters, taking into account the Brownian motion at room temperature. The results highlight the great potential of two-color surface waves for optical manipulation of Mie-resonant nanoparticles.

Optical levitation of a Mie-resonant silicon nanoparticle in the evanescent field of two-color surface electromagnetic waves

Shilkin D.A., Fedyanin A.A.
JETP Letters 115, issue 3 (2022)

The genesis of complex elastic waves emitted from a hot spot produced by strong laser heating is studied. There is a connection/bridge between (A) laser shock peening by strong laser action and (B) linear optoacoustics by weak laser action.

1. Laser-induced hydrodynamics results in surface layer hardening. The laser heating leads to plume formation, melting, crater formation, formation of a dense dislocation field around the crater with residual deformations and stresses. At the same time, shocks running from the forming crater into the target pass from elastic-plastic regime of propagation to nonlinear elastic regime (nonlinear elastic shocks). Nonlinear elastic shocks are attenuated to linear elastic waves used in optoacoustics.
2. Optoacoustics at the micro- and nanoscale, i.e. photon-phonon conversion, is in great demand for advanced applications of photon-phonon transducers in telecommunications, acoustic magnetization switches and in sensors (detection of elastic characteristics). In such applications, a weak laser beam excites an elastic acoustic wave system. But researchers here are interested mainly in the surface Rayleigh wave or consider a one-dimensional geometry with plane wave fronts with neglecting the side effects.

Figure shows a wave configuration at transition from elastic-plastic propagation regime to pure elastic regime. Near the hot spot with a plume, a zone of plastic deformations imprinted in the matter is formed. Elastic waves emitted from this spot have a complex mixed longitudinal-transverse polarization and consist of a combination of compression waves, rarefaction waves, vortex/shear waves and the surface Rayleigh wave.

Figure. Snapshots from molecular dynamics simulation of aluminum layer with 120 million atoms at time 25.2 ps. The normal to free surface coincides with direction [111] of FCC crystal. The layer dimensions are 200 nm along the normal, 500 nm in transverse direction, and 20 nm in thickness perpendicular to the Figure plane. Laser beam size is 100 nm, and heat penetration depth is 20 nm. Pressure reaches 49 GPa just after femtosecond laser heating.

(a) Map of von Mises stress. The blue arrows mark the wedge-shaped unloading waves running along the surface and spreading into the volume. The wedge waves are originated in the contact point of the incident shock with the free surface.

(b) Field of the normal velocity is presented.  Material moves to the right in the red-colored areas, and it moves to the left in the green areas. The red arrows show the surface Rayleigh waves forming inside a complex wave configuration.

N.A. Inogamov, E.A. Perov, V.V. Zakhovsky, V.V. Shepelev, Yu.V. Petrov, S.V. Fortova
JETP Letters 115, issue 2 (2022)

Laser ablation into liquid (LAL) is used to produce nanoparticles (NPs). Ultra-short ablation (femto- picosecond fs/ps-LAL) and nanosecond ablation (ns-LAL) are available. During fs/ps-LAL, cavity nucleation occurs beneath the irradiated surface. Then the detachment of the spallation layer (SpL) takes place. In the fs/ps-LAL, nucleation, foaming, and disintegration of the SpL significantly affect the number and size distribution of the resulting NPs.

There is no subsurface nucleation during ns-LAL considered here. There is no SpL, no capillary decay of the SpL. Then the standard process of NPs formation consists of three links: (1) evaporation - (2) diffusion in the receiving substance (which is air or liquid; in our case, liquid/water, see Figure) - (3) condensation.

At absorbed fluences F~1 J/cm², the gold-water contact boundary (cb) is a few nanoseconds above the critical point in the gold phase diagram – this is the supercritical time interval. The importance of this circumstance is great. At this time interval the capillary barrier disappears, which should be overcome by evaporation (surface tension is zero). Then, firstly, the diffusion flux is sharply intensified and, secondly, cooling of the evaporating melt due to large heat of evaporation disappears.  Thus, link 1 in the 1-2-3 chain drops out. Link 1 drastically reduces the amount of LF, see figure.

In the case of supercritical states, the entropy of gold S_cb at contact boundary (cb) exceeds the critical entropy S_cr. Gold of the [S_cb-S_cr] segment of the material profile comes under the binodal through the condensation curve (cc); except for the amount that diffused through point “cb” into the water. However, gold [S_cb-S_cr] does not form NPs!

Split the segment [S_cb-S_cr] into layers “S”: S_cb > S > S_cr. The layers “S” cross the condensation curve sequentially from lower entropy values to higher values. Consider two adjacent layers S_cc > S of this sequence. Let the layer S_cc cross the condensation curve “cc” at time t. Layer S must be in a two-phase state with saturated vapor pressure P_sat(S,t). Pressure P_sat(S,t) is less than the pressure P_cc = P_sat(S_cc,t). Therefore, the two-phase layer S collapses (shrinks) into a one-phase liquid. Accordingly, there is no NP contribution from the S layer.

N. A. Inogamov, V. V. Zhakhovsky, V. A. Khokhlov
JETP Letters 115, issue 1 (2022)

In this study, Auroral Kilometric Radiation (AKR) is used as a remote diagnostic tool for processes in the Earth's magnetosphere. Using satellite data and the spectrum of AKR fluctuations at different frequencies, we study fractal properties of the auroral region of the magnetosphere depending on the source height and the radiation generation frequency. Scaling is used to determine fractal characteristics (Hurst exponent and fractal dimension) of the medium in the region of AKR generation and their dynamics depending on the height and frequency. It is shown that with an increase in height (or, which is the same, with a decrease in signal frequency), the value of scaling and Hurst exponent increases, while the fractal dimension decreases with height. We considered different cases of AKR registration under various geomagnetic conditions, when AKR intensity differed by an order of magnitude; however, there is a steady trend towards a decrease in the fractal dimension with height during the AKR generation. The obtained values of the scaling and fractal parameters indicate that the processes under consideration exhibit self-similarity and long-range dependence.

Upper panel is a dynamic spectrogram of the AKR power according to measurements from the Interbol-2 satellite for November 22, 1997. Bottom panel is dependence of fractal dimension D and Hurst exponent H on height and frequency.

A.A. Chernyshov, D.V. Chugunin and M.M. Mogilevsky
JETP Letters 115, issue 1 (2022)

Recently, it was reported the observation of acoustically induced transparency (AIT) of stainless-steel foil for resonant gamma-ray photons with an energy of 14.4 keV emitted from a radioactive Mossbauer source ⁵⁷Co [1]. Similar to the electromagnetically induced transparency (EIT) and Autler–Townes splitting (ATS), AIT constitutes the appearance of a spectral domain of very weak absorption of radiation, located at the place of a nuclear resonant spectral line (Fig.1). However, in contrast to EIT and ATS, AIT doesn’t require a strong coherent electromagnetic driving field and can occur already in a two-level system. AIT is caused by coherent uniform oscillations of nuclei with ultrasonic frequency, which can be implemented by piston-like vibration of a solid absorbing medium. Similar to EIT and ATS, the material dispersion in the AIT spectral window has a sharp slope (Fig.1), which corresponds to a decrease in the group velocity of propagating radiation. In this paper, we show that under the same experimental conditions as in [1], single 14.4 keV photons emitted by the ⁵⁷Co source can be slowed down below 6 m/s at room temperature in a stainless-steel foil of a certain thickness, enriched with ⁵⁷Fe nuclide, oscillating at an optimal frequency. The corresponding single-photon wave packet of gamma radiation having a duration of about 80 ns can be delayed by about 100 ns.

Fig. 1. Absorption (red curve, right axis) and dispersion (blue curve, left axis) of the vibrating resonant absorber ⁵⁷Fe in the case of AIT in the laboratory reference frame, at the vibration amplitude of 0.38 $\lambda $ (where $\lambda $ is the radiation wavelength) and frequency of 3$\gamma_{21}$ (where $\gamma_{21}$ is the halfwidth of the nuclear absorption line). The black dashed curve (right axis) is the absorption line of the motionless absorber. In the case of the incident wave packet with Lorentz spectrum of the halfwidth $\gamma_{21}$ , the black dashed curve also represents the incident field spectrum.

[1] Radeonychev, Y.V., Khairulin, I.R., Vagizov, F.G., Scully, M. & Kocharovskaya, O. Observation of acoustically induced transparency for $\gamma $-ray photons. Phys. Rev. Lett. 124, 163602 (2020).

Y. V. Radeonychev, I. R. Khairulin, and Olga Kocharovskaya
JETP Letters 114, issue 12 (2021)

Multicharged ions, positive ions with a large ionization multiplicity, play a significant role in the processes occurring in high-temperature laboratory and astrophysical plasma. Their properties are important for X-ray astronomy and astrophysics, in the physics of ion thermonuclear fusion, for the study of the interaction of ions with matter, in medicine, etc.

Among the most important characteristics of ions are their potentials (in volts) or ionization energies (in electron volts) numerically coinciding with them. For light elements, almost all ionization energies have been experimentally measured, but in medium and heavy ions, only the first few have been measured. These values for multicharged ions are obtained either by semiempirical methods or as a result of the application of various theoretical models.

The totality of available data on the ionization energies $I_{N_e}(Z)$ (eV) of atoms and ions for elements with atomic numbers $Z \leq 110 $ is presented in the tables of National Institute of Standards and Technology (NIST). However, the use of extensive tables in practice is not very convenient. The need for a sufficiently accurate approximation of tabular data determined the motivation of our study, which considered ions with the number of electrons $N_e\leq 46$ of elements with atomic numbers of $55 \leq Z \leq 95$.

Ions are often considered in isoelectronic series, grouped by the number of electrons $N_e$ in them coinciding with their number in neutral atoms. For example, hydrogen-like ions with $N_e=1$, helium-like ions with $N_e=2$, and so on.
In our work it is shown that in such series the atomic number similarity law is fulfilled. This means that the ionization potentials of the ions in the reduced coordinates are almost parallel lines that are well approximated by quadratic polynomials (see Fig.1).  This makes it possible, knowing the ionization potentials of several elements of the isoelectronic series, to estimate with good accuracy the ionization potentials of ions for other elements.

However, information is usually required on the ionization potentials of an element with an atomic number of $Z$ depending on the number of electrons $N_e$ in the ion. Therefore, the next step was to analyze the dependence of quadratic interpolation coefficients on the number of electrons.   Their polynomial interpolation made it possible to estimate the ionization energies of 1886 ions with an accuracy of a fraction of a percent on the basis of four small tables.

Ionisation energies from database NIST (symbols) in the reduced coordinates. $K$ and $L$ shells are on the left,  $M$ shell is on the right. Lines are quadratic interpolations.

G.V.Shpatakovskaya
JETP Letters 114, issue12 (2021)

The study of the energy structure of materials with a nontrivial topology, as well as their topological classifications when intersite Coulomb interactions (ICI) are taken into account, constitutes one of the main directions of the theory of condensed matter. The correctness of describing the ICI in topological insulators (TI) is of particular interest since in these materials there is an overlap of the initial valence band and the conduction band. To emphasize the importance of this circumstance it is sufficient to note that when conduction band overlaps with valence one the inclusion of ICI can radically change the structure of the ground state through the formation of an excitonic dielectric phase.  

In this work within framework of the BHZ+V model, which reflects the energy structure of the HgTe quantum well and for which ICI are taken into account the problem of the spectrum of bulk and edge states was solved.  It is shown that charge fluctuations lead to a qualitative renormalization of the TI energy structure: the Fermi spectrum consists of not only of the conduction and valence bands, but also of two fluctuation states bands (FSB). This spectrum is shown in the left panel of Fig.1.  

The energies of the edge states are located between the upper and lower FSB (right panel Fig.1). The dielectric gap is determined by the energy interval between the bottom of the FSB of conductions electrons and the top of the valence FSB.

Fig.1. Left panel bulk spectrum of Fermi excitations in TI when intersite Coulomb interactions are taken into account. The additional bands are due to charge fluctuations. Right panel – the dispositions of the spectrum of edge states. It is essential the energies of edge states are spaced between the fluctuation state bands.

V.V. Val’kov
JETP Letters 114, issue12 (2021)

   The vibration properties of a single crystal of yttrium iron garnet (Y₃Fe₅O₁₂) were studied at high quasi-hydrostatic pressure by Raman spectroscopy. Raman spectra were measured with diamond anvil cells (DAC) in the pressure range of 0-72 GPa at room temperature. In the pressure region of ~ 50 GPa, a radical change in the spectra was found, indicating a phase transition. This correlates with the transition from the crystalline to the amorphous state, which was previously detected by the X-ray method, as well as with the metallization effect established from the optical absorption spectra. At this transition a spin crossover also undergoes in iron ions Fe³⁺, which transit from a high-spin state (HS, 3d⁵, S = 5/2) to a low-spin state (LS, 3d⁵, S = 1/2). In this work, the pressure dependences of the phonon modes in Y₃Fe₅O₁₂ from ambient pressure to the critical pressure of the phase transition are documented in detail. To further study the unique electronic properties of Y₃Fe₅O₁₂ garnet at pressures in the phase transition region, it is necessary to measure electrical resistance at high pressures and cryogenic temperatures.

The results of this study are very important, both for the physics of systems with strong electron correlations, and for geophysics, where various iron oxides are considered as one of the constituents of the Earth's mantle

Figure 1. (a) Photo of a Y₃Fe₅O₁₂ crystal ~ 10 μm thick in a DAC cell in an experiment with an NH₃BH₃ medium. (b) Raman spectrum of a Y₃Fe₅O₁₂ crystal in different frequency ranges at ambient pressure and room temperature. (c) Evolution of the Raman spectra of the Y₃Fe₅O₁₂ crystal with increasing pressure in the quasi-hydrostatic NH₃BH₃ medium, and (d) the dependence of the Raman frequencies on the pressure. The shaded area indicates the pressure range of the proposed dielectric-to-metal transition. At a pressure of ~ 47 GPa, the shape of the spectrum changes dramatically, indicating the onset of the phase transition, which ends after 54 GPa. The Raman spectra were excited using a COBOLT DPSS laser with a wavelength of 660 nm.

Aksenov S.N., Mironovich A.A., Lyubutin I.S., Troyan I.A., Sadykov R.A., Siddharth S. Saxena (Montu), Gavriliuk A.G.
JETP Letters 114, issue 12 (2021)

The interplay between nontrivial band structure and magnetic order in topological insulators is a rich source of remarkable quantum phenomena such as quantum anomalous Hall effect, axion electrodynamics, Majorana fermions, etc. These phenomena are manifested through topologically protected electron states appearing at the sample boundaries. A qualitatively new stage of investigations in this topic is triggered by the discovery of materials that combine topological properties with intrinsic antiferromagnetic order.

In this letter we present a theoretical investigation of modification of low-energy surface electron structure caused by the noncollinear magnetic domain walls in intrinsic antiferromagnetic topological insulator. The study is carried out on the basis of the Hamiltonian for quasirelativistic fermions by using a continual approach and tight-binding calculations. A bound one-dimensional state is shown to appear at the domain wall, in addition to the surface exchange gap modulation and the shift of a two-dimensional Dirac cone in momentum space. We describe the main characteristics of the bound state such as the energy spectrum (see the figure), spatial localization and spin polarization depending on orientation of domain magnetizations.

We consider possibilities of experimental observation of the bound states associated with the noncollinear magnetic domain walls and their contribution to quantum effects on the (0001) surface of the antiferromagnetic topological insulators of the MnBi2Te4 -type.

Spectral dependencies of the one-dimensional bound state (red color) induced by magnetic wall and projection of the Dirac cone two-dimensional states for different orientations of the domain magnetizations.

V. N. Men’shov, I. P. Rusinov, E. V. Chulkov
JETP Letters 114, issue 11 (2021)

Relativistic self-trapping of high-intensity ultra-short laser pulse (“laser bullet”) is manifested as formation of a 3D soliton structure in the form of a plasma cavity with evacuated background electrons filled by laser light and self-consistent plasma electric and magnetic fields – all propagating at almost speed of light in dense gas plasma. Such laser bullet propagates in plasma to distances exceeding the Rayleigh length considerably and requires certain matching of the size of the laser spot to the plasma density and the laser pulse intensity when the diffraction divergence is balanced by the relativistic nonlinearity such that the laser beam radius is unchanged during pulse propagation. Relativistic self-trapping of intense ultra-short laser pulse is similar to the so-called self-trapping of radiation of low-intensity quasi-stationary laser beam, which has been known since the 1960s for the quadratic nonlinearity of the medium’s dielectric permittivity and, as has been established now, takes place for the relativistic plasma nonlinearity as well.

Strong longitudinal plasma electric field of a laser bullet is able to accelerate significant number of electrons (up to tens of nC) with energies in the multi-hundred-MeV range. Currently, relativistic self-trapping is the best chose in terms of maximizing the total charge of the generated electron bunches for different applications, such as electron radiotherapy, radiation x-ray and gamma-ray sources, obtaining of photonuclear reaction products. However, the success in the implementation of such applications critically depends on the realization of the relativistic self-trapping mode in an inhomogeneous medium, since only this is possible in experiments.

This letter gives an answer to the possibility of self-trapping of extreme laser light (Fig. 1) in inhomogeneous plasma, that is important for targeted experiments. For the considered case of a near-critical density medium, (most promising for generation of high-current electron bunches) this letter is argued that relativistic self-trapping regime can be realized by proper focusing of a high-power laser pulse on a density profile at the vacuum-plasma interface. This justifies the possibility of creating an efficient source of high-energy electrons for socially significant applications.

Fig.1 Plasma cavity with accelerated electrons for the relativistic self-trapping mode of laser pulse propagation.

V.Bychenkov, M.Lobok
JETP Letters 114, issue10 (2021)

We study the kinetics of long-lived cyclotron spin-flip collective exitations  in a purely electronic quantum Hall system with filling factor $\nu=2$. The initial coherent state of the excitations with zero two-dimensional wave vector induced by laser pumping is stochastized over time due to emission of acoustic phonons. The elementary emission process requires participation of two excitations. So the effective rate of phonon emission is proportional to the excitation density squared, and the stochastization process occurs nonexponentially with time. The final distribution of these excitations over 2D momenta, established as a result of stochastization at zero temperature, is compared with equilibrium distribution at finite temperatures.

It is known that the lifetime of considered excitations (purely electronic spin-cyclotron excitons, SCEs) reaches a record magnitude, up to $1\,$ms, in a spin-unpolarised quantum Hall system.  The decay of an initial coherent multi-excitonic state, where all excitations have equal 2D momenta ${\bf q}\!=\!0$, occurs into a diffusive incoherent state provided that the total number of excitations remains constant. When the `zero momentum' ensemble becomes stochastic, the main mass of excitons in the $K$-space diffuses to the vicinity of their energy $q$-dispersion minimum corresponding to a finite absolute value $q\!\approx\!0.9/l_B$ ($l_B$ is the magnetic length). In the future, the diffuse state is thermalized, and finally SCEs completely relax/annihilate. The stochastization occurs without any change of the spin state, thus, certainly, it is much faster than the total SCE-relaxation process. However, the stochastization is associated with emission of phonons and limited by the laws of conservation of energy and momentum. In the  translationary invariant system, the one-exciton process associated with the emission of a phonon is kinematically forbidden: the energy and momentum preservation conditions are never fulfilled in the case.
We calculate the total probability $R_{ p}$ of transition of the coherent state to a state, where, due to the phonon emission, two SCEs acquire nonzero momenta, and one of them has a fixed value: ${\bf q}\!=\!{\bf p}$ .

The physical meaning of the value $R_{p}$  is that it represents the rate of appearance of a SCE with momentum ${\bf p}$ due to the considered process of direct transition from the coherent state. When studying the problem kinetically, it will mean the rate of filling of a `one-particle' excitonic state with specific momentum  $p$. The total stochastization rate induced by phonon-emission, $R\!=\!\sum_{\bf p}R_p$, is the rate of appearance of nonzero-momentum SCEs.  When dividing the `partial' rate $R_p$ by the total one $R$ we obtain a `one-particle' distribution function $F_p$ of nonzero excitons.
Value $F_p$ is time-independent and represents the final distribution function when only non-coherent excitations with nonzero momenta are present in the system. Our approach is suitable if the temperature is sufficiently low to ignore any phonon-absorption processes. In this case thermalization in the studied electron system should be a much longer process than the stochastization considered. It is interesting to compare the distribution function established due to stochastization to a thermodynamically equilibrium distribution corresponding to some temperature. The latter should be Boltzmann due to the assumed rarefaction of the exitonic gas. The time dependence of the coherent ensemble decay is parameterized by value ${\cal T}$ calculated for a specific GaAs/AlGaAs quantum well (see Fig. 1). The number of zero excitons decreases by half during time ${\cal T}\!/n(0)$ where $n(0)$ is the initial SCE concentration with respect to the density of magnetic flux quanta. A tenfold decrease takes time  $\approx\!10{\cal T}\!/n(0)$, therefore, for $n(0)\!\leqslant\!0.01$ it occurs during $\gtrsim\!1\,\mu$s.

Caculated function $F_p$ of SCEs emerging due to the stochastization process (the black line), and the thermodynamically equilibrium distribution functions $F_p^{(T)}$ at different temperatures. All graphs correspond to $B=4.18\,$T. 

Dickmann S., Kaysin B.D.
JETP Letters 114, issue 10 (2021)

In this work, an experimental scheme and results on direct detection of the normalized second-order correlation function g⁽²⁾ of the optical-terahertz biphoton fields are demonstrated for the first time. Optical – terahertz biphotons, the quantum-correlated photon pairs consisting from one photon of optical frequency and one terahertz frequency photon, were generated via spontaneous parametric down conversion in a nonlinear crystal Mg:LiNbO₃ pumped by nanosecond pulses of optical laser radiation. The terahertz part of the biphoton field was detected by an analog superconducting hot electron bolometer, the optical part was recorded using the single-photon avalanche photodiode or an analog photomultiplier tube.  The methods developed for investigation and quantitative measuring of the quantum correlation characteristics of the optical – terahertz biphotons will be of key importance in future applications of quantum optical technologies, such as quantum sensing, photometry, ghost imaging, in the terahertz frequency range.

The left figure shows the pump power dependences of the biphoton correlation function g⁽²⁾. The values of g⁽²⁾ were obtained with a specially proposed heralding method for discrimination of noise readings of the analog bolometer which were recorded simultaneously with the noise samples from the single-photon optical detector. The direct measuring results are in a good agreement with theoretical predictions on the quantum excess of g⁽²⁾ over its classical level 1 for the multimode field. Another method of direct discrimination of the readings below some selected threshold values, applicable to readings of both analog optical and terahertz receivers, was tested at different threshold levels. The right figure demonstrates dependence of the effective correlation function g_eff, evaluated by this method, on the threshold signal and idler photocurrents. It is shown that application of this method makes it possible to register high effective levels of biphoton correlation due to attraction of additional contributions from correlation functions of higher orders.

Left: Pump power dependences of the normalized second-order biphoton correlation function g⁽²⁾.
Right: Threshold signal and idler current dependences of the effective biphoton correlation function g_eff.

A.A. Leontyev, K.A. Kuznetsov, P.A. Prudkovskii, D.A. Safronenkov, G.Kh. Kitaeva
JETP Letters 114, isuue 11 (2021)

In some strongly correlated systems, the formation of exotic topological quantum states occurs. The compound Co₃Sn₂S₂ provides a bright example of coexistence of a non-trivial topology (Weyl points, Fermi arcs and nodal rings in the electron spectrum near the Fermi surface) and half-metallic ferromagnetism in a quasi-two-dimensional system. These factors are important for non-usual phase transitions and anomalies of electronic properties, including giant anomalous Hall effect.

Lifshitz-type transitions with vanishing of quasiparticle poles can be viewed as quantum phase transitions with a topological change of the Fermi surface, but without symmetry breaking. In the phase with a gap, usual Fermi surface (determined by the poles of the electron Green's function) does not exist, but the topology can be preserved if we take into account the Luttinger contribution (determined by the zeros of the Green's function). Then the Luttinger theorem (the conservation of the volume enclosed by the Fermi surface) is still valid. Indeed, the Fermi surface is the singularity in the Green's function, which is characterized by topological invariant N₁ and is topologically protected, being the vortex line in the frequency-momentum space [1]. For example, the Fermi surface becomes ghost (hidden) after the correlation-induced metal-insulator transition in the insulating (Mott) phase, and the fractionalization of electron states occurs, including spin-charge separation of electron into a neutral fermion (spinon) and charged boson (holon) [2]. A similar picture occurs in the situation of a half-metallic ferromagnet (where the gap at the Fermi level occurs for one spin projection), but for minority states with this spin projection only, the electron-magnon scattering being crucial for these states.

On the contrary, the transitions with disappearance of the Weyl points are essentially topological: topological invariants are changed. In the Weyl semimetal phase, the Weyl points have topological charges N₃= +1 and – 1 and annihilate in the critical Dirac semimetal. Further on, in the normal paramagnetic state the topology owing to the Berry curvature in the electron spectrum vanishes. Thus the conservation law for the topological charge is fulfilled. A still more complicated situation occurs in the case of Chern insulators with a change of the Chern number [3].

Both with increasing temperature in Co₃Sn₂S₂ and at hole doping in the Co_3-xIn_xSn₂S₂ system, suppression of ferromagnetism is accompanied with decreasing the Berry curvature. In the paramagnetic strongly correlated phase the time-reversal symmetry is restored and the topological features disappear. A corresponding description can be given in terms of slave-fermion representation in the effective narrow-band Hubbard model.

1. G. E. Volovik, Phys. Usp. 61, 89 (2018).
       2. T. Senthil, Phys. Rev. B 78, 045109 (2008).
       3. V. Yu. Irkhin and Yu. N. Skryabin, J. Exp. Theor. Phys. 133, 116 (2021).

Irkhin V.Yu., Skryabin Yu.N.,
JETP Letters 114, issue 9 (2021)

Ultracold trapped ions remain one of the most rapid-growing platforms for quantum computation. Their strong Coulomb interaction, combined with the ability to precisely manipulate them using laser radiation, offer relatively fast and highly efficient implementations of elementary quantum procedures, such as entanglement, quantum state preparation and detection. One of these procedures, namely state detection, is considered in more detail in this letter with respect to the optical qubit in the ¹⁷¹Yb⁺ ion.

The laser system that is used for Doppler cooling of the ion can also be utilized for quantum state detection in an ion optical qubit due to state-dependent fluorescence. In the letter we develop a theoretical model of the detection process in this system and analytically derive the expression for the state detection fidelity as a function of atomic, as well as experimental parameters, such as detection time, laser intensities, photon collection efficiency, dark count rate and discriminator threshold. These parameters have then been numerically optimised so as to achieve the maximal fidelity value.

For the detection scheme considered in the letter, the optimal fidelity approaches a limit of 99.4% as the photon collection efficiency increases. This limit is independent of the experimental parameters and exists because of the transition process that takes place at the beginning of detection, which partially pumps the ion from one qubit state to another with the probability of 0.6%, correspondingly lowering the fidelity by that much.

The characteristic values of the photon collection efficiency, at which the fidelity is sufficiently close to the limit, does depend on experimental parameters, especially on the dark count rate, such that more efficient photon collection is required for higher dark count rates. However, for reasonable dark count levels the sufficient collection efficiency does not exceed 1 percent, which is easily achievable with modern optics.

Optimized infidelity as a function of the photon collection efficiency at different values of the noise parameter (proportional to the dark count rate). Dashed line denotes the 0.6% limit

N. Semenin, A. Borisenko, I. Zalivako, I. Semerikov, K. Khabarova, N. Kolachevsky
JETP Letters 114, issue 8 (2021)

It has been shown recently that radiation with orbital angular momentum (OAM) has advantages for quantum cryptography. Creation, manipulation and detection of OAM beams become an important task for researchers. Previously, the three-dimensional refractive elements or bulky systems consisting of many elements were used for this purpose. On the other hand, the possibility of effective manipulation over the basic properties of light such as polarization states, phase profile, and amplitude has been recently experimentally demonstrated by using ultrathin nanostructures – metasurfaces, which can replace bulky refractive optical components in many practical applications.
Figure.

Figure. 1 (a) The operational principle schematics of a resonant silicon metasurface for spatial separation of scalar beams with different OAM values; (b) phase profile of light beams at the system input (input beam) and corresponding images in the output plane (image plane).

In this work we numerically design and demonstrate a proof-of-concept polarisation insensitive metasurface implementing spacial separation of scalar light beams with different values of OAM. The proposed metasurface consists of 2D arrays of silicon nanodiscs, in which both electrical and magnetic dipole resonances can be excited in the nearinfrared spectral range. Due to the spectral overlap of these modes in the nanostructure it’s possible to create a phase profile with arbitrary shape while maintaining high transmittance. We obtain optimal parameters of the metasurface realising phase profile corresponding to Log-Pol conformal transformation and numerically demonstrate the OAM beams spacial sorting. We show feasibility for efficient OAM splitting that can be used for creation of new functional meta-devices for manipulation of optical beams with OAM.

A.D.Gartman, A.S.Ustinov, A.S.Shorokhov and A.A.Fedyanin

JETP Letters 114, issue 8 (2021)

One of the most effective methods of generating of  terahertz radiation is  based on the effect of optical rectification of the subpicosecond and femtosecond laser pulses in the crystals with quadratic optical nonlinearity. In this case, an optical photon decays in the nonlinear medium into two photons, one of which has a terahertz frequency. The Cherenkov’s condition of synchronism, under which this generation takes place, follows from the conservation laws of the energy and momentum for this elementary process and has the  following form: $\nu_g cos \theta = c/n_T $. Here $c $ is the speed of light in vacuum, $\nu_g $ is the group velocity of optical pulse at its carrier frequency, $n_T$ is the terahertz refractive index, $\theta $ is the angle between the propagation directions  of optical and terahertz signals. Note that the optical and terahertz pulses propagate in different directions under this condition. As a result, the efficiency of the generation weakens. To increase this efficiency, the technique of tilted fronts of optical signals is used in experiments. In such a case,  $\theta $ is the angle between the group and phase wave-fronts of optical pulse. Then, the terahertz signal is fed permanently by the energy of the optical pulse, and the efficiency of the generation is increased significantly.

The terahertz pulses generated by the optical method contain about one (or even half) period of electromagnetic oscillations, i.e. they have properties of extremely short (or unipolar) pulses. Therefore, the approximation of slowly varying envelopes, which is standard for the quasimonochromatic signals, is not applicable in theoretical studies of the interaction of these pulses with matter. At the same time, the optical pulse is quasimonochromatic. Therefore, this approximation is valid for it.  

In order to describe theoretically the process described above, we derive in this paper the new nonlinear equations for the envelope of the electric field of optical pulse and for the electric field of terahertz signal. We refer to these equations as the Yajima – Oikawa – Kadomtsev – Petviashvili (YOKP) system. This system contains optical-terahertz and purely terahertz quadratic nonlinearities, dispersion and diffraction of both components. Also, we found the solution of the YOKP system in the form of optical  $E_0$ and terahertz $E_s$ soliton-like pulses propagating in a bound mode (see figure). The angle $\theta $ between the phase and group wave-fronts of the optical soliton is determined in this case by the Cherenkov's condition. At the same time, purely terahertz unipolar soliton $E_T$, which is a solution of the Kadomtsev – Petviashvili equation, propagates in the direction of movement of the phase fronts of the optical pulse. The polarities of the terahertz components $E_s$ and $E_T$ are opposite. The relationship between the temporal durations and amplitudes of the terahertz components is found from the condition of equality of their "areas". It turns out that the soliton component $E_s$ should be much shorter and more intense than the component $E_T$ in a case of $LiNbO_3$ crystal.

Schematic representation of the propagation of optical-terahertz $E_0 + E_s$ and purely terahertz $E_T$ pulses under the angle $\theta $ between the phase and group velocities of the optical signal; the phase fronts and the terahertz soliton propagate along the $z$ axis, and the group fronts propagate along the $ z' = z~ cos \theta + x~ sin \theta $ axis.

The soliton mode of the generation described above is possible if the dispersion parameter of the group velocity of optical pulse is positive and exceeds the critical value determined by the angle $\theta $ of inclination. In this case, the nonlinear susceptibility of the second order corresponding to the carrier frequency of the optical pulse should be negative.

S. V. Sazonov and N. V. Ustinov
JETP Letters 114, issue 7 (2021)

Since the recent experimental discovery of anyonic statistics of quasiparticles in the 1/3 fractional quantum Hall effect regime, this system has been of exceptional interest. In this work we investigated the spectra of resonance reflection of light from a two-dimensional electronic system in the conditions of formation of Laughlin liquid in fractional state 1/3. It is shown that the main lines in the spectra of resonant reflection of light do not correspond to singularities in the two-particle density of states of the excited electron-hole system, but are associated with the birth and destruction of neutral excitations. Thus, the resonant reflection of light in fractional state 1/3 is an analogue of the Raman process with the creation and destruction of neutral excitations in transitional scattering states, while two-particle (excitonic) optical transitions are not observed experimentally. The suppression of two-particle optical transitions is presumably due to the incompressibility of the ground state of a two-dimensional electronic system.

A.S. Zhuravlev, L.V. Kulik, L.I. Musina, E.I. Belozerov, A.A. Zagitova, I.V. Kukushkin
JETP Letters 114, issue 7 (2021)

Experimental results on the coherent properties of a recently discovered new collective state, the magnetoexcitonic condensate, are summarized in the present letter. The condensation occurs in a fermionic system, a quantum Hall insulator (filling factor $\nu  = 2$), as a result of the formation of a dense ensemble of long-lived (experimentally measured lifetimes achieve ~1 ms) triplet cyclotron magnetoexcitons (TCMEs), composite bosons with spin S = 1. The magnetoexcitons are formed by an electron vacancy (Fermi hole) at a completely filled zero electron Landau level and an excited electron at an empty first Landau level. At temperatures T < 1 K and TCME concentrations n_ex ∼ (1-10)% of the density of magnetic flux quanta a transition occurs to a qualitatively new phase. The condensate shows a sharp decrease in viscosity and the ability to spread over macroscopically large distances, on the order of a millimeter, at a speed of ~10³ cm/s. This work is devoted to the study by interferometric methods of the degree of spatial coherence in the magnetoexcitonic condensate.

The main method for detecting TCMEs is photoinduced resonant reflection of light. This method finds photoexcited Fermi holes that are part of cyclotron magnetoexcitons (TCMEs themselves are “dark” quasiparticles that do not interact in the dipole approximation with an electromagnetic field). The figure shows the profile of interference fringes (red) in Michelson interferometer with a mirror in one arm, and a right angle prism in the other, which are observed in the light resonantly reflected from magnetoexcitonic condensate. Here, the envelope of fringes profile is nothing more than a first-order correlator g⁽¹⁾ as a function of distance $\delta $. The blue line is the theoretical curve (instrumental function) that best describes the central peak corresponding to thermally excited non-condensed TCMEs. The black curve is the result of adding with weights of 0.8 and 0.2, respectively, of the instrumental function and its convolution with $exp (−|\delta|/\xi )~ at~ \xi = 10 \mu m.$

A.V. Gorbunov, A.V. Larionov, L.V. Kulik, V.B. Timofeev
JETP Letters 114, issue 7 (2021)

Identification of solid-like clusters is  important problem of condensed matter physics. Here, we use the bond orientational order parameters (BOOP), introduced by P. Steinhardt to characterize   the arrangement of neighboring particles with respect to central one. Set of rotational invariants (RI) being calculated via BOOP method for each atom describes the fine details of the local orientational order of the system of atoms. We propose a new method to identify distorted solid-like clusters, including difficult-to-determine bcc-like clusters. Within the method we calculate the rotational invariants of second (q4, q6) and third (w4, w6) orders by using a fixed number of nearest neighbors (NN) which is typical for close packed structures: NN = 12. In that case ideal bcc lattice gives two sets of RIs only, which are well separated from another close packed structures (fcc, hcp, ico). Using 2D distributions of RIs (shown in Figure) the most important solid-like clusters (even being strongly distorted) can be easily identified.  

Distribution of distorted atoms of different symmetry (fcc, hcp, bcc, ico) on the plane of  rotational invariants (q4-q6) and (w4-w6). The distributions were calculated via fixed number of nearest neighbors (NN), which corresponds to close packed (NN = 12) structures. In that case ideal bcc lattice degenerates into two sets of rotational invariants only which are; this method  provides easy way to identify any type of symmetry of distorted solid-like clusters.  

                                                                                                                            B.A. Klumov
                                                                                                              JETP Letters 114, issue 7 (2021)

Anderson localization is observed in a highly disordered two-dimensional (2D) electron-hole system in a HgTe-based quantum well, the behavior of which is significantly different from that observed in widely studied two-dimensional one-component electron and hole systems. It was found that a two-stage localization occurs in the system: the two-dimensional holes are localized first, as particles with an effective mass almost an order of magnitude greater than that of electrons. Then the electrons are localized. It was also found that there is no metal-insulator transition in the system under study: even at values of conductivity σ > e²/h, a dielectric temperature dependence is observed. At electron densities (N_s) exceeding those of holes (P_s), when the transport is determined by electrons, localization behavior is not described by one-parameter scaling despite the smallness of the interaction parameter (r_s < 1). Probably it is necessary to take into account the electron-hole and the hole-hole interaction, as well as the spin-orbit interaction to get the right description of the Anderson localization in the electron-hole system. Obviously, further experimental and theoretical research of the discovered phenomenon will be of interest.

Figure. (a) - Resistivity gate voltage dependences at different temperatures, (b) - Resistivity temperature dependences at N_s > P_s , (c) - Resistivity temperature dependences at P_s > N_s , (d) -

Z.D.Kvon, E.B.Olshanetsky
JETP Letters 114, issue 6 (2021).

Simulation of quantum systemson a quantum computer using the Zalka-Wiesner method with allowance for quantum noise is considered. The efficiency of the developed methods and algorithms is demonstrated by the example of solving the nonstationary Schrödinger equation for a particle in the Pöschl–Teller potential. The developed analytical theory of the effect of quantum noise on the simulation accuracy is compared with the results of numerical calculations by the Monte-Carlo method. The forecast of the accuracy of the solution of the Schrödinger equation for a multibody electron system is carried out depending on the number of electrons and for various noise levels.

To estimate the accuracy of the Zalka-Wiesner algorithm we analyze the accuracy of the gates included in the QFT circuit. Based on these values, we obtain an estimate of the QFT algorithm accuracy, which can be easily extended to the case of the Zalka-Wiesner algorithm. The main advantage of this approach is the ability to evaluate quantum circuits with an extremely large number of qubits.

The figure shows the level of influence of quantum noise on the Schrödinger equation solution accuracy obtained on a quantum computer. The quantum state evolution of a 9 qubits register was considered over a time interval  $0\leq t \leq1 $ with a time step  $\Delta t= 0.05$ at a noise amplitude level $e = 0.01$.

Illustration of the density distribution evolution in the coordinate representation. Initial state – dashed line, final state at $t = 1$ - solid line, noisy Zalka-Wiesner solution is represented by a set of points.

Yu. I. Bogdanov, N.A. Bogdanova, D.V. Fastovets, V.F. Lukichev
JETP Letters 114, issue 6 (2021)

¹³C is usually recognized a good example of a "normal" nucleus well described by the shell model. Its level scheme is reliably determined up to the excitation energies 10 MeV. However, some new ideas and results renewed interest in ¹³C. The most ambitious among them is hypothesis about possible existence of 𝛼-particle Bose-Einstein condensation (𝛼BEC). Some features of the condensate structure were predicted and observed in the second 0⁺, 7.65 MeV state of ¹²C (so called Hoyle state). It was also suggested that the structures analogous to the Hoyle state may exist in neighbor nuclei ¹³C. Recently a hypothesis was put forward about a new type of symmetry in the ¹³C - 𝐷′_3h symmetry. On the basis of this symmetry, the rotational nature of a whole group of low-lying ¹³C states was predicted. If this hypothesis is confirmed, our understanding about the ¹³C structure will radically change.

To solve these questions our group has made experiments on scattering of 𝛼-particles on ¹³C at (𝛼) = 65 MeV and 90 MeV. New experimental data was got for the 1/2⁻₃, 11.08 MeV state. Obtained data was analyzed using Modified diffraction model (MDM), developed by our group. rms radius of this state within errors coincides with the radius of the 1/2⁻₂ 8.86 MeV state in ¹³C and the Hoyle state in ¹²C (see Fig.). This result is an argument for close cluster structure of these states.

¹

Previously our MDM analysis showed that 3/2⁻, 9.90 MeV in ¹³C is compact and has decreased by 10% rms radius. This unusual result we tested via consideration of its isobar-analog state (IAS) in ¹³N – 3/2⁻, 9.48 MeV state. We found that this state has normal non-increased radius. Also we clarified our previous result for the rms radius of the 9.90 MeV state and obtained that within the error limits, the value of the radius obtained for the 9.90 MeV in ¹³C coincides with the radius of the 9.48 MeV in ¹³N. Obtained normal radius for the 3/2⁻, 9.90 MeV destroyed one of the rotational bands predicted by 𝐷′_3h symmetry in ¹³C.

Demyanova A.S., Danilov A.N., Dmitriev S.V., Ogloblin A.A., Starastsin V.I., Goncharov S.A., Janseitov D.
JETP Letters 114, issue 6 (2021)

During the last several decades the study of lowdimensional electron systems became one of the main and actively developing research areas in condensed matter physics. Such interest was caused by, on the one hand, the possibility to study new fascinating physical phenomena, and the opportunity for technological applications, on the other hand. Continuous progress in fabrication of 2D structures, quantum wires and quantum dots helped to create new unique systems for investigation and had enormous impact on development of planar semiconductor devices. In that case, study of transport properties of a 2DEG became extremely important.

Such investigation revealed an intriguing effect of giant oscillations of longitudinal magnetoresistance in a 2DEG with sufficiently high mobility in the presence of weak magnetic field and illuminated by microwave radiation, named MIRO [1, 2], and led to the discovery of the zero-resistance states (ZRS). Observed phenomena created a new branch of non-equilibrium physics and demonstrated how combination of weak microwave radiation and weak Landau quantization could drastically change transport properties of a 2DEG.

Despite the fact that MIRO has been actively studied for more than twenty years, the physical understanding of its origin is still a subject of wide discussion. Two mechanisms which consider the bulk origin of the phenomenon, did not explain a number of experimental results. These contradictions led to the creation of alternative theories that associate the causes of MIRO with the influence of edges and near-contact area. As a result, an experimental study of the contribution of these regions to microwave-induced magnetoresistance oscillations is of great interest.

Present work is devoted to the contactless measurements of microwave-induced oscillations of high-frequency conductivity in the relatively new 2DES - ZnO/MgZnO heterojunction. Experimental technique was based on the analysis of a transmission signal between two T-shaped antennas, capacitively coupled to a 2DES (Fig. 1(a)). Absence of Ohmic contacts or deposited metallization on the sample surface allows to eliminate the influence of near-contact regions on MIRO and testing how universal are the properties of MIRO obtained earlier on a completely different material system such as ZnO/MgZnO heterojunction (Fig. 1(b)). Such measurements provide additional information for understanding the nature of the MIRO origin.

Fig. 1. (a) Schematic drawing of the experimental setup. (b) Typical dependencies of the variation of the output voltage on the magnetic field B induced by an exciting microwave radiation f = 64; 74 and 84 GHz. The voltage variation $\delta V$ was normalized by the voltage value at zero magnetic field $V_0$. The positions of the first oscillations are indicated. The sample temperature was equal T = 1:5 K.

[1] M. A. Zudov, R. R. Du, J. A. Simmons, and J. L. Reno, Phys. Rev. B 64, 201311(R) (2001).
  [2] P. D. Ye, L. W. Engel, D. C. Tsui, J. A. Simmons, J. R. Wendt, G. A. Vawter, and J. L. Reno, Appl. Phys. Lett. 79, 2193 (2001).

It is well known that in parametric down-conversion in a nonlinear crystal, the pump photon decays into two photons with lower frequencies. Such photon pairs form quantum biphoton states, which have long been used in quantum optics and information, absolute calibration of radiation brightness, and nonlinear interferometry. Usually the frequencies of both photons are in the visible or near-IR range. However, if the frequency of one of the photons is very close to the pump frequency, then the frequency of the second one is several orders of magnitude lower and may lie in the terahertz range. The possibility of generating terahertz radiation using parametric down-conversion has been studied for more than ten years, but optical-terahertz biphoton states have not yet been registered.

One of the difficulties in studying the optical-terahertz biphoton field is the large wavelength of the terahertz photon, comparable to the width of the pump beam. This leads to a complex structure of spatial modes of biphoton radiation. In this paper, it is shown that the nonlinear interaction operator describing the production of optical-terahertz biphotons can be diagonalized in the space of azimuthal angles. As a result, it is possible to obtain the azimuthal eigenmodes of the scattered radiation, shown in the figure. In the basis of these eigenmodes, it is easy to obtain a scattering matrix that describes any correlation properties of optical-terahertz biphoton radiation at arbitrary values of the parametric gain.

The obtained scattering matrix was used to calculate the correlation function of the intensities of the optical and terahertz scattered radiation and the dispersion of the difference in the numbers of optical and terahertz photons depending on the angular apertures of the photodetectors used in the experiment. The obtained results allow us to clarify the conditions under which it is possible to register the non-classical properties of optical-terahertz biphoton fields.

An example of the structure of azimuthal eigenmodes of optical-terahertz biphoton radiation (at a terahertz radiation frequency of 0.5 THz).

P.A.Prudkovskii
JETP Letters 114, issue 4 (2021)

We have recently shown that the use of micropillar resonators, which comprise a cylindrical semiconductor cavity sandwiched between the Bragg mirrors can substantially increase the quality factor preserving the mode volume, and thus substantially enhance the local fields [Optics Letters Vol. 45, 1, 181-183 (2020)]. Here, we show that these structures can facilitate the significant enhancement of the second harmonic generation efficiency. We provide a specific design of the AlGaAs/GaAs pillar microcavity and use the numerical modelling to directly show the resonant enhancement of the SHG efficiency in so-called quasi-BIC (bound states in the continuum) regime. In this regime the quality factor of the first harmonic drastically increases due to the destructive interference of two low-quality modes of cavity. Q-BIC regime appears at specific geometric parameters of cavity that results in approximately two orders gain in second harmonic generation efficiency. 

Kolodny S.A., Kozin V.K., Iorsh I.V.
JETP Letters 114, issue 3 (2021) 

Chains of ultracold ions trapped with varying electric fields are one of the most promising platforms for quantum computations, which is being actively studied at the moment. It features long coherence time, well-developed and high-fidelity techniques for quantum state initialization and readout as well as a strong Coulomb interaction between particles, which allows to efficiently entangle them. One of the approaches to this platform further development is a search for more suitable ion species or new ways of encoding quantum information in their electronic structure.

In this letter, we experimentally investigate quantum information encoding in an optical quadrupole transition in ¹⁷¹Yb⁺ ion, which is already widely used for quantum computations but with microwave qubit encoding. Optical qubits are easier to individually address with laser beams than microwave ones as there is no need for bichromatic laser emission from different directions and only one beam is sufficient. Initialization and readout of optical qubits are also usually more accurate. These properties may help to overcome one of the major issues with ion quantum computers – scalability problems. On the other hand, optical qubits suffer from shorter coherence times.

We compare proposed optical qubit with microwave qubit in ¹⁷¹Yb⁺ ion as well as with the most widespread at the moment optical qubit in ⁴⁰Ca⁺. We also experimentally demonstrate and characterize fidelity of a single-qubit Pauli-X operation and fidelities of our preparation and detection schemes.

Level scheme of ¹⁷¹Yb⁺ ion, showing both microwave qubit in the ion as well as proposed optical qubit. States proposed to use for qubit encoding are shown as |0> and |1>.

The microwave photoconductance of a short (100 nm) constriction (QPC) in a two-dimensional electron gas under its irradiation at a frequency of (2-3) GHz has been studied for the first time. The experiment and conductance calculations showed a giant QPC photoconductance in the tunnel mode and negative photoconductance in the open mode. According to the developed model, this behavior results from  co-phase harmonic electric field additions to the gate voltage V_g and to the measuring voltage applied to QPC, determined by the frequency and power P of the microwave source. The voltage dependences of conductance G(V_g) at 4.2 K don’t show a pronounced quantization in units of G₀ = 2e²/h due to the small constriction length, but exhibit anomalous bending at (0.7–0.5)G₀. The microwave replicas of these anomalies were found in the form of peak-dip features at the lower step of photo-transconductance. The basic behavior of G(V_g)  remains qualitatively the same at 77 K; this result opens possibility of development of a new kind of microwave detectors.

((a, b) The measured gate characteristics of conductance G(V_g)/G₀ and transconductance dG(V_g)/G₀dV_g at Т = 4.2 K for  various microwave power P/P₀ at 2.4 GHz frequency (G – conductance, V_g – gate voltage, G₀ =2e²/h) in the transition of a short QPC with split gate from the tunnel to the open mode. Line type and color in each panel with a common scale in V_g and on insert to (a) correspond to the indicated P/P₀.

V.A. Tkachenko, A.S. Yaroshevich, Z.D. Kvon, O.A. Tkachenko, E.E. Rodyakina, A.V. Latyshev
JETP Letters 114, issue 2 (2021).

In a series of numerical experiments, within the framework of the incompressible 3D Euler equations, we have studied evolution of the high vorticity regions, which arise during the onset of developed hydrodynamic turbulence. These regions represent compressing pancake-like structures (thin vortex sheets), which can be described locally by a new exact self-similar solution of the Euler equations combining a shear flow with an asymmetric straining flow. The vorticity maximum on the pancake ω_max increases exponentially with time, while its thickness l₁ exponentially decreases, with the Kolmogorov-type scaling relation between the two,

ω_max ∞  l₁^-2/3.

This law is confirmed numerically for most of the pancakes, and is also supported by analytical arguments in terms of the so-called vortex line representation.
The exponential growth of the vorticity maximum together with the exponential decrease of the pancake thickness would seem to indicate a double exponential amplification of the pancake perturbations relative to the Kelvin-Helmholtz (KH) instability. However, in our numerical experiments we have not observed this type of instability.
In the present paper, we provide several arguments to explain this fact. In particular, we show that the KH instability is suppressed by the self-similar shear flow of the pancake, which leads to reduction of the tangential velocity jump ΔV ∞ l₁^1/3 with the pancake thickness. Additionally, we demonstrate that vortex pancakes have an internal fine structure consisting of three vortex layers (see the figure), which may also prevent development of the KH instability.

Normalized second component of the vorticity ω₂/ω_max as a function of x₁/l₁ at different times, demonstrating the three-layer internal structure of the pancake.

D.S. Agafontsev, E.A. Kuznetsov, A.A. Mailybaev
JETP Letters 114, issue 2 (2021)

According to the measurements of the electric component of the electromagnetic field in the frequency range 2 kHz - 10 MHz recorded by the Japanese ERG satellite, two generation regions of radiation  are defined: the  kilometric “continuum” radiation type and new hectometer “continuum” radiation type. It is shown that the kilometric “continuum” radiation is observed mainly on the dayside of the magnetosphere, its source is located near to the plane of the geomagnetic equator, and the source size does not exceed ± (0.1–0.3Re) across this plane, where Re is the Earth's radius. The hectometer radiation mainly observed in the nightside of the magnetosphere has two sources. One of them is located near to the plasmasphere and could be far from the plane of the geomagnetic equator up to 3Re. The second source is located near to the Earth at distances not exceeding 2Re. It was shown earlier that "continuum" radiation was observed on all planets with a magnetic fields. The high stability of the “continuum” radiation indicates the possibility of its use as a second marker of exoplanets with a magnetic field. The first marker is the Auroral Kilometric Radiation (AKR), which is characterized by high amplitude but relatively short lifetime. The “continuum” radiation is weaker than the AKR by 3 - 5 orders, but high stability of the “continuum” radiation makes it possible to carry out a long-term accumulation of the signal and thus second marker could be formed. The presence of two markers will increase the reliability of detecting exoplanets with a magnetic field by 8 times.

The figure shows the change in the polarization of hectometer radio emission when the satellite crosses the radiation source. The upper panel is a dynamic spectrogram of the electric field component amplitude (in logarithmic scale) and the lower panel is a spectrogram of the polarization coefficient (in linear scale).

Mogilevsky M.M. et al.
JETP Letters 114, issue 1 (2021)

The three-particle multichannel Coulomb scattering problem is an important milestone of the multichannel quantum scattering theory. Being in principle numerically solvable on modern computers without any approximations it would allow one to observe and check the concepts and effects of multichannel scattering of charged particles with applications in atomic, molecular and nuclear physics. However, there is still a number of theoretical issues to overcome in order to mark the problem as “solved”.

          Moving along this path, we treat the three-particle multichannel Coulomb scattering problem with rearrangement channels by the potential splitting approach incorporated into the framework of differential Faddeev-Merkuriev (FM) equations. These equations have been designed to treat uniformly the elastic, excitations and rearrangement processes. We have developed a highly efficient theoretical and computational approach based on solving the FM equations which in total orbital momentum representation are reduced to a finite set of three-dimensional partial differential equations.

          In this letter, we outline our approach and apply it to calculations of the antihydrogen formation cross section for antiproton scattering off the ground and excited states of the positronium. This reaction is of utmost importance for the AEgIS and GBAR experiments on antimatter based on the use of the Antiproton Decelerator facility that are planned and performed at CERN. Using moderate computational resources we have achieved a supreme energy resolution of both total and partial cross sections that allows us to obtain with high quality such cross section peculiarities as Feshbach resonances.

The P-wave partial cross sections for formation of the antihydrogen in the ground state (blue) and the first excited state (red) in the process of antiproton scattering off the ground state of the positronium. Vertical dashed lines mark positions of resonances obtained with good accuracy in independent calculations.

V. A. Gradusov, V. A. Roudnev, E. A. Yarevsky, S. L. Yakovlev
JETP Letters 114, issue 1 (2021)

After seven years of construction of the Nuclotron-based Ion Collider fAcility (NICA) at the JINR in Dubna, Russia, the first in the chain of three proton synchrotrons – the Booster - has   its beam! We present in our paper the first run of the commissioning of the Booster. The single-charged helium ions were injected into the Booster at energy 3.2MeV/nucleon and a stable ion circulation was obtained.
In this letter we describe vacuum conditions  in the Booster and present results of  measurements of the lifetime for a beam of single-charged helium ions at the injection energy, and a demonstration of ion acceleration up to an energy of 100 MeV/nucleon.

The figures show the time variation of the beam intensity (fast current transformer signals, red curves) and dipole magnetic field (green curves) at injection energy (upper figure) and at acceleration   to an energy of 100 MeV/nucleon, followed by deceleration.

The measured value of the beam lifetime τ_exp = (1.32 ± 0.06) s is comparable with the theoretical calculation τ_theor = (1.74 ± 0.50) s, obtained using original computer  with heavy ions. The NICA complex will allow to study of the nuclear matter properties in the energy region of maximum baryonic density in collision heavy gold ions at energies corresponding to the deconfinement phase transition (4.5 GeV/nucleon). The main experiment at NICA will access the transition of the quark-gluon plasma into hadrons.
The achievement of first beam at Booster is very important step in the NICA project realization.

A. V. Butenko, A. R. Galimov, I. N. Meshkov, E. M. Syresin, I. Yu. Tolstikhina, A. V. Tuzikov, A. V. Philippov, H. G. Khodzhibagiyan, V. P. Shevelko
JETP Letters 113, issue12 (2021)

Light bullet is a wave packet extremely compressed both in space and in time. It occurs during the filamentation of a femtosecond radiation under condition of anomalous group velocity dispersion in transparent dielectrics. The estimation of its duration according to measurements by different methods is ambiguous and depends on the diameter of the aperture used in the experiment.

In this letter one introduced absolute parameters of a light bullet, determined by the spatio-temporal distribution of electric field strength in the area of localization of a strong light field. Introduced parameters are independent of the spatio-temporal deformations of a wave packet, its spectrum transformation during nonlinear optical interaction with the medium, and are not linked with the size of an aperture.

For the considered mid-IR radiation the increase in the carrier wavelength λ₀ leads to the monotonous increase in the radius of a light bullet from 1.2λ₀ to 3.3λ₀, the duration does not change and is equal to 1.8 periods of optical oscillation. Obtained estimations of light bullet parameters one can consider as a lower limit of experimental measurements. The developed approach to determining the parameters of optical radiation on the basis of spatio-temporal distribution of the electrics field strength generalizes the characteristics of a quasi-monochromatic wave packets to light bullets, the radius and duration of which are close to the wavelength and the period of the light field, respectively.

Spatio-temporal distribution of electric field strength in the light bullet during filamentation in LiF of a femtosecond pulse at the wavelength of 3100nm.

E.D. Zaloznaya, A.E. Dormidonov, V.O. Kompanets, S.V. Chekalin, V.P. Kandidov

JETP Letters 113, issue 12 (2021)

The efficiency of practically used quantum electronic  interferometers is limited by rather stringent requirements, for example, very low temperature for interferometers based on superconducting SQUIDs or the requirement of very strong magnetic fields for interferometers based on the edge states of Quantum Hall Effect systems.

         A promising opportunity for a technological breakthrough in this direction is associated with the discovery of topological insulators, which are materials insulating in the bulk, but exhibiting conducting one-dimensional helical channels at the surface or at the boundaries. The electron transport via helical edge states is ideal, in the sense that electrons do not experience backscattering from conventional non-magnetic  impurities.

         We review recent studies of the spin-dependent tunneling transport via Aharonov-Bohm interferometer (ABI) formed by helical edge states. We focus on the experimentally relevant case of relatively high temperature, T,  as compared to level spacing, Δ. The tunneling conductance of helical ABI is structureless in ballistic case but shows sharp  periodic antiresonances  as a function of  magnetic flux - with the period of one half flux quantum - in  the presence of  magnetic impurities.   

         The helical ABI with magnetic impurity may serve as an effective spin polarizer. The finite polarization appears even in the fully classical regime and is therefore robust to dephasing. There is also a quantum contribution to the polarization, which shows sharp identical resonances as a function of  magnetic flux  with  the same period as conductance. This polarization  survives at relatively high temperature.  The interferometer can be described in terms of ensemble of T/Δ  flux-tunable  qubits giving equal contributions to conductance and spin polarization.   With increasing the temperature number of active qubits participating in the charge and spin transport increases. These features of tunneling helical ABI open a wide avenue for applications in the area of quantum computing.

Strong magnetic  impurity blocks transmission of one component of the electron spin. For open setup this leads to 100 % polarization. Polarization reverses sign, when strong impurity is moved from upper to lower shoulder.

Niyazov R.A., Aristov D.N., Kachorovskii V.Yu.
JETP Letters 113, issue 11 (2021)

 In condensed matter the states with negative temperature have been experimentally studied in detail, and even the magnetic phase transitions occurring at negative temperature have been detected. The equilibrium thermodynamics at negative temperature is, however,  not possible, because the environment has positive temperature. The heat will be transferred from the negative temperature system to the environment, and the whole system will relax to the conventional state with positive temperature.

The negative temperature states are possible for the quantum vacuum in the relativistic quantum field theories. The Universe with negative temperature is obtained using the Dirac picture of the quantum vacuum. The conventional Dirac vacuum represents an infinite sea of particles with negative energy (left figure). In the vacuum on the right figure all the positive energy states are occupied and the negative energy states are empty. This vacuum with inverse population can be obtained by the PT symmetry operation, where P and T are space and time reversal transformations correspondingly. Due to the symmetry between the vacua the inverse vacuum has exactly the same physics as the vacuum on the left. If it fills the whole Universe, this vacuum becomes thermodynamically stable.

The matter in this mirror Universe has negative energy, and thermodynamic states are characterized by negative temperature. However, inhabitants of the mirror Universe would think that they live in the normal Universe with positive energies for matter and positive temperature. With respect to our Universe their temperature and energies are negative. But with respect to their Universe it is our Universe, which looks strange.

G.E. Volovik                                        
JETP Letters 113, issue 9 (2021)      

Topological insulators form a class of materials for which surface electronic states with the Dirac dispersion relation (and, consequently, zero effective mass) necessarily appear due to specifics of the bulk energy band structure. Mercury cadmium telluride solid solutions Hg_1-xCd_xTe exhibit a transition from the topological phase at x < 0.16 to the trivial one at x > 0.16. Previously, we have observed unusual PT-symmetric terahertz photoconductivity in heterostructures based on thick Hg_1-xCd_xTe films being in the topological phase [1]. The films were grown on a GaAs substrate via several intermediate buffers and a graded gap Hg_1-yCd_yTe layer for which the cadmium telluride content y gradually decreases and crosses the critical y = 0.16 value (see the inset in Fig.1). The photoconductivity was excited by short ~ 100 ns terahertz laser pulses in magnetic field directed normally to the sample surface. The photoconductivity amplitude turned out to be not an even function of the magnetic field applied which is equivalent to the T (time reversal) – symmetry breaking. It is also different for two mirror symmetric pairs of potential leads of a Hall bar which corresponds to the P (parity) – symmetry breaking. At the same time, changing both factors simultaneously keeps the photoconductivity amplitude intact (PT-symmetry) (Fig.1). It should be stressed that the equilibrium characteristics of the structures, such as magnetoresistance, are both P – and T – symmetric, so breaking of these symmetries is observed only in non-equilibrium situation.

Later on, it was demonstrated that appearance of the PT-symmetric photoconductivity comes up as a result of superposition of the conventional photoconductivity and the unusual chiral non-local photoconductivity [2]. The latter one corresponds to appearance of chiral photocurrents flowing along the sample edge around it. The photocurrent direction, i.e., its chirality, changes to the opposite one every time the magnetic field of the electric bias applied is reversed. The chiral photocurrent is absent if the electric bias or the magnetic field is zero. The non-locality clearly demonstrates that the chiral photocurrents responsible for appearance of the PT-symmetric photoconductivity flow in the interface area between the trivial buffer layer and the topological film.

In this paper we show that though the PT-symmetric photoconductivity reveals itself at the interface, the source of non-equilibrium electrons providing the effect is the bulk of a film. When the active layer thickness decreases, the PT-symmetric photoconductivity drops, and it is not observed in films thinner than 1 mm anymore (see the right panel of the Fig.1). Apparently, the photoexcited electrons diffuse from the bulk to the interface area, where they provide appearance of the effect.

Observation of the PT-symmetric photoconductivity does not require too sophisticated equipment. A question arises, why it was not observed previously. The results of this paper give an answer. Two conditions for the observation are necessary: existence of an interface between the topological and the trivial phase and an active layer of not less than 1 mm thickness. Hg_1-xCd_xTe single crystals widely studied back in 1960-1990s, possessed no interface with the trivial phase material. Later on, with advent of 2D heterostructures,  the experimental attention was focused on the heterostructures with the active layer thickness less than 100 nm.

Fig.1. Right panel – magnetic field dependence of the photoconductivity amplitude for two mirror-like pairs of potential leads 1-2 and 3-4. The inset shows the experiment electric circuit and geometry. Left panel – dependence of the photoconductivity amplitude asymmetry on the active layer thickness. The inset shows the heterostructure composition.

[1] Scientific Reports, 10, 2377 (2020). DOI: 10.1038/s41598-020-59280-0
   [2] Scientific Reports, 11, 1587 (2021). DOI: 10.1038/s41598-021-81099-6

A.S.Kazakov, A.V.Galeeva, A.V.Ikonnikov et al.
JETP Letters 113, issue 8 (2021)

Self-assembled Ge quantum dots epitaxially grown on Si are of particular interest as they are fully compatible with Si-CMOS and can be applied for 1.3– 1.55 µm optical communication applications. Despite the recent progress in fabrication of near-infrared Ge/Si quantum dot photodetectors, their quantum efficiency still remains a major challenge and different approaches to improve the quantum dot photoresponse are under investigation. It was recently demonstrated that the integration of Ge/Si heterostructures with arrays of metal nanoparticles on the semiconductor surface leads to a significant increase in the near-infrared photocurrent. The results were explained by the excitation of surface localized plasmon modes by the light wave. A drawback of this approach is the large ohmic losses in the metal and the small penetration depth of the plasmon field into the semiconductor.

In this letter, we have implemented an alternative approach based on the concept of photonic crystals. At present, the effects of the interaction of optical transitions with modes of various microcavities, including radiation modes of photonic crystals, are actively used to enhance luminescence signals in structures with a low efficiency of radiative recombination, including laser and LED structures. The idea of ​​the approach proposed in this work is to use photonic crystals in processes opposite to emission: optical absorption in thin layers of quantum dots embedded in photonic crystals. We found that the incorporation of Ge/Si quantum dot layers into a two-dimensional photonic crystal leads to multiple (up to 5 times) enhancement of the photocurrent in the near infrared range. The photonic crystal was a regular triangular lattice of air holes in a Si/Ge/Si heterostructure grown on a silicon-on-insulator substrate. The results are explained by the excitation of planar photonic crystal modes by the incident light wave propagating along the Ge/Si layers and effectively interacting with interband transitions in quantum dots.

(a) Image of a fragment of the profile of the band diagram of the Ge/Si heterostructure with Ge quantum dots and possible interband electronic transitions leading to the exitation of a photocurrent in the near infrared range. (b) Schematic section of a planar photodetector with Ge quantum dots in a Si matrix on a silicon-on-insulator substrate embedded in a photonic crystal. (c) - Schematic image of a photodetector representing a two-dimensional photonic crystal in the form of a periodic lattice of subwavelength air holes in Si/Ge/Si layers. (d, e) - Images of a fragment (d) of the surface and (e) of the cross-section of a triangular lattice of circular holes in the Si/Ge /Si heterostructure, obtained in an electron microscope.

A.I. Yakimov  et al.
JETP Letters 113, issue 8 (2021)

Topological materials with the Berry phase monopoles in the spectrum of Weyl fermions provide the possibility to study quantum anomalies, such as the Adler-Bell-Jackiw chiral anomaly and the gravitational anomaly. The analogue of the gravitational anomaly is produced by the effective gravitational fields acting on Weyl fermions: tetrads, spin connection and torsion fields. We show that the electromagnetic field in chiral Weyl superconductors plays the role of spin connection in the effective tetrad gravity. As distinct from the conventional chiral anomaly, the gravitational anomaly in chiral superconductors leads to the Adler-Bell-Jackiw equation with the extra factor 1/3.

In neutral chiral superfluids with Weyl fermions, such as superfluid 3He-A, the gravitational anomaly is produced by the analogue of the gravitational instanton. The latter is the process of creation or annihilation of the 3D topological objects, hopfions. The creation of hopfions is accompanied by the anomalous creation of the chiral charge. This is the gravitational analogue of the Kuzmin-Rubakov-Shaposhnikov electroweak baryogenesis.

G.E. Volovik                                           
JETP Letters 113, issue 8 (2021)     

Multi – fermion systems appear in solid state physics and in the description of fermionic superfluids. Such systems are also used as the building blocks for the construction of certain Unified theories in high energy physics. The general (though, rare) property of multi – fermion systems is the appearance of the two – component Weyl spinors at low energies. These spinors are formed in equilibrium systems close to the Fermi points, which are the band level crossing points in momentum space. Typically the Fermi points are unstable and exist only if protected by topology. Therefore, the effective description in terms of the two - component spinors survives in the case when the topological invariants protecting the Fermi points are nonzero.

Previously it was generally believed that there is a single topological invariant N₃ responsible for the stability of the Fermi points. It may be expressed as an integral of an expression composed of the two – point Green function. The integral is over a closed hypersurface surrounding the Fermi point in four – dimensional momentum space (Brillouin zone and Matsubara frequency axis). This topological invariant takes integer values. Correspondingly, these values give rise to the classification of the Fermi points.  The Fermi points with nonminimal values of N₃ may split due to perturbations into those with minimal values. Weyl fermions existing close to the Fermi points with N₃ = +1 are called the left – handed, while those close to the Fermi points with N₃  = - 1 are called the right – handed.  

In the present paper it is shown that in fact there exist two different topological invariants responsible for the stability of Fermi points. One of them is the mentioned above N₃. Another one, N⁽³⁾₃ is composed of the Green function at vanishing Matsubara frequency. The difference between these two topological invariants was overlooked previously.

Correspondingly, the Weyl points are classified according to the values of both N₃  and N⁽³⁾₃. For their minimal values it is proposed to call the Weyl points according to the following table.

The difference between the Weyl points and the anti – Weyl points may be detected if both these types of Fermi points are present. Then, for example, the two left – handed Weyl points may merge giving rise to the marginal Fermi point with (N_3, N⁽³⁾₃) = (2,0).

In the lattice systems with discretized space coordinates and continuous (imaginary) time the topological theorem requires that the sum of N⁽³⁾₃  over the Fermi points is zero (provided that there are no zeros of the Green function in momentum space). In this case there may exist the systems with left – handed Weyl points and left – handed anti – Weyl points without the right – handed Fermi points. If the imaginary time axis is discretized as well as space coordinates, then, in addition, the sum of N₃ over the Fermi points has to be equal to zero. In this case the numbers of left – handed and right – handed Fermi points are to be equal.

We suppose that the proposed classification may be relevant both for the condensed matter physics, and for the high – energy physics. In the former case the anti – Weyl points may appear in the systems with strong interactions. In the latter case the Weyl points of different types may appear dynamically in quantum gravity as a result of the fluctuations of vierbein.  

M.Zubkov
JETP Letters 113, issue 7 (2021)

Ferroelectric properties of different chalcogenides are of great interest due to the underlying physics and potential applications. Recently, three-dimensional WTe₂ single crystals were found to demonstrate coexistence of metallic conductivity and ferroelectricity at room temperature. The latter usually belongs to the insulators, but it occurs in WTe₂ due to the strong anisotropy of the non-centrosymmetric crystal structure. Out-of-plane spontaneous polarization of ferroelectric domains was found to be bistable, it can be affected by high external electric field.

Scattering of the charge carriers on the domain walls is known to provide noticeable contribution to the sample resistance. Thus, coexistence of metallic and ferroelectric properties should produce new physical effects for electron transport, and, therefore, it should be important for nanoelectronic applications.

Here, we investigate electron transport along the surface of WTe₂ three-dimensional single crystals. We find that non-linear behavior of dV/dI(I)  differential resistance is accompanied by slow relaxation process, which originates from  the additional polarization current in ferroelectric  WTe₂ crystal.  The possibility to induce polarization current by source-drain field variation is unique for WTe₂ , since it is a direct consequence of ferroelectricity and metallic conductivity coexistence.

Schematic diagram of the domain wall region, arrows indicate ferroelectric polarization direction. Due to the coexistence of metallic conductivity and ferroelectricity, there are two possible directions of the external electric fields in our setup. Gate field Egate = Vg/d is directed normally to the WTe2 surface, while source-drain field Esd is parallel to it, being induced by the flowing current Esd = ρj. The achievable values of the fields are too small to align polarization of the whole WTe2 flake, so they mostly affect the domain wall regions. Thus, any variation of the electric fields leads to the additional polarization current. The latter we observe as slow relaxation in dV /dI, since polarization current is connected with lattice deformation in ferroelectrics.

N.N. Orlova, N.S. Ryshkov, A.V. Timonina, N.N. Kolesnikov and E.V. Deviatov
JETP Letters 113, issue 6 (2021)

Photon-stimulated transport (PST) has been studied for 60 years, and until recently, all its resonances have been associated with the specific features of the density of states of the structures under study. In quantum point contact (QPC), such resonances are missing due to the smooth saddle potential. However, recently, when studying the microwave and terahertz photoconductance of the QPC in tunneling regime, PST was found in just such potential. It turned out that the tunneling transmission of a one-dimensional smooth barrier resonantly depends on the frequency and number of microwave or terahertz photons absorbed by an electron, leading to the appearance of giant microwave and terahertz photoconductance. The developed theory of the PST through such a barrier explains the discovered effect by a sharp increase in the probability of transition of a sub-barrier electron to the top of the barrier. It also gives a radical decrease in it to zero when the photon energy transferred to the electron leads to its transition above the barrier, thereby confirming another experimental fact: the absence of a photo-effect when the frequency of terahertz radiation is increased several times.

(a)- Micrographs of the Hall bridge on the basis of high mobility 2D electron gas in GaAs quantum well with two QPC options (split gate, bridged gate).

(b) - Behavior of the measured (points) and calculated photoconductance (lines) for three different QPCs ((1,2) - bridged gate, (3) - split gate), when the samples are irradiated by terahertz radiation at two indicated frequencies (G_ph – photoconductance, G_dark – dark conductance, G₀ =2e²/h).

V.A. Tkachenko, Z.D. Kvon, O.A. Tkachenko, A.S. Yaroshevich, E.E. Rodyakina, D.G. Baksheev, A.V. Latyshev
JETP Letters 113, issue 5 (2021)

Studies of topological insulators (TI) are currently marked by a growing interest to the origin of strong impact of various defects and local charge inhomogeneities on the fundamental properties of surface current carriers. One of the key ingredients of the progress here consists in the ability to get the reliable information on the TI local properties, since the standard transport measurements provide only nonlocal one.

In this letter we propose the contactless visualization of local charge and spin inhomogeneities using electron spin resonance (ESR) of the bulk charge carriers in the insulating region between conducting surfaces of the 3D topological insulators Bi_1.08Sn_0.02Sb_0.9Te₂S.

The standard ESR technique makes it possible to obtain a signal from the bulk charge carriers with a given g-factor. An analysis of the properties of the observed ESR signal allows one to conclude that the current carriers participating in the resonance are arranged in a random array of electron or hole droplets of nanoscale sizes which are located at large distances from each other. It is essential that electrons and holes from these droplets do not participate in transport, since they cannot travel from one droplet to another.

The importance of the above results is due to the fact that such droplets, being in the vicinity of the TI surface, can affect surface current carriers. Surface current carriers can penetrate into these droplets via tunneling and interact inelastically with the current carriers located in them. Then, after some time, they can tunnel back to the surface, which should undoubtedly affect their transport properties and, in particular, lead to non-zero backscattering.

The experimental scheme. A plate sample placed in the magnetic field of the  ESR spectrometer is excited by an alternating magnetic field of a given frequency (wavy line).  By changing magnetic field, the spin resonance of bulk current carriers (black resonant peak) can be achieved. The analysis of the resonance response shows that the current carriers participating in the resonance are organized into a random set of nanosized hole and electron droplets (grey circles) separated by a large distance.

Sakhin V., Kukovitsky E. , Talanov Yu/ , Teitel’baum G.
JETP Letters 113, issue 4 (2021)

Self-organized quantum dots (QDs) grown by the epitaxial method are considered as the basis for various applications in quantum photonics due to their unique properties, such as small spectral linewidth, fast radiative decay time, and high quantum efficiency. Among such applications is the generation of single photons with a high degree of indistinguishability, which is necessary for the implementation of linear optical quantum computing schemes. Most modern quantum computing protocols require a sufficiently large number of parallel channels with indistinguishable photons. One of the approaches to their formation is the use of many independent QDs emitting photons identical in all parameters. Another approach is based on the use of only one perfect QD, which emits with a high efficiency a sequence of single-photon pulses, which are then demultiplexed over N parallel channels.

In this letter, we demonstrate the possibility of combining these two approaches by creating high-quality single-photon sources, which in principle allow integration within a single semiconductor chip. For this purpose, structures were fabricated with a self-assembled InAs/GaAs QD placed in a columnar optical microcavity with distributed Bragg reflectors, possessing a relatively low Q factor. The experiment on measuring two-photon interference, performed in the Hong-Ou-Mandel scheme at various delays between two photons successively emitted under resonant coherent excitation of a single QD, showed the possibility of achieving up to 93% indistinguishability at a 250 ns delay. It is assumed that the use of such microcavity structures with a low Q factor and a sufficiently wide spectral resonance will simplify the precise tuning of the single-photon generation wavelength, which will make it possible to increase the number of parallel channels in the circuits of optical quantum computers by integrating several independent sources of indistinguishable photons with a degree of indistinguishability sufficient to effectively demultiplex the photon flux emitted by each source.

A histogram measured in the Hong-Ou-Mandel scheme of two-photon interference with a delay between photons of 250 ns under conditions of resonant coherent excitation by a π-pulse of a  microcavity with  a single InAs/GaAs QD.

Galimov A.I., Rakhlin M.V., Klimko G.V. et al.
JETP Letters 113, issue 4 (2021)

Discovery of the Higgs boson in 2012 by ATLAS and CMS experiments finally confirm the truthiness of the Standard Model (SM), but there still remain many open questions. Among them: inability of SM to explain the neutrino oscillation and baryon asymmetry, the problem of the particle mass hierarchy etc. This gave rise to the development of the new theories which extend the SM - Beyond Standard Models (BSM): Two Higgs Doublet Model (2HDM), Minimal Supersymmetric Standard Model (MSSM), Higgs Triplet Model (HTM) etc. These models predict new resonances in the extended Higgs sector, e.g. in 2HDM the electroweak symmetry breaking leads to five Higgs particles: two neutral Higgs bosons that are CP-even (scalar) ℎ, 𝐻, one neutral and CP-odd (pseudoscalar) 𝐴, and charged Higgs boson 𝐻^±.

A search for new particles from the extended Higgs sector were performed in the ATLAS and CMS experiments and covered many decay channels and final states. As a result of these searches the upper limits on the production cross sections or on the masses of new heavy resonances and the constrains on the BSM extensions parameters were obtained.

In this paper we review the recent and most significant results on heavy Higgs bosons searches obtained by the ATLAS and CMS experiments and based on the data collected in LHC Run I (2011-2012) and Run II (2015-2018) with proton-proton interactions at $\surd s$ = 7, 8, 13 TeV.

Excluded regions (light shaded or dashed) of the hMSSM model parameters 𝑚_𝐴, 𝑡𝑎𝑛  via direct searches for heavy Higgs bosons and fits to the measured rates of observed Higgs boson production and decays obtained in ATLAS experiment.

Yu.G. Naryshkin
JETP Letters 113, issue 4  (2021)

The enhancement of nonlinear Raman interactions paves a way towards implementing on-chip Raman-based technologies, such as Raman amplification and lasing, sensing and superresolution imaging. Specifically, this allows us to reduce the size and pumping power requirements of nonlinear Raman devices. In recent years, the enhanced nonlinearities have been demonstrated using microresonators, waveguides, plasmonic nanostructures and all-dielectric antennas. The underlying materials of these structures fall into two groups: dielectrics (positive real permittivity) and metals (negative real permittivity). A disadvantage of dielectric structures is that their size cannot be enough small compared to the wavelength of light. Whereas metallic nanostructures suffer from high ohmic losses.
In this Letter, we develop a novel approach to increase the efficiency of stimulated Raman scattering (SRS). Our strategy is based on the use of epsilon-near-zero (ENZ) materials, for which the real and imaginary parts of permittivity are close to zero. The ENZ materials, lying between metals and dielectrics, possess the field enhancement performance and low optical losses simultaneously. We theoretically find optimal conditions imposed to the permittivity for boosting the SRS within the ENZ media. It is shown that the SRS spectra of ENZ structures can be modified due to the frequency-dependent shift of the Raman gain factor.

Incident light (input) is converted into longer-wavelength emission (output) through stimulated Raman scattering. The enhancement of the Raman nonlinearities of ENZ media allows to perform a frequency conversion on the nanoscale and suppress a nonlinear threshold

A.P.Gazizov, A.V. Kharitonov, S.S.Kharintsev
JETP Letters 113, issue 3 (2021)

Gyrometric devices based on new physical principles is a topical and actively investigated area of research. Advances in experimental techniques of creation and control of cold atomic ensembles and, particularly, atomic Bose-Einstein condensates (BEC) allow using them for building perspective inertial sensors. The existing proposals for quantum gyrometric devices with cold atoms rely on direct registration of matter waves, which implies destruction of spatial coherence and atom loss. In this Letter, we propose and theoretically investigate a new scheme of quantum gyrometry which does not involve imminent decoherence of the condensate.

Figure 1: A concept of atom-optical quantum gyroscope. The rotation axis is assumed to be orthogonal to the plane of a ring trap.

The conceptual scheme of our setup is presented in the figure. The atomic BEC is localized in a ring-shaped trap, and a small region of it is illuminated by a travelling wave light field formed in a ring cavity. This field creates a potential barrier (or well), breaking the axial symmetry of the trapping potential and making the state of BEC sensitive to rotations of the reference frame. Specifically, the atomic phase density in the area of potential defect gains dependence on the angular velocity of such rotations. In the dispersive interaction limit, the output of the ring cavity gains a phase proportional to the number of atoms in the illuminated area. This phase is detected in the interferometric experiment, e.g. as a shift of the interference pattern of Mach-Zehnder interferometer, and from it the angular velocity is calculated. Thus, no direct interaction of matter waves is required. Our calculations, done under certain approximations, show that with a condensate of $\sim10^{6}$ $^{87}$Rb atoms trapped in a ring-cavity of $R\sim0.2$cm, it is possible to measure angular velocities of the scale of the Earth's rotation with a signal-to-noise ratio $\sim 30$ (due to atomic shot-noise).
 

  V.A. Tomilin and L.V. Il'ichev
JETP Letters 113, issue 3 (2021)

Superconducting spin valve based on superconductor/half-metal system with record values of the effect has been created.

In the last two decades of the 21st century there has been tremendous theoretical and experimental interest in the development of logic elements for superconducting spintronics. In addition to the basic elements for computers of the future, passive elements are also needed that will turn on/off the superconducting current. Such a device can be a superconducting spin valve (SSV). Superconducting spin valve is an alternating sequence of ferromagnetic (F) and superconducting (S) layers. By combining the number and sequence of layers of F- and S-materials, it is possible to control the properties of the spin valve. This is due to the fact that the properties do not change abruptly at the boundary of the S/F layers - there is a region of interpenetration of the properties of two materials. This phenomenon is called S/F proximity effect.

In this work, we have studied the superconducting spin-valve effect in F1/F2/S heterostructures containing the Heusler alloy Co₂Cr_xFe_1-xAl_y as one of two ferromagnetic (F1 or F2) layers. We used the Heusler alloy layer in two roles: as a weak ferromagnet on the place of the F2 layer and as a half-metal on the place of the F1 layer. In the first case, the full switching between the normal and superconducting states is realized with the dominant aid of the long range triplet component of the superconducting pair condensate which occurs at the perpendicular mutual orientation of magnetizations. In the second case, we observed separation between the superconducting transitions for perpendicular and parallel configurations of magnetizations reaching 0.5 K. We also find a good agreement between our experimental data and theoretical results.  The results obtained in this work are record-breaking for F1/F2/S structures.

The record value of the magnitude of the superconducting spin valve effect in F1/F2/S structure.

Kamashev A.A. , Garifullin I.A.
JETP Letters 113, issue 2 (2021)

We have developed a sensitive spectroscopic technique for study of a dilute ultracold plasma (UCP) using a laser induced autoionization of Rydberg atoms. In our experiment the ultracold ⁴⁰Ca Rydberg atoms and ions are prepared in a magneto-optical trap by several cw lasers. The laser beam diameters are order of 2×10^-3 m. The technique allows to detect the plasma with ion and electron densities below 10⁹ m^-3. For observation of the autoionization effect we used the two-photon Rydberg transition 4s3d ¹D₂ – 90 ¹D₂ (with lasers 672 nm and 798 nm) and the ionization two-photon channel with lasers 423 nm and 390 nm. The autoionization resonance is observed as a variation of the resonance fluorescence of the ⁴⁰Ca ions at a wavelength of 397 nm. The dependence of the autoionization resonance magnitude on the ion density is recorded. The ability to create an UCP with well-controlled parameters allows us to calibrate of the autoionization resonances. The technique can be applied to detect small electric fields by means of ⁴⁰Ca Rydberg atoms. The developed technique can be useful for the measurements of the small fields in development of the ultra-precise atomic clock, as well as for experimental simulations of the ultracold low-density plasma in the Earth's ionosphere.

Dependence of the resonance amplitude at the 4s3d ¹D₂ – 90 ¹D₂ Rydberg transition on the power P₃₉₀ of the ionizing laser (λ = 390 nm) and the ion density in the UCP. The peak density of the neutral atoms is $n_a = 10^{15}$m^-3.

B.B. Zelener, E.V. Vilshanskaya, S.A. Saakyan, V.A. Sautenkov, B.V. Zelener, V.E. Fortov
JETP Letters 113, Issue 2 (2021).

In the past few decades, the intensive development of angle-resolved photoemission spectroscopy (ARPES) made it possible to experimentally observe the electronic band structure for various classes of materials with a  high instrumental resolution and in a wide binding energy range. The corresponding ARPES data are represents maps on which the electronic states are characterized by position in energy, in reciprocal space, width and intensity.
On the other hand, the improvement of theoretical methods for calculating electronic band structure also allows one to obtain the spectral function maps. For example, the density functional theory (DFT) and its combination with various methods take into account electronic interactions (for example, LDA+DMFT). This led to the need for a quantitative comparison of the theoretical and experimental electronic bands. For this, in the theoretical and experimental data, it is necessary to compare not only the qualitative energy position of the electronic bands, but also their relative intensities and widths.
In this work, a technique is proposed for taking into account a number of experimental details for theoretical spectral functions: the photoemission cross-section, experimental energy and angular resolutions, the photo-excited hole lifetime effects. The study was done on the high-temperature iron-based superconductors (NaFeAs and FeSe on a SrTiO3 substrate). It is shown that a significant share in the broadening of quasiparticle bands is associated precisely with taking into account the experimental details in the theory.

(a) LDA + DMFT spectral function for NaFeAs in the M-G-M direction, (b) taking into account the experimental details, (c) ARPES. Fermi level - zero energy (white dotted line).

I.A. Nekrasov, N.S. Pavlov
JETP Letters 113, issue 2 (2021)

A review is given of unusual many-particle effects discovered in strongly interacting two-dimensional electronic systems in quantizing magnetic fields in MgZnO/ZnO heterostructures. The studied two-dimensional systems have unique properties - strong Coulomb interaction, characterized by the high values ​​of the Wigner-Seits parameter r_s~5-10 and, at the same time, high low-temperature mobilities, which enable detecting numerous many-particle effects. The properties of collective electronic excitations in the regime of the integer quantum Hall effect are investigated by the method of inelastic light scattering. Many results concerning both the structure of the ground state and many-particle contributions to the energy of collective excitations go far beyond the well-known concepts of the microscopic structure of quantum Hall states. Despite the absence of a rigorous theory of 2D electron systems for r_s>>1, the observed effects can be described in terms of Fermi-liquid quasiparticles with renormalized parameters. The phenomena of renormalization of the quasiparticle effective mass, its spin susceptibility, ferromagnetic instabilities at even filling factors, as well as the strongest renormalization of their exchange interaction are studied experimentally. The observed effects are quantitatively described by calculations performed using the method of exact diagonalization of the energy spectrum, which takes into account the Coulomb mixing of  Landau levels . The results of the analysis allow to reveal the characteristics of Fermi-liquid quasiparticles, smeared across multiple Landau levels and to probe their Hall quantization (see the figure).

A.B. Vankov and I.V. Kukushkin
JETP Letters 113, issue 2 (2021)

Seven years ago, IceCube neutrino telescope has discovered neutrinos of Peta-electronvolt energies coming from yet unidentified astronomical sources. Active Galactic Nuclei (AGN) powered by supermassive black holes ejecting relativistic jets are considered as possible source of the IceCube astrophysical neutrino signal. Direct verification of this hypothesis is however difficult because of the low statistics of the neutrino signal and moderate angular resolution of the IceCube telescope.

Interactions of high-energy protons and atomic nuclei that result in production of astrophysical neutrinos in AGN inevitably produce also gamma-rays, electrons and positrons that initiate electromagnetic cascade releasing its energy into Giga-electronvolt (GeV) to Tera-electronvolt (TeV) range.  Thus, it is natural to expect that the sources of astrophysical neutrinos have GeV-TeV gamma-ray counterparts. However, contrary to expectations, arrival directions of astrophysical neutrinos detected by IceCube do not correlate with positions of brightest gamma-ray emitting AGN detected by Fermi LAT gamma-ray telescope. At the same time, surprisingly, recent analysis of correlation between neutrino arrival directions and positions of AGN brightest in the radio band by Plavin et al. (2020) has revealed significant correlation.
This is puzzling, because theoretical models of neutrino production in AGN typically assume that high-energy protons interact with ultraviolet photons produced by the hottest part of accretion flow onto the supermassive black hole, close to the AGN “central engine”. Its size is about the size of the Solar system, much smaller than that of the parsec-scale jets producing radio synchrotron emission. Moreover, the proton-photon reaction that can in principle produce both neutrinos and electrons / positrons has very high energy threshold. This reaction cannot directly produce electrons and positrons generating radio synchrotron emission.
The letter “Radio-to-gamma-ray synchrotron and neutrino emission from proton-proton interactions in active galactic nuclei” proposes a solution to these puzzles. High-energy protons in the AGN jet can efficiently interact on parsec-scale distances with low-energy protons from the circumnuclear medium. The energy threshold of proton-proton reaction that produces neutrinos, electrons and positrons is moderately low so that electrons with energies close to the threshold emit synchrotron radiation in the radio band. In this model the neutrino and radio fluxes are correlated because both are determined by the power of the primary proton beam reaching parsec-scale distances in the AGN jets.

A.Neronov, D. Semikoz
JETP Letters 113, issue 2 (2021)

The interfaces between superconductors (S) and ferromagnets (F) are known to be the origin of rich physics associated with the proximity effect. The exchange field inside the ferromagnets converts the spin-singlet Cooper pairs into the spin-triplet ones. Such unusual spin structure of superconducting correlations is responsible for the spatial oscillations of the Cooper pair wave function and a great variety of resulting interference phenomena.

Recently, it has become clear that the proximity effect also drastically modifies the electrodynamics of S/F structures. As an example, spin-triplet pairs can damp the usual diamagnetic Meissner response down to zero, and its vanishing was shown to be the hallmark for the emergence of the peculiar Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase with the superconducting order parameter modulated in the plane of the layers [1, 2]. Another electromagnetic consequence of the proximity effect is the anomalous long-range transfer of the magnetic field from the ferromagnet to the superconductor even in the case when the F layer does not produce a stray magnetic field [3, 4]. This so-called electromagnetic proximity effect originates from the generation of the superconducting currents inside the F layer due to the direct proximity effect and the subsequent appearance of the compensating Meissner currents flowing in the S layer.

In this paper we review the recent results related to the physics of the in-plane FFLO states and electromagnetic proximity effect in S/F hybrids. Also we analyze the interplay between these two phenomena revealing through the boosting of the spontaneous magnetic field generated in the S layer due to the electromagnetic proximity effect in the vicinity of the phase transition from the uniform superconducting state to the in-plane FFLO phase.

Leakage of the magnetic field from the ferromagnet to the superconductor due to the electromagnetic proximity effect and qualitative plot illustrating the increase in the amplitude of the spontaneous magnetic field when approaching the transition to the FFLO phase (with the decrease of temperature).

[1] S. Mironov, A. Mel’nikov, A. Buzdin, Phys. Rev. Lett. 109, 237002 (2012)
       [2] S. V. Mironov, D. Yu. Vodolazov, Y. Yerin, A. V. Samokhvalov, A. S. Mel’nikov, A. Buzdin, Phys. Rev. Lett. 121, 077002 (2018)
       [3] S. Mironov, A. S. Mel’nikov, A. Buzdin, Appl. Phys. Lett. 113, 022601 (2018)
       [4] Zh. Devizorova, S. V. Mironov, A. S. Mel’nikov, A. Buzdin, Phys. Rev. B 99, 104519 (2019).

S. V. Mironov, A. V. Samokhvalov, A. Buzdin, A. S. Mel’nikov
JETP Letters 113, issue 2 (2021)

Half-metals are rather unusual and promising materials. The Fermi surface of a half-metal is completely spin-polarized. Namely, electronic states with only one spin projection value reach the Fermi energy. States with the other spin projection are pushed away from the Fermi level. This makes half-metals useful for spintronics. Typically, half-metallicity arises in strongly correlated electron systems, or when localized magnetic moments are present. We demonstrated that doping a density-wave insulator even in the weak-coupling limit may stabilize new types of half-metallic states, such as spin-valley half-metal and charge-density wave (CDW) half-metal.

In a simple model Hamiltonian describing two Fermi surface pockets (or valleys) with nesting, the electron-electron repulsion generates spin- or charge-density wave state, see Fig.1(a). If charge is added or removed from such a system, the situation becomes less clear-cut: several states with close energies are competing. Such possibilities as incommensurate density wave, electronic phase separation, stripes, etc. are discussed in the theoretical literature. We demonstrate that yet another type of many-body state is available. In the doped system, the two-valley Fermi surface emerges. One valley is electron-like. It is composed mostly of states of electron band, with spin σ. Another valley is hole-like, composed predominantly of states from hole band, with spin σ'. These Fermi surface valleys have half-metallic character: the states in electron band with spin -σ, as well as states in hole band with spin –σ', do not reach the Fermi level and have no Fermi surface.

Depending on the parameters, the spin polarizations of the electron-like valley and hole-like valley may be parallel (σ = σ') or antiparallel (σ = -σ'), see Fig.1(b,c). The former case is similar to the usual half-metal: quasiparticles at the Fermi surface are completely spin-polarized. In addition, the system exhibits a finite CDW order parameter. For this reason, we refer to such a state as the CDW half-metal. When σ = -σ', the total spin polarization averages to zero. It is proven, however, that in this situation, the so-called spin-valley polarization is nonzero. Thus, the state is called the spin-valley half-metal. The specific features of these half-metallic states are discussed. Namely, we demonstrate that the electric current can be accompanied by the transfer of spin or of the spin-valley quantum number. Such effects could be of interest for spintronics and pave the way to spin-valley-tronics. We also discussed the possibility of using the inelastic neutron scattering to detect the half-metallic states.

Band structure of (a) undoped density wave, (b) spin-valley and (c) charge density wave half-metals. Horizontal line shows the Fermi level, arrows indicate spin polarizations of the Fermi surface.

A.V. Rozhkov, A.O. Sboychakov, D.A Khokhlov  and A.L. Rakhmanov and A.D. Kudakov
JETP Letters 112, issue 11 (2020)

The magnonic Bose condensed state was first discovered in superfluid ³He under magnetic resonance conditions. The repulsive interaction between magnons stabilizes this state. The transfer of magnetization by a magnon supercurrent was also discovered [1].  Quite similar phenomena were observed in a nonplanar magnetized film of yttrium iron garnet (YIG), but at room temperature. When the deviation of the magnetization in YIG is more than 3 degrees, the density of non-equilibrium magnons exceeds the critical one [2], and a magnon Bose condensate is formed. Due to the superfluidity of magnons, the BEC state can fill the entire sample and the angles of magnetization deviation exceed 20 degrees [3].

Magnon BEC was studied in a YIG film epitaxially grown on a gadolinium gallium garnet (GGG) plate 0.5 mm thick. The Gilbert attenuation determines the field shift of the BEC observation. It has been found to be highly frequency dependent. It increases significantly when the frequency matches the standing sound waves in the GGG (peaks A in Fig. 1). The magnetoelastic interaction excites phonons, which dissipate energy. Unexpectedly, we also detected antiresonant signals (dips B in Fig. 1). We can explain this by the coherent mediation of circularly polarized phonons, which return their angular momentum after being reflected from the other side of the GGG plate. This observation shows the coherent transfer of the angular momentum of phonons through non-magnetic material on a macroscopic distance.

[1] G. E. Volovik, J. Low Temp. Phys., 153,  266 (2008)

[2] Yu.M.Bunkov, V. L. Safonov, J. Mag. Mag. Mat., 452 30–34 (2018)

[3] P. M. Vetoshko, G. A. Knyazev, A. N. Kuzmichev, A. A. Cholin, V. I. Belotelov, Yu. M. Bunkov, JETP Letters 112,  313 (2020).

P. M. Vetoshko, G. A. Knyazev, A. N. Kuzmichev, V. I. Belotelov, Yu. M. Bunkov
JETP Letters 112, issue11 (2020).

        The ability to explain when and why an isolated quantum mechanical system can be accurately described with equilibrium statistical mechanics is one of the key challenges in modern statistical physics. Such description may be possible even for time-dependent Hamiltonians, and much attention has focused on the emergence of quasi-equilibrium states in many-particle periodically driven systems. Numerous approximate methods have been developed to describe dynamics of such systems, known as Floquet dynamics. Interesting results were previously obtained when the external driving frequency significantly exceeds the strength of the interaction in the system in frequency units (the averaging condition).

        NMR in solids was one of the first areas where experimental and theoretical investigations of dynamics and thermodynamics in periodically driven systems were performed. The powerful experimental technique of NMR and relatively simple analytic tools allowed the creation of  “spin  alchemy” with very interesting results.

     In this letter we work out a numerical method to investigate Floquet dynamics in the simplest multi-pulse NMR experiment in a system of 14 spins connected by dipole-dipole interactions. We discover that a quasi-thermodynamic equilibrium is established under the averaging condition. When this condition is not met, instead of a quasi-equilibrium state, we find that the polarization decays to zero.

The decay of the polarization in multi-pulse NMR spin-locking with π/8 RF pulses. The initial polarization equals 1. The horizontal line is the thermodynamic  equilibrium polarization.The number of the spins is 14. The averaging condition is satisfied.

G.A.Bochkin, S.G.Vasil’ev, A.V.Fedorova, E.B.Fel’dman
JETP Letters 112, issue 11 (2020)

The problem of searching new high-energy-density materials (HEDM) is very actual from both applied and fundamental points of view. Choosing nitrogen as a promising element for creating HEDMs have several reasons. Under normal conditions, nitrogen exists in the form of diatomic N₂ molecules with a triple covalent bond, which is one of the strongest covalent bonds in nature, its energy is 4.9 eV/atom. The energies of double and single bonds for nitrogen are 2.17 eV/atom and 0.83 eV/atom, respectively. Those for nitrogen the sum of three single bonds energies is much less than energy of triple bond; therefore, single-bonded nitrogen crystal structures will store energy. At the same time, the release of energy is an environmentally friendly process.

In this article, the existence of a metastable, single-bonded crystalline nitrogen phase with symmetry P-62c is predicted theoretically. This phase is a direct-gap semiconductor and can store the largest amount of energy among all nitrogen crystals predicted to date, which are stable at low pressures. This structure of non-molecular nitrogen has all the necessary attributes of dynamic (in terms of the phonon spectrum) and mechanical (in terms of elastic moduli) stability of a bulk medium at pressures less than 40 GPa, including zero pressure. In the entire pressure stability range phase P-62c is metastable. For its synthesis, it is necessary to search new methods, for example, synthesis through excited states.

K.S.Grishakov and N.N.Degtyarenko

JETP Letters 112, issue 10 (2020)

After the discovery of Mott insulating states and superconductivity in the so-called magic angle twisted bilayer graphene in 2018, the study of this material became a hot topic in condensed matter physics. In single-particle approximation, the system under study has four almost flat almost degenerate bands near the Fermi level. The electron-electron interaction lifts this degeneracy stabilizing some order parameter in the system. The mottness of the ground state of the magic angle twisted bilayer graphene manifests itself in the sequence of conductivity minima observed for several doping levels.

The nature of the ground state of the magic angle twisted bilayer graphene is not yet known. Here, we assume that the emerging non-superconducting order parameter is a spin density wave, and study the evolution of such ordered state with doping. We show that in the range of electron densities, where the order parameter is nonzero, the homogeneous state of the system can be unstable with respect to the phase separation. Phases in the inhomogeneous state are characterized by an even number (n = 0, ±2, ±4) of electrons per a superlattice cell. This allows us to explain some features in the behavior of the conductivity of the system with doping. Thus, we are able to explain the fact that the conductivity minima, that could occur at doping levels corresponding to an odd number (n = ±1, ±3) of electrons per supercell, are absent in some samples under study (phase separation occurs) and are present in other samples (phase separation is suppressed by the long-range Coulomb repulsion).

Free energy of the system as a function of doping. The solid (red) curve corresponds to the free energy of the homogeneous state. The energies of the inhomogeneous states obtained by the Maxwell construction are shown by dashed (green) lines

A.O. Sboychakov, A.V. Rozhkov, K.I. Kugel, and A.L. Rakhmanov
JETP Letters 112, issue 10 (2020)

Recently emerged new field of all-dielectric resonant metaphotonics (also called “Mie-tronics” aims at the manipulation of strong optically-induced electric and magnetic Mie-type resonances in dielectric nanostructures with high refractive index. Unique advantages of dielectric resonant nanostructures over their metallic counterparts are low dissipative losses combined with strong enhancement of both electric and magnetic fields, thus providing competitive alternatives for plasmonics including optical nanoantennas, nanolasers, biosensors, and metasurfaces.

Importantly, high-index dielectric nanoparticles supporting multipolar Mie resonances are building blocks of advanced metamaterials. By combing both electric and magnetic multipolar modes, one can modify far-field radiation patterns and also localize the electromagnetic energy in open resonators by employing the physics of bound states in the continuum.  Changing the resonator parameters or combining the resonators into a planar geometry of metasurfaces allow achieving much higher values of the Q factor.

This mini-review highlights some recent advances in the field of all-dielectric Mie-resonant metaphotonics driven by the development of high-Q dielectric structures for nonlinear nanophotonics, nanoscale lasing, and efficient sensing applications.  

Example of 310 nm nanolaser based on lead halide perovskite CsPbBr₃ nanocuboid and operating at room temperature. Multipole decomposition of the lasing mode demonstrates the dominant contribution of the third-order magnetic dipolar Mie mode.

P.Tonkaev, Y.Kivshar
JETP Letters 112, issue10 (2020)

The theoretical prediction of the early seventies about the existence in a solid of a new state of "quantum spin liquids" is now finding real experimental confirmation. "Spin-liquid" compounds have a specific frustrated lattice consisting of triangles, at the vertices of which there are magnetic atoms that do not allow establishing long-range order. Due to quantum fluctuations and strong correlations between spins, frustrated magnets remain disordered even near absolute zero. 

This work presents results of an experimental study of the electronic system of a highly frustrated quasi-two-dimensional organic metal κ- (ET) 2Hg (SCN) 2Cl by the Shubnikov-de Haas quantum oscillation method. At temperatures above 30 K, this compound behaves like a metal with a half-filled band with strong electron-electron correlations. In the region of T = 30 K, a Mott metal-insulator transition is observed in the compound, and at low temperatures the system passes into the state of a quantum spin liquid (N.M. Hassan, and all, npj Quantum Materials 5, 15, 2020).

Organic conductors are fairly  soft materials, and application of pressure can significantly change the conduction band and affect their physical properties. The application of a hydrostatic pressure of 0.7 kbar suppresses the metal-insulator transition and restores the metallic state of κ- (ET) 2Hg (SCN) 2Cl. This enables studying the behavior of the interlayer magnetoresistance at helium temperatures. The field dependence of the magnetoresistance shows an unlimited growth according to a power law, which is a rare phenomenon for organic conductors and may indicate the presence of the polaron mechanism in interlayer transport. The spectrum of the detected oscillations of the magnetoresistance facilitates better understanding of the shape and dimensions of the Fermi surface and to estimate the parameters of the electron system.

Field dependence of the interlayer longitudinal magnetoresistance in κ- (ET) 2Hg (SCN) 2Cl at T = 0.47 K and p = 0.7 kbar. Inset 1: Fourier spectrum of magnetoresistance oscillations. Inset 2: schematic representation of the Fermi surface.

R.B. Lyubovskii, S.I. Pesotskii, V.N. Zverev, E.I. Zhilyaeva, S.A. Torunova, R.N. Lyubovskaya
JETP Letters 112, issue 9 (2020)

With the recent progress in observing new “locally incompressible” fractional quantum Hall states (FQHE), at the forefront of physics of two-dimensional systems (2DES's), there arises a necessity to develop  experimental approaches for the direct monitoring of bulk FQHE states. Since the transport characteristics of the FQHE insulators are not very informative (only the edge channels spatially separated from the bulk states contribute to conductivity), we employ optical techniques that can provide the required information. One of the confirmed experimental techniques for studying bulk electronic states in the QHE and FQHE regimes is the resonant reflection. However, the resonant reflection technique, because of  its high complexity, is not suitable for routine studies of FQHE states. Application of the nonresonant reflection for the same purpose is impossible for an uncontrolled photo-induced contribution to the experimental results. Up to now, all attempts to employ the photoluminescence technique for analysis of the FQHE states have not lead to reasonable results, despite the fact that in the QHE regime, nonresonant photoluminescence is one of the most powerful tools for studying bulk states. The reason for the incorrect use of this experimental technique became obvious only recently. In the nonresonant photoluminescence, the contribution to the signal is produced not only by two-particle excited states of 2DES, for which the conditions of “hidden symmetry” are satisfied but also by three-particle states, for which there are no symmetry restrictions on the spectral characteristics of the photoluminescence signal. The photoluminescence signal of three-particle complexes in the FQHE regime can have a complex structure with several spectral components due to the nontrivial dispersion of two-particle complexes (magnetoexcitons), from which three-particle complexes are constructed. In the presented work, we employ the resonant photoluminescence for studying FQHE state 1/3, with which we have got rid of unwanted photoluminescence of three-particle complexes. In this case, no violation of the “hidden symmetry” is observed, however, the amplitude of the resonant photoluminescence signal from the FQHE 1/3 state modifies so dramatically, that this modification can serve as an experimental marker of the 1/3 state. On the other hand, such a change in the amplitude of the resonant photoluminescence response indicates  the formation of a nonequilibrium coherent spin-excitation ensemble in 2DES, which is believed to consist of the quasi-particles with fractional charges.

L.V. Kulik et al.
JETP Letters 112,  Issue 8 (2020)

Titanium dioxide (TiO₂) is actively used in the modern world: as an E171 additive in the food industry, in the fabrication of paints and varnishes, solar panels, gas sensors, etc.
For many practically significant applications, especially for the food industry, it is important to determine the composition of TiO₂ powders (the proportion of nanoparticles that have toxic properties in the powder). Spectroscopic methods are promising for studying the composition of TiO₂ powders; however, the optical properties of titanium dioxide remain not fully understood. For this reason, the mechanisms of radiative recombination of the anatase titanium dioxide, which are responsible for intense emission lines in the visible and near-infrared range are being actively discussed. Various authors associate TiO₂ luminescence with various mechanisms: from the recombination of autolocalized excitons to the mechanism in which an electron bound to a donor impurity recombines on a hole bound to an acceptor impurity (the so-called luminescence of distant donor-acceptor pairs).
In this work, a simple model is proposed that allows one to identify the power-law decays of the luminescrence signal in TiO₂ micropowders with the emission of donor-acceptor pairs located in the volume of microcrystals. Based on this model, the change in the power-law decay of the luminescence signal of donor-acceptor pairs in nanopowders is described within the framework of nonradiative recombination associated with the surface. The presented experimental results are promissing for fullu optical detection of toxic TiO₂ nanoparticles in the well known E171 food aditive.

a) Luminescence decay for so-called green luminescence band at 2.3 eV, measured for a micropowder (grey curve), and its approximation by a power-law t^-x dependence with x = 0.8 (red dashed line). b) Luminescence signal decay of the same band, measured for the toxic nanopowder (grey curve), and approximation of its fragments by power dependences with x = 0.5 (yellow dashed line) and x = 1.44 (red dashed line).

V.S. Krivobok et al.
JETP Letters 112, issue 8 (2020)

The planar phase of superfluid 3He has two Dirac points in the quasiparticle spectrum – the Berry phase monopoles. The quasiparticles with fixed spin behave as Weyl fermions. While in the chiral superfluid  $^3He$-A the spin-up and spin-down fermions
have the same chirality, in the planar phase these fermions have opposite chiralities forming massless Dirac fermions. As in 3He-A, the Dirac fermions experience effective gravity and gauge field produced by the deformation of the superfluid order parameter.
In both superfluid phases the primary variables, which give rise to the effective metric acting on Weyl and Dirac particles, are the vielbein fields. As distinct from the 4 x 4 matrix in the conventional tetrad gravity and in the effective gravity emerging in  $^3He$-A, the vielbein field in the planar phase has mixed dimensions: it is the 4 x 5 matrix.
The planar phase has the analog of Dirac magnetic monopole in the real space. In this monopole, the Dirac strings of different chirality compensate each other. In the presence of the monopole the effective metric describes the conical spacetime
produced by the global monopole in general relativity. But instead of the solid angle deficit, the effective spacetime in the planar phase has the solid angle excess, which corresponds to the repulsive gravity, G < 0.

 G.E. Volovik 

JETP  Letters 112, issue 9  (2020) 

The question of the influence of potential disorder on superconductivity has a rich research history dating back to the celebrated Anderson theorem about the insensitivity of the superconducting critical temperature to the disorder strength. However, a large body of empirical evidence indicates that the transition temperature is typically suppressed with disorder, which is in particular prominent for superconducting films of a mesoscopic thickness. This effect is conventionally attributed to disorder-related enhancement of Coulomb repulsion, which provides a negative contribution to the Cooper coupling, thus suppressing superconductivity.

Quantitative study of this effect in the assumption of a two-dimensional diffusive nature of electron motion was done in 1980ies by a number of authors. The first-order correction was later generalized by Finkel'stein, who derived a non-perturbative expression for the critical temperature degradation as a function of the sheet resistance of the film. The latter has become a widespread tool for fitting experimental data.

In this work, based on the theoretical treatment accompanied by the analysis of experimental data, it is argued that for the substantial fraction of superconducting films the main contribution to the critical temperature suppression stems from the region of three-dimensional ballistics rather than two-dimensional diffusion. The ballistic effects are governed by the parameter $k_F l$ (where $k_F$ is Fermi momentum and $l$ is the mean free path), which is a measure of the proximity to the three-dimensional Anderson localization.

Suppression of the critical temperature is given by the integral over the momentum $q$ carried by the electron-electron interaction. The figure is a sketch of the corresponding integrand. The integral is logarithmic in the region of two-dimensional diffusion, $q < 1/d$ ($d$ is the film thickness). It linearly diverges in the three-dimensional region $q>1/d$, extending from the diffusion to the ballistic region with a different numerical coefficient. Therefore the main contribution comes from the upper cutoff at $q \sim k_F$.

Antonenko D.S., Skvotsov M.A.
JETP Letters 112, issue 7 (2020)

Balancing an inverted pendulum subject to a given time-dependent horizontal force is a famous mathematical challenge known as the Whitney problem. For any initial and final position of the pendulum in the upper half-plane, there exists a trajectory that remains in the upper half-plane at the entire time interval. Remarkably, a non-falling solution to the Whitney problem is unique.

Assuming that the horizontal force is a random process, a formal mathematical problem of the existence of a non-falling trajectory gets translated into the context of stochastic dynamics, with the main goal of describing statistical properties of such a non-falling trajectory. Quite unexpectedly, the latter formulation has many notable connections with other mathematical physics problems: control theory, Burgers turbulence, theory of minimizers, rear events in stochastic differential equations, disordered superconductivity, etc.

A new analytical method for describing statistics of the never-falling trajectory on an infinite time interval has been recently developed by the authors of this Letter, in the framework of a supersymmetric field-theoretical approach to stochastic dynamics. In this Letter, the technique is generalized to finite time intervals and different-time correlation functions on the non-falling trajectory. In particular, it allows determining the Lyapunov exponent, which governs decay of memory correlations on the non-falling trajectory.

Examples of non-falling trajectories for the pendulum equation of motion obtained for two time intervals and the same horizontal force (a), (b). Shown are 25 such trajectories with five initial and five final positions in the upper half-plane. The memory of the boundary is lost exponentially with the rate determined by the Lyapunov exponent. (c) An inverted pendulum under the action of a horizontal force.

Stepanov N.A., Skvotsov M.A.
JETP Letters 112, issue 6 (2020)

The Standard Model unequivocally predicts parity violation in high energy hadronic interactions of polarized hadrons. However, the experimental confirmation of this prediction is still elusive. One of the possible observables is the parity violating single-spin asymmetry in scattering of the longitudinally polarized protons and deuterons. High intensity polarized beams will be available at NICA facility under construction at JINR, Dubna. The reported estimates of asymmetries in polarized proton-deuteron scattering are an extension of systematic analysis [1,2] of possibilities of experiments at NICA. Experimental observation of asymmetries in the total cross sections, expected to be well below 10^-7 , is extremely challenging, and it is suggested to take advantage of substantial enhancement of asymmetry in elastic scattering. In the case of polarized deuterons, similar enhancement is shown to persist in the deuteron dissociation channel.

[1]  I.A. Koop, A.I. Milstein, N.N. Nikolaev, A.S. Popov, S.G. Salnikov, P.Yu. Shatunov, Yu.M. Shatunov, Strategies for Probing P-Parity Violation in Nuclear Collisions at the NICA
       Accelerator Facility, Physics of Particles and Nuclei Letters, 17(2), 154-159 (2020)
       [2]  A.I. Milshtein, N.N. Nikolaev, S.G. Salnikov,  Parity Violation in Proton–Proton Scattering at High Energies, JETP Letters, 111(4), 197-200 (2020)

A.I. Milshtein, N.N. Nikolaev, S.G. Salnikov,  Parity Violation in Proton–Proton Scattering at High Energies

JETP Letters 112, issue 6 (2020)

Bilayer graphene nanoribbons (BGNR) are quasi one dimensional materials which have a wide variety of properties depending on their width, geometry of edges, defects and external influences, such as mechanical deformations or electric and magnetic fields. Combination of nanoribbons with various properties can open wide prospects of their use as two dimensional electronic devices.

This work aims to investigate electronic transport in BGNR with a pore by means of the wave packet dynamics method. Wave packet (WP) is injected from metallic electrode to the BGNR and interacts with atomic structure of nanoribbon and with nonopore. The results of these calculations are the time dependent wave functions. Two types of system were considered where the electrode is connected with: (i) both layers, and (ii) with only one layer. Time dependent currents through the BGNR cross-sections were obtained, both ahead of and behind the hole. It was shown that the presence of nanopore is important for the WP propagation: it complicates the pattern of WP spreading and leads to localized states formation on the pore (Fig.1). For type (ii) connection to electrode, the nanopore plays a role of the signal separator. Currents flow after passing the nanopore are significantly different in each layer.

The propagation of the wave packet is influenced by many parameters of the nanoribbon, such as its width, hole geometry, defects, type of connection to electrode etc. This study may be the first prerequisite for potential use of such objects as elements of electronic circuits

Figure 1. Wave packet probability density in the bilayer graphene nanoribbon with a hole, in the layer connected to the electrode (left), and in the layer unconnected (right) at t = 4.2 fs

V.A. Demin, D.G. Kvashnin, P. Vancso, G. Mark, L.A. Chernozatonskii
JETP Letters 112, issue 5 (2020)

The process of spontaneous parametric down-conversion (SPDC) is a significant source of biphotons. Biphoton is a pair of quantum – correlated photons. Due to the high degree of correlation, biphotons are used in many areas such as quantum processing, quantum tomography, spectroscopy, etc. Recently, the generation of optical - terahertz biphotons under strongly frequency-non-degenerate parametric down-conversion has attracted more attention.
The paper proposes an approach that allows using the same detector with a limited dynamic range for the registration of terahertz radiation under parametric down-conversion (PDC) at a different parametric gain. This approach is based on the change of the wavelength of the optical pump and can be used to achieve the spontaneous PDC to obtain optical – terahertz biphotons with a high degree of correlation. By doubling the frequency of a pulsed laser source, we experimentally demonstrated a decrease of the parametric gain more than fivefold in the minimum value, at which terahertz (idler) radiation can be detected against the background of detector noises. The terahertz radiation generated by the PDC was detected under the record low parametric gain conditions.

The experimental setup for the generation a terahertz - optical biphotons and idler radiation detecting terahertz frequency power at the PR in two modes at the pump wavelength $\lambda_p$ = 1046.7nm and $\lambda_p$  = 523.35 nm

V.D. Sultanov, K.A. Kuznetsov, A.A. Leontyev and G.Kh. Kitaeva
JETP Letters 112, issue 5 (2020)