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Superconducting system with current in the ground state
L.N. Bulaevskii Institute of Theoretical Physics, ETH, Zurich, Switzerland Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
About the paper SUPERCONDUCTING SYSTEM WITH WEAK COUPLING TO CURRENT IN GROUND-STATE by BULAEVSKII L.N., KUZII V.V., SOBYANIN AA
In the paper Pis'ma Zh.Eksp. Teor. Fiz. 25, 314, 1977, Bulaevskii, Sobyanin and Kuzii (BSK) introduced conception of SIS $\pi$ junction consisting two singlet s wave pairing superconductors S separated by the dielectric I with magnetic impurities. This advance was based on previous finding by Kulik (Zh. Eksper. Teor. Fiz. 49, 1211, 1965) that magnetic impurities inside dielectric I in SIS junctions diminish the superconducting critical current. The physical reason for that is that tunneling of Cooper pair with opposite spins of electrons gives negative contribution to the critical current (and thus to junction superconducting energy) as compared with contribution of tunneling via nonmagnetic atoms. BSK argued that if tunneling via magnetic atoms becomes dominant over nonmagnetic ones, critical current will be negative resulting in the junction ground state with the phase difference $\pi$ instead of 0 as in ordinary junctions. In both cases, $\pi$ or 0 junctions, supercurrent in the ground state vanishes. However, BSK showed that if one connects (shorts) the superconducting electrodes with the inductance L (e.g. superconducting wire), one may expect the spontaneous supercurrent circulating in the loop, passing through the junction and through inductance clockwise or counterclockwise. This supercurrent is spontaneous and direction of its circulation is chosen at random. Such a supercurrent will induce a magnetic field which can be detected experimentally. The magnetic flux passing through the loop will have the value in the range from 0 to a half of magnetic flux quanta, i.e. from 0 to $\Phi_0/2$, depending on the value of inductance $L$.
Created by I. Podyniglazova, 2014-12-24 16:28:02
About the paper "Two-dimensional massless electrons in an inverted contact". B.A. Volkov and O.A. Pankratov, 1985.
O.A. Pankratov University of Erlangen-Nürnberg, Germany A discovery of topological insulators [1] and the booming interest in topologically protected electron states went to benefit for our paper of 1985 [2]. The effect that we thought was an interesting but exotic possibility occurred to be a precursor of a new quantum state of matter. Moreover, semiconducting compounds $Pb_{1-x}Sn_xTe$, the model systems that we considered, indeed turned out to be topological insulators [3]. The dynamics of the Bloch electrons in solids may drastically differ from that of the free Schrödinger particles. In particular, in narrow gap semiconductors there are two closely lying energy spectrum branches, the conduction and the valence band, which dominate their properties. This band structure is well described by the Dirac relativistic spectrum with the band gap $\varepsilon _{g}$ playing the role of $2mc^2$. Henceforth these materials are described by the Dirac theory rather than the Schrödinger theory. Yet in contrast to the “true” Dirac particles, not only the value of the gap but also its sign (which determines the relative position of the two bands) matters here. The ordering of the bands is an observable with the band edges labeled by different symmetries of the wave functions. For example, in $PbTe$ the conduction band is odd and the valence band is even. This band ordering is, by convention, “normal” and it corresponds to $\varepsilon > 0$. On the contrary in $SnTe$ the bands are “inverted” i.e. the conduction band is even, the valence band is odd, and $\varepsilon < 0$. The question that we asked to ourselves in 1985 was: what happens if we put together two materials with opposite signs of the band gap? Such an “inverted” contact can be fabricated e.g. by varying the composition in the alloy $Pb_{1-x}Sn_xTe$ between the normal $(PbTe)$ and the inverted ($SnTe$ phases during the crystal growth. The answer comes from solving the Dirac equation with the variable band gap $\varepsilon _{g}(Z)$. We found that, independently of a particular shape of the function $\varepsilon _{g}(Z)$, this equation always has a solution localized at the interface, the only requirement being the change of a sign of $\varepsilon _{g}(Z)$ on the boundary. In an (ideal) contact plane, the solution is, naturally, a plane wave. Herewith the energy depends linearly on the in-plane momentum – exactly as for the Dirac electrons in graphene [4]. However, in contrast to graphene, the spin structure of the wave functions is fixed i.e. the interface states show a giant spin splitting. As the spin degree of freedom is frozen, the interface particles obey the Weyl (not Dirac) equation. All these features are precisely the same as of the protected surface states on topological insulators [1]. Of course, the latter were not known at that time. In our paper, we only referred to a similarity with soliton states in the one-dimensional Peierls chains [5]. In the second part of the paper, we worked out the interface Landau levels in an external magnetic field applied perpendicular to the contact plane. A simple calculation gives a non-equidistant spectrum $\varepsilon (n)=\pm (\surd 2n \hbar \nu)/L$ , where parameter $\nu$ plays the same role as a speed of light in the Dirac Hamiltonian and $L$ is a magnetic length. This formula was later repeatedly discussed in conjunction with an anomalous quantum Hall effect in graphene [4]. Having the Landau levels, we calculated the diamagnetic susceptibility and the quantum oscillations of the induced magnetic moment; we hoped that these signatures might be helpful for identifying the Weyl states in experiment.
To the best of my knowledge, the inverted $Pb_{1-x}Sn_xTe$ contact has never been manufactured. Yet in 2007, the paper was published on a first experimental realization of a topological insulator – an “inverted” quantum well $CdTe/HgTe/CdTe$ [6]. Indeed, the $Cd_{1-x}Hg_xTe$ alloy also offers the band inversion and hence an opportunity for the Weyl states. In fact, we discussed this opportunity already in 1987 [7]. The situation here is somewhat more complicated because one of the bands is degenerate. It consists of the light and the heavy hole branches and only the light branch (which is mirrored to the conduction band) undergoes the inversion. As a result, the inverted state (occurring in $HgTe$) is metallic, or, more precisely, it is a semiconductor with zero band gap. This circumstance is harmful for the interface states. It is an advantage of the quantum well, that here the band degeneracy is lifted due to the quantization in Coming back to $Pb_{1-x}Sn_xTe$, it is nowadays clear that with these materials there is no need of fabricating the inverse contact to observe the Weyl particles. Namely, the “contact” to vacuum is enough! Since the “inverted” material $SnTe$ is, by itself, a topological insulator it always has the Weyl states on its surface. Their topological protection is guaranteed (in spite of an even number of the band extrema in the Brillouin zone) by the crystal symmetry [8]. In summary, a simple model that we considered almost 30 years ago, turned out to be a first example of a topological insulator. The origin of the topological nontriviality of the band structure in materials like $SnTe$ can be uncovered with a simple tight binding theory [9, 10] that B.A. Volkov and myself developed in the early 80-s for this material class. This work eventually guided us to ask a question: what happens if we bring two materials with opposite signs of the band gap in contact?
[1] M.Z. Hasan and C.L. Kane, Rev. Mod. Phys. 82 (2010) 3045. [2] B.A. Volkov and O.A. Pankratov, JETP Letters 42, 145 (1985) [3] Y. Tanaka, Zhi Ren, T. Sato, K.Nakayama, S. Souma, T.Takahashio, K.Segawa, and Y. Ando, Nature Phys. 8 (2012) 800. [4] Castro Neto, A.H.F. Guinea, N.M.R. Peres, K.S. Novoselov, and A.K.Geim, Rev. Mod. Phys. 81 (2009) 109. [5] S.A. Brazovskii, Zh.Eksp. Theor. Fiz. 78 (1980) 677 [Sov. Phys. JETP 51 (1980) 342. [6] M. Koenig, H. Buhmann, L.W. Molenkamp, T. Hughes, C.X. Liu, X.L. Qui, and S.C. Zhang, Science, 318 (2007) 766. [7] O.A. Pankratov, S.V. Pakhomov, and B.A. Volkov, Solid State Comm. 61 (1987) 93. [8] T.H. Hsieh, H. Lin, J. Liu, W. Duan, A. Bansil, and L. Fu, Nature Comm. 3 (2012) 982. [9] B.A. Volkov and O.A. Pankratov, Zh.Eksp. Theor. Fiz. 75 (1978) 1362 [Sov. Phys. JETP 51 (1980) 34. [10] B.A. Volkov, O.A. Pankratov, and A.V. Sazonov, Zh.Eksp. Theor. Fiz. 85 (1983) 1395 [Sov. Phys. JETP 51 (1980) 34.
Created by I. Podyniglazova, 2014-11-28 16:59:02
NORMAL-PRESSURE SUPERCONDUCTIVITY IN ORGANIC METAL (BEDT-TTF)2I3 [BIS(ETHYLENEDITHIOLO)TETRATHIAFULVALENE TRIIODIDE]" by E.B. Yagubskii, I.F. Schegolev, V.N. Laukhin, P.A. Kononovich, M.V. Kartsovnik, A.V. Zvarykina and L.I. Buravov (1984)
E.B.Yagubskii IPCP RAS Chernogolovka, Moscow District 142432, Russia The paper [1] is a result of a 17-year purposeful search for organic superconductors. In 1966 Igor F. Schegolev put together a team consisting of physicists, chemists and crystallographers at the Branch of Moscow Institute of Chemical Physics in Chernogolovka, and set them the task to create organic superconductors.The impetus to this task had been a work by the American physicist-theorist W.A. Little. In 1964 W.A. Little proposed a new electron-electron (exciton) mechanism of superconductivity and a hypothetic high-temperature superconducting macromolecule to realize this mechanism. Little's model involves a linear conducting polyene chain, which contains easily polarizable substituents. Electron vibrations in such substituents were expected to provide effective attraction between conduction electrons resulting in superconductivity with high critical temperature Òñ. Though arguments and calculations of W.A.Little were not quite rigorous, his work attracted great attention. This is quite understandable since at that time the traditional direction associated with the design of superconducting alloys was almost exhausted. Despite consolidated efforts of physicists, metallurgists and materials scientists, critical temperature of superconducting transition, reaching 18K, has not grown for the past 15 years. Moreover, some publications claimed in theory that the phonon mechanism realized in conventional superconductors could not provide Òñ higher than 30 -40 K. We faced the problem of choosing the objects to be studied. It should be noted, however, that at that time not that superconductors, but even normal organic metals did not exist, and the problem of possible states in linear electron systems was far from being clear. Schegolev made a choice in favour of conducting molecular crystals rather than conducting polymers. It was supposed that the search for organic superconductors would be long and could be successful only through the successive analysis of a correlation between structure and electron properties. Now it is obvious that such strategy was valid. Organic superconductors were found in early 80ies among molecular crystals, while polymeric organic superconductors have not been obtained so far. At initial stage of our research we concentrated on the crystals of tetracyanoquinodimethane (TCNQ) radical anion salts, which had been synthesized in the USA shortly before, and some of them had shown essentially high room-temperature conductivity (~100 Ohm 1cm 1). However, physical properties of the salts were practically unstudied. Planar TCNQ molecules easily accept one electron to form stable radical anions packed above each other in the crystals of TCNQ salts to form continuous stacks. Anisotropic character of wave functions of -electrons gives rise to a noticeable overlapping of molecular -orbitals in the direction perpendicular to the plane of TCNQ molecules and, as a result, to sufficient room-temperature conductivity along the stacks, while conductivity in transverse directions is several orders of magnitude lower. So form the quasi-one-dimensional conducting chains in which electric current can flow in one direction, as in the hypothetic polymer Little molecule. However, by the middle 70ies the study of quasi-one-dimensional conductors clearly showed that one-dimensional systems are unfavorable for the design of superconductors because of very strong dielectric instabilities, first of all those associated with the effect of disordering and the Peierls metal-insulator transition. To attain superconductivity, one had to give up one-dimensionality. Higher overlapping of electron wave functions of molecules from the neighboring stacks was required to provide more than one direction for electron motion. In 1977 we synthesized a radical cation salt, tetraselenotetracene chloride, (TSeT)2Cl, which up to now has a record room-temperature conductivity among organic molecular compounds (2.5?103 Ohm 1cm 1 along the TSeT stacks). The presence of four large selenium atoms in the TSeT molecule provides certain overlapping of wave functions of -orbitals in the transverse direction (across the stacks). As a result, electron motion is "not so one-dimensional", and a metal-semimetal transition rather than a metal-dielectric one is realized in (TSeT)2Cl at low temperature (27K). A year later it was found that the transition is suppressed by applying low pressure of 4.5 kbar to the (TSeT)2Cl crystals, and the compound retains metallic properties ( = 105Ohm 1cm 1 at 4.2 K). Though this first really stable organic metal appeared to be non-superconducting, the existence of a stable metallic state in organic compounds implied that organic superconductivity is possible. Metals tend to become superconductors. So it happened soon. In 1979 K. Bechgaard from the Hans Christian ?ersted Institute in Copenhagen synthesized a radical cation salt based on another selenium containing donor, tetramethyltetraselenafulvalene, of (TMTSeF)2PF6 composition, which showed a metal-insulator transition at very low temperature (12 K). In 1980 the group of D. Jerome from the University of Paris-Sud found that this transition is fully suppressed at 11 kbar pressure, and (TMTSeF)PF6 undergoes a superconducting transition at 0.9 K. Thus, the first organic superconductor was found. In 1981-1983 six more superconductors based on TMTSeF salts with octahedral and tetrahedral anions were found, and there was only one superconductor at ambient pressure, tetramethyltetraselenafulvalene perchlorate, (TMTSeF)2ClO4, with Òñ = 1.2 K. However, soon it became clear that the family of organic superconductors based on TMSeF salts is quite narrow. All seven superconductors of the TMTSeF family are isostructural and show low values of Òñ (1-2 K). The attempts to extend the number of superconductors by varying counter ions in the TMTSeF salts turned unsuccessful. The next principally important step in the field of organic superconductivity was made in Chernogolovka. In 1983 we synthesized the first quasi-two-dimensional organic superconductor at ambient pressure, bis(ethylenedithio)tetrathiafulvalene triiodide, (BEDT-TTF)2I3 with Tc = 1.4 K. Unlike quasi-one-dimensional superconductors of the TMTSeF family, (BEDT-TTF)2I3 has a quasi-two-dimensional Fermi surface. In the structure of the salt, BEDT-TTF radical cation layers alternate with the layers formed by I3 anions. Conductivity in the BEDT-TTF layers is nearly isotropic, while in the direction perpendicular to the layers it is three orders of magnitude lower. The increase in the electron dimensionality of BEDT-TTF salts is due to structural features of this donor molecule: the presence of many sulfur atoms (eight) and noncoplanar terminal CH2-CH2 groups. Sulfur atoms provide interaction between stacks, while noncoplanar CH2-CH2 groups generate certain steric hindrances for the interactions between the radical cations inside the stacks. Soon we found that a new superconducting state with Òñ = 8 K emerges in the (BEDT-TTF)2I3 crystals under low pressure (~ 0.5 kbar). Later on, we succeeded in stabilizing this phase at normal pressure. It was found also that in contrast to the Òñ = 1.4 K phase which has a structural disorder associated with the arrangement of terminal CH2-CH2 groups, the phase with Òñ = 8 K is completely ordered. The discovery of quasi-two-dimensional organic superconductors strongly affected the trend of search for organic superconductors and provided a rapid development of chemistry of BEDT-TTF derivatives and the synthesis of multiple related salts with various anions. Now the number of organic superconductors of the BEDT-TTF family is more than one hundred, and Òñ grew up to 12.6 K. Regarding the crystal and electronic structure and some properties (low concentration of charge carriers, mixed oxidation state, high values of upper critical fields, proposed d-wave coupling), layered organic superconductors are close to high-temperature metal oxide superconductors and can be considered as models for the study of superconductivity mechanism in HTSC. It should be noted also that the search for organic superconductivity gave birth to a new class of low-dimensional solids, the study of which provided new important results in different areas of solid state physics, such as metal-dielectric and metal-superconductor transitions, coexistence of superconducting and dielectric transitions, charge and spin density waves, magnetic field-induced phase transitions, quantum spin liquid state, giant quantum and semi-classical oscillations of magnetoresistance and others [2]. [1] E.B. Yagubskii, I.F. Schegolev, V.N. Laukhin, P.A. Kononovich, M.V. Kartsovnik, A.V. Zvarykina., L.I. Buravov Sov. Phys. JETP Lett. 39, 12 (1984). [2] The Physics of organic superconductors and conductors Springer Ser. in Materials Science, v. 110. ed. by A.G. Lebed, Springer-Verlag, (2008).
Created by I. Podyniglazova, 2014-10-28 12:37:02
About the paper "TWO-DIMENSIONAL ELECTRONS IN A STRONG MAGNETIC-FIELD" BYCHKOV Yu. A., IORDANSKII S.V., ELIASHBERG G.M (1981)
S.V. Iordanskii Landau Institute for Theoretical Physics, Chernogolovka, Moscow District, 142432, Russia In the beginning of 1980 I have met Yu. A. Bychkov (we were co-authors of a couple of articles), who has just read current physics literature (which he did regularly). He told me that after reading an article of H. Fukujama, published in Technical Report ISSP Ser A 993 (1979) (Japan), he has found new field of activity. An article was about Wigner crystal research. This crystal is created by two-dimensional electrons in an extremely strong magnetic field, and energy of interaction with the field is much bigger than energy of Coulomb interactions between electrons. The problem was that Landau levels for electrons in magnetic field have multiple degeneration. This makes considering Coulomb interactions nearly impossible, even by using perturbation theory. Soon, G. M. Eliashberg joined us. With him, we have tried to consider Coulomb interactions for a small number of electrons in the first order of the perturbation theory. It was discovered, that this problem can be solved analytically only for two or three interacting electrons. For a larger number, you will need to solve secular problem, order of which rises with this number. The only simple solution is when all electrons are on the same Landau level with a fully asymmetric wave function with a constant density that corresponds to a full local filling of the level. The paper [1] was the first attempt to apply the ideas of the perturbation theory for a multi-electron problem. An actual idea had been acknowledged by the physics community, and several articles had appeared on this topic. However, a reasonable calculation method, for obtaining the state with a fractional filling of the Landau level was not created. Than, we knew nothing neither about the discovery of the Integer Quantum Hall Effect (K. Klitzing.1981), nor about the discovery of a Fractional Quantum Hall Effect (Tsui, Stoermer, Gossard.1982). We have found about it on the Soviet-American symposium in the autumn 1982 in Sweden. A boom in the physics of the two=dimensional electron systems placed in the strong magnetic field has started. Focus was on the search of the energy gap, separating states occupied by the electrons from non-occupied, needed for the existence of the FQHE. An American R. Laughlin (1983) had the most success, constructing multipartical function (Laughlin's function) from the wave functions of the lowest Landau level with the density of the 1/3 of the density of the fully filled quantum level. However, he did not find any proof of existence of the energy gap (see, e.g. [2]). Physical reason for the appearance of this gap turned out to be linked to thermodynamic instability of states with fractionally filled Landau levels and creation of the vortices. This is because vortex speed of the electrons is followed by the appearance of the magnetic momentum of the current, which decrease free energy in the fixed external magnetic field (we can neglect with weak edge current and magnetic field created by it). Decrease in the free energy of the sample is proportional to the area , but its internal energy is increased as logarithm of its size [3]. This phenomenon (creation of vortex structure) is similar to creation of vortices at rotation of quantum liquid. This way, in a two-dimensional system, periodic vortex lattice appears. Energy gaps in a "vortex crystal" appear only at rational number of flux quantums of the "effective" field (sum of flow of external magnetic field and fluxes of vortices) This gives an explanation about all observed densities in FQHE [3]. Another part of the article [1] was luckier. Electron excitations for fully filled lowest Landau level, when one electron gets excited and goes on the next Landau level with the same direction of spin, or just changed the direction of spin, was studied. Such excitation is neutral, as it is made out of electron and hole. That is why it's momentum has to be conserved, even in external magnetic field. A neutral exciton is formed. For Mott's exciton in a crystal it had been shown by L. P. Gorkov and I.E. Dzyaloshinskiy [4]. Accurate calculations were carried out by I. V. Lerner and Y. E. Lozovik [5]. Our case is a bit different from Mott's exciton and allows direct analytical consideration of wave function of exciton and direct calculation of commutators with Hamiltonian including Coulomb interaction. This gives an expression for energy of such exciton, depending only on its momentum (in both cases of Coulomb and spin exciton). All of this was rather trivial, so in the article only answers for energies are given. Later, approaches found in the article were used for different more complicated excitations. In conclusion, I would like to say, that publication of the paper abroad in the 80's of the last century was a really hard thing, as an article had been send by mail, which took many months. Our work was published in JETP Letters that, luckily, were often read abroad. C. Kallin and B. Halperin's work [6] on the same topic (exciton) was published 3 years later in Phys. Rev. Unknown to me reviewer pointed out to authors, that main result had already been achieved earlier. Authors had to include reference to our work, but their work was published in Phys. Rev. and later foreign references were, as a rule, on their work only. My work [7] about QHE, made during symposium in Sweden, was sent from there by mail to Solid State Communications. Editors of the journal, had sent me corrections to USSR by mail, and I've sent replies with occasional people traveling abroad. All of this caused unnecessary delays, and almost cost me my priority. It is good to live in the epoch of emails! [1] Ю.А.Бычков, С.В.Иорданский, Г.М.Элиашберг Письма в ЖЭТФ 33,152 (1981) [2] Квантовый эффект Холла, Москва, МИР(1989) [3] Иорданский С.В., Любшин Д.С., J.Phys.: Condens. Matter 21, 405601 (2009) [4] Горьков Л.П., Дзялошинский И.Е., ЖЭТФ 53, 717 (1967) [5] Лернер И.В.,Лозовик Ю.Е., ЖЭТФ 78,1167 (1980) [6] Kallin C., Halperin B.,Phys.Rev. B 30 ,5655 (1984) [7] Iordansky S. V., Sol. State Comm., 43, 1 (1982).
Created by I. Podyniglazova, 2014-09-29 11:24:02
The paper "Fully quantum treatment of the Landau-Pomeranchuk-Migdal effect in QED and QCD'' (B.G. Zakharov, 1996)
In the work [1] a formalism for calculation of the processes of the type $a\to bc$ in amorphous media at high energies (when the energies of the particles $a$, $b$ and $c$ are much bigger than their masses) induced by multiple scattering in the medium has been developed. In calculating of such processes one faces a problem of accounting for the Landau-Pomeranchuk-Migdal (LPM) [2, 3] effect related to large coherence length for $a\to bc$ transition at high energies. In this regime $a\to bc$ process involves interactions with many medium constituents. The problem becomes especially complicated in the non-abelian case when all the particles undergo multiple rescatterings in the medium. The approach [1] is applicable both in QED for ordinary materials (for instance, for the photon emission from electrons $e\to \gamma e$) and in QCD (for instance, for the gluon emission from fast quarks $q\to g q$ in a hot quark-gluon plasma or in a cold nuclear matter). The formalism is valid for any magnitude of the LPM suppression of the cross section. It accounts for accurately the Coulomb effects in multiple scattering and works both for infinite and finite-size matter. The spectrum in the Feynman variable $x_{b}=E_{b}/E_{a}$ has been expressed through the Green function of a two dimensional Schrodinger equation with an imaginary potential. This Green function describes the in-medium evolution on the light-cone $t=z$ ($z$ is coordinate along the momentum of the initial fast particle $a$) in the transverse plane of the fictitious system $bc\bar{a}$ from point-like to point-like state. In the $bc\bar{a}$ system the particle $\bar{a}$ is located at the center of mass of the $bc$ pair. In the above Schr\"odinger equation the coordinate $z$ plays the role of time, and the Schrodinger mass equals $x_{b}(1-x_{b})E_{a}$, which is the reduced mass of the system $bc$ in the impact parameter plane (where the role of masses are played by the particle energies). The imaginary potential is proportional to the product of the matter density and the cross section for interaction with a medium particle of the $bc\bar{a}$ system. The derivation is based on the representation of the wave function of each fast particle in the form of the product of the plane wave $\exp{[E(t-z)}]$ and a slowly varying "transverse'' wave function $\phi(\vec{\rho},z)$, which satisfies a two dimensional Schrodinger equation with mass $M=E$ ($E$ is the energy of the particle). Each transverse wave function has been written through the relevant Green function. It allows one, after integrating over the variable $t-z$ in each vertex (which leads to the mass conservation $M_{a}=M_{b}+M_{c}$ in the vertexes $a\to bc$), to obtain the diagrammatic representation of the amplitudes in terms of the transverse propagators. Making use of the Feynman path integral representation for the transverse propagators one can obtain the cross section of the process $a\to bc$ in a path integral form in the transverse plane on the light-cone $t=z$. Of course, the functional integral for the amplitude cannot be calculated analytically. However, it turned out that for the cross section, after averaging over the medium states, all the functional integrations, except for the integration over the transverse distance between $b$ and $c$, can be taken analytically similarly to the case of the functional integral for the electron density matrix [4]. And the remaining integral over the relative transverse vector $\vec{\rho}_{b}-\vec{\rho}_{c}$ gives the above mentioned Green function for the system $bc\bar{a}$. An important feature of the obtained diagrammatic representation for the cross section is that for the QCD case the calculation of the color factors becomes trivial.
An analysis of the LPM effect and the parton energy loss in QCD matter is of great interest both from general theoretic and phenomenological point of view. At the time of its publication the work was of special interest due to the interest in the radiative parton energy loss in the quark-gluon plasma, which was expected to be produced in future experiments on heavy ion collisions at RHIC and LHC. It has been expected that the energy loss of the fast quarks and gluons produced in hard processes as they traverse the quark-gluon plasma would suppress the hadron spectra at high transverse momenta (similarly to the reduction of radiation in a concrete nuclear reactor containment). Subsequently, it turned out to be case, and analyzing of the suppression of the high-$p_T$ spectra (usually called "jet quenching'') became one of the major methods in diagnostics of the QCD matter in heavy ion collisions at RHIC and LHC. The analysis [1] turned out to be the first consistent calculationof the radiative energy loss in QCD matter. The previous attempts [5-7] to calculate them, even in the soft gluon approximation, have not been successful. Practically simultaneously with [1] the induced gluon radiation in QCD matter was addressed in works [8], where only the regime of strong LPM effect and in the soft gluon approximation was studied. However, later on, it became clear that the calculations [8] contain conceptual errors, that were subsequently corrected in [9]. It worth noting that at the time of carrying out the analysis [1] there was also considerable interest to the LPM effect in QED stimulated by the first high-precision measurement of the effect for the photon emission from electrons at SLAC [13]. The well known approach by Migdal [3] based on the Fokker-Planck approximation has uncertainties that are much bigger than the accuracy achieved in the experiment [13]. Within the approach [1] the Fokker-Planck approximation corresponds to replacement of the exact Green function by the oscillator one. An analysis beyond the oscillator approximation within the formalism [1] carried out in [14, 15] demonstrated agreement with the SLAC data [13] and with the later data from CERN SPS [16] at the level of the radiative corrections. The formalism [1] was the theoretical basis of the well known ASW (Armesto, Salgado and Wiedemann [17]) approach to jet quenching. The formulation in terms of the path integral and diagram technique dealing directly with the probability of the radiative processes given in [1] turns out to be very convenient for the study of the jet modification in the quark-gluon plasma accounting for the multiple gluon emission [18, 19]. This study is of great importance for physics of heavy ion collisions at energies of the RHIC, LHC and future colliders, and is now under active development.
Created by Alexander Prokofiev, 2014-08-26 16:07:02
About the paper "METASTABLE STATES OF 2-DIMENSIONAL ISOTROPIC FERROMAGNETS" A.A.Belavin, A.M.Polyakov JETP LETTERS 22, 245 (1975)
In Alexander Polyakov's and mine paper "Metastable States of 2-Dimensional Isotropic Ferromagnets" [1], we have found metastable states of Heisenberg's ferromagnet. Such states now are called "instatons". The main reason for our search and discovery of such states was a hypothesis that such states would create an infinite correlation length at very low temperatures, obstructing spontaneous symmetry breaking. Later, this hypothesis was proven by calculation of partition function in the model using saddle-point method, taking instantons into account. Actually, there was another reason for the search. The fact is that quantum theory of the field, which describes Heisenberg's 2-dimensional ferromagnet, is in many ways similar to the Yang-Mills theory. In the beginning of 1960s, Gell-Mann has suggested that all elementary particles are made out of quarks. Since the beginning of 1970s, theoretical physicists have begun to assume that theory, which describes quark interaction, is Yang-Mills theory. Experiments that were trying to study proton's structure have confirmed presence of quarks in them, but on the other hand, separately, quarks are not observed. This paradox is called color confinement. As G. 't Hooft has shown [2], quarks will not fly out, if Yang-Mills theory has no spontaneous breaking of local calibration symmetry. In turn, an obstacle for such a breaking would be metastable states, instatons, if they appear in Yang-Mills theory. Such states were later found in our work with Polyakov, Schwartz and Tyupkin [3]. [1] A.A. Belavin, A.M. Polyakov, JETP Letters 22, 245, (1975) [2] G. 't Hooft Nuclear Physics B 33, 173 (1971). [3] А.А. Belavin, А.М. Polyakov, А.S. Schwartz, Yu.S. Tyupkin, Phys.Lett. 59 B ,85 (1975)
Created by I. Podyniglazova, 2014-07-29 10:50:02
The paper "Possibility of Orienting Electron Spins with Current " ( Dyakonov M.I., Perel' V.I. 1971)
The work [1] appeared in the course of theoretical studies in a completely new domain (at the time): the creation and registration of non-equilibrium spin polarization of carriers in semiconductors. This field was opened in 1968 by the pioneering work of Lampel [2] who introduced to solid state physics the ideas and methods of optical orientation and alignment of atomic angular momenta in gases developed by Kastler [3] and his school. Both for atoms and electrons in semiconductors, absorption of circularly polarized light results in orientation of electron spins. Because of this, the luminescence (or recombination radiation) also become circular polarized and this can be easily registered. During the time interval between the creation of spin-polarized electrons and their recombination, the spin might be subject to precession in magnetic field, besides spin relaxation occurs, as well as interesting processes of interaction between the electron spins and the lattice nuclear spins. All such subtle phenomena can be (and actually were) studied by small research groups at A.F. Ioffe Institute in Leningrad and at Ecole Polytechnique in Paris. This paper has predicted a new phenomenon: current induced electron spin orientation, now called Spin Hall Effect, and has introduced for the first time the notion of spin current. The phenomenon is related to the Anomalous Hall Effect in ferromagnets, which was discovered by Hall himself in 1881, remained a mystery during about 70 years, and is not yet fully understood even today. Simply speaking, due to the spin-orbit interaction the flow of spin-up electrons is deviated, say, to the right, while the flow of spin-down electrons is deviated to the left - in full analogy with what happens to a rotating tennis ball (the Magnus effect). In a ferromagnet, the electrons are spin- polarized, thus in the presence of current they will be predominantly deviated sideways, perpendicular to the directions of both current and magnetization, creating a quasi Hall voltage. In a nonmagnetic conductor, the spin polarization is absent, however this "Magnus effect" still exists, though it does not lead to the appearance of a net electric current. Instead, it gives rise to a spin current: spins-up go to the right, while spins-down go to the left. This does not produce any observable effects in the bulk of the conductor, however it leads to spin accumulation at the lateral boundaries. As a result, spin polarization (of opposite signs) should appear at these boundaries. This prediction did not attract much interest at the time (although the so-called "inverse spin Hall effect" was discovered [4]), mainly because experimental means were lacking to measure the relatively weak spin polarization in narrow ($~ 1\mu m$) surface layers. The situation has changed 30 years later, when highly sensitive methods for registration of spin polarization were developed, based on Faraday (or Kerr) rotation. In 2004 the current-induced spin polarization predicted in this paper was observed experimentally for the first time [5]. Since then, hundreds of experimental and theoretical publications were devoted to the spin Hall effect. It was observed not only in semiconductors, but also in metals, at cryogenic as well as at room temperature. See the review chapter [6] for more details. The hopes for practical applications of this phenomenon rely mainly on the possibility of switching magnetic domains by injecting spin currents in ferromagnetic films. [1] Дьяконов М.И, Перель В.И., Письма в ЖЭТФ 13, 206 (1971) [2] G. Lampel, Phys. Rev. Lett. 20, 491 (1968) [3] A. Kastler, Science, 158, 214 (1967) [4] N.S. Averkiev and M.I. Dyakonov, Sov. Phys. Semicond. 17, 393 (1983); A.A. Bakun et al, JETP Lett. 40, 1293 (1984) [5] Y.K. Kato et al, Science 306, 1910 (2004); J. Wunderlich et al., Phys. Rev. Lett. 94, 047204 (2005) [6] M.I. Dyakonov and A.V. Khaetskii, "Spin Hall Effect", in: Spin Physics in Semiconductors, M.I. Dyakonov (ed), Springer, Berlin (2008), p. 211
Created by I. Podyniglazova, 2014-06-27 17:15:02
The paper "Magnetic-flux quantization in a cylindrical film of a normal metal" D.Yu. Sharvin and Yu.V. Sharvin (1981)
The paper [1] is one of the last papers from the time of romantic physics. To have success in experimental investigations at that time, it was necessary to reasonably formulate the aims of the experiment, to be able to use appropriate experimental techniques, and to prepare the object of investigations by one's own hands without using high technology methods.
Created by Alexander Prokofiev, 2014-05-28 18:22:02
The paper "SUPERCONDUCTIVITY WITH LINES OF GAP NODES: DENSITY OF STATES IN THE VORTEX " (G. E. Volovik, 1993)
The paper [1] has been written immediately after the experiments with angle-resolved photoemission (ARPES) on high-$T_c$ material $Bi_2Sr_2CaCu_2O_8$ revealed that the electronic spectrum in this cuprate uperconductor is gapless [2]: there are nodal lines in the spectrum. The problem was, what could be the observable consequences of the gapless spectrum in superconductors. Actually the answer came from the physics of heavy fermionic superconductors with gapless electronic spectrum, which in turn was based on the physics of superfluids, in particular of superfluid $^3He-A$, where fermionic excitations are also gapless. As distinct from superconductors, in superfluids the fermionic quasiparticles, Bogoliubov excitations, are electrically neutral. But otherwise, they have similar properties. If the quasiparticles have a gap, their density of states (DOS) is zero for all energies below the gap, $|E|< \Delta$. If the gap has nodes, the DOS is zero at $E = 0$, but is nonzero for any $|E| > 0$. This means that different perturbations of the energy spectrum may lead to the finite DOS at $E = 0$. In particular this can be caused by the mass current in superfluids, which leads to the Doppler shift of the quasiparticles spectrum.
What happens in the charged electronic liquid in superconductors? In superconductors the applied external magnetic field $B$ gives rise to the lattice of Abrikosov vortices. In each vortex there is the circulating electric The heat capacity, which is linear in $T$ and is proprtional to $ \sqrt B $, has been first observed in Stanford in experiments on $YBa_2Cu_3O_6$ [4]. Now the $\sqrt B$ behavior of DOS serves for identification of line odes in superconductors, and is known as Volovik effect.
1. G. E .Volovik, JETP Lett. 58 , 469 (1993). 2. Z.-X. Shen, et al., Phys. Rev. Lett. 70, 1553 (1993). 3. G E Volovik, J. Phys. C: Solid State Phys. 21 L221 (1988). 4. K. A. Moler, et al., Phys. Rev. Lett. 73, 2744 (1994).
Created by Alexander Prokofiev, 2014-04-22 14:37:02
About the article PARTICLE CONDUCTIVITY IN A TWO-DIMENSIONAL RANDOM POTENTIAL L.P. Gor'kov, A.I. Larkin, D.E. Khmelnitskii JETP LETTERS 30, 228 (1979)
D.E.Khmelnitskii
These are the recollections about the circumstances under which The story begun in late March 1979. The issue of Physical Review Letters with the paper [1] by Abrahams et al appeared in Chernogolovka, and I was able to read it. The paper made a very strong impression. At its four pages, the author painted a broad and universal picture. It is not surprising that their narration contained a number of gaps, which inspired a desire to feel these gaps. Strongly excited, I discussed the issue - separately - with L.P.Gorkov and A.I.Larkin. This finally ended up with our joint paper, the only paper in which L.P. and A.I. were coauthors. After the simplest part - the calculation of the quantum correction to conductivity - had been performed, the question arose what is the next. And Tolya Larkin suggested that we must calculate the contribution to conductivity at low frequency $\omega$, which would be proportional to $\log^2 \omega \tau$. If the Renormalization group conjectured by the authors of Ref [1] are correct, then the coefficient at the front of $\log^2 \omega \tau$ must vanish. The calculation turned out to be lengthy and tedious and took good two months. Finally, after numerous mistakes, I found a missing term, and the whole collection of different contributions collapsed cancelling each other. I showed this to Larkin and convinced him, and Tolya said to Gor'kov. Time of Summer vocations approached, and we decided to write a text of the paper, for which I carefully checked all the coefficients. When I returned from my white-water rafting trip to Sayan Mountains, I discovered that the manuscript of our paper - written a months ago - was brought to Editorial office of JETP Letters at the last week. As Tolya explained to me, Gor'kov was busy. When he got time, he took several pages of clean paper and reproduced all the calculations in order to check the formulae, written in our draft. All the coefficients coincided, and the manuscript went to the typists and further to the Journal. The article begun with the sacral words that the aim of the authors was to understand the validity of the claims made by the authors of Ref [1]. II. Fast Development Development begun for us with the Soviet-American Symposium, hold on 1-21 September 1979 at Sevan Lake in Armenia. This was a response to the similar Symposium hold at Aspen, Colorado in the Summer 1977. American delegation consisted of J.R.Schrieffer, J.Sak, A.Luther, C.Pethick, T.C.Lubensky, P.A.Lee, D.S.Fisher, S.Kirkpatrick, M.J.Stephen, K.Maki, G.Mazenko, J.Hertz, W.F.Brinkman. As for Soviet group, it was much larger and included both the veterans and very young theorists. Among the youngest, one yet PhD students Boris Altshuler from Leningrad was there. Unfortunately, Arkady Aronov could not come. All participants live in an empty Hotel, belonging to the Council of Ministers of Armenia, which was staying just at the Lake shore. Nobody was around. Armenian early autumn - dry and warm - bare hills around and the lake at 2000 meters above sea level, an opportunity of a very informal contacts - all created unique atmosphere, I cannot forget even now, 35 years later. From the conversation - on my very bad English - with Americans, I understood that the results of calculation of the quantum correction to conductivity, reported in our paper, is known to them, although the relevant article [2] was not yet published1. Still, there were no agreement among the American theorists whether the Renormalization group, conjectured by the authors of Ref [1], is valid. The most outspoken was Patrick Lee, who reported at Sevan the results of his numerical studies [3]. Patrick claimed that the results of these calculations demonstrate that the G4-conjecture is wrong2 In light of these doubts, the calculation of the $\log^2$ terms in correction to conductivity and the claim that these terms cancel each other, in agreement with the G4-conjecture, sounded a revelation. Being away from the libraries, we did not know about the paper [4] by Wegner3, in which he conjectured the new Field Theory for Localization - the Non-Linear $\sigma$-Model. It was known for some time, that the models of this kind are renormalizable and the Renormalization group equation coincides with that conjectured by $G4$. Wegner's paper reduced, therefore, the meaning of our efforts to check the validity of $G4$-conjecture to a shire banality. Still, the ability to calculate the quantum correction brought numerous benefits. First of all, it was discovered at Sevan that the quantum correction to conductivity is extremely sensitive to magnetic field. As the result, although the quantum correction is small in comparison with the total value of conductivity, its dependence on magnetic field determines the dependence of the whole conductivity, leading to negative magnetoresistance. This result was later published in the paper [5] co-authored by Boris Altshuler, Patrick Lee, Larkin and me.
Necessity to present the results of the theory to the broad community of experimentalists demanded a different language, which had been developed not immediately. I gave several talks [8] on this subject, in which new qualitative language had been exposed. Qualitative picture turned out to be very useful for theoretical work. I would especially mentioned here our papers[9] with Arkady Aronov and Boris Altshuler about effect of high-frequency electromagnetic field on conductivity and about rate of dephasing of electrons in disordered conductors. In conclusion, the lessons brought by this paper is that, if you have a question you don't know the answer to, try to work out the answer. An immediate result could be not so spectacular. Still, this allows to you to see a broader picture and ask new questions.
Created by Alexander Prokofiev, 2014-03-31 21:52:02
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