At the birth of quantum mechanics, E. Schrödinger realized that a free relativistic electron, described by the Dirac Hamiltonian, exhibits oscillations in space resulting from the interference of the positive and the negative-energy solutions of the Dirac equation [1]. Recently, it was suggested that Zitterbewegung is not limited to free electrons but is a common feature of systems with a gapped or level-split spectrum exhibiting a formal similarity to the Dirac Hamiltonian [2]. Here, we study the motion of electrons in a semiconductor system with spin-orbit coupling and the Zeeman gap opened by an external magnetic field. It is shown that, in addition to the well-known Brownian motion, electrons experience an inherent trembling motion of quantum-mechanical nature. The effect originates from the fact that the electron velocity is not a conserved quantity and contains an oscillating contribution. The Zitterbewegung occurs for all the electrons, also for electrons in thermal equilibrium. Experimental study of the electron Zitterbewegung in such conditions requires the use of noise spectroscopy. We show that the Zitterbewegung of individual electrons can be phase-synchronized by initializing the electrons in the same spin state. In this case, the coherent precession of the individual electron spins drives their back-and-forth motion in real space giving rise to a macroscopic high-frequency electric current. Such a coherent Zitterbewegung is maintained as long as the coherent spin precession of the electrons is not destroyed by the processes of spin dephasing. We develop a theory of the coherent Zitterwebegung for the cases of ballistic and diffusive electron transport, predict its enhancement at the plasmon resonance conditions, and discuss its relation to the spin-galvanic effect [3,4].

[1] E. Schrödinger, Über die kräftefreie Bewegung in der relativistischen Quantenmechanik, Sitz. Press. Akad. Wiss.Phys.-Math. 24, 418 (1930).

[2] W. Zawadzki and T. M. Rusin, Zitterbewegung (trembling motion) of electrons in semiconductors: a review, J. Phys.: Condens. Matter 23, 143201 (2011).

[3] E.L. Ivchenko, Yu.B. Lyanda-Geller, and G.E. Pikus, Current of thermalized spin-oriented photocarriers, Sov. Phys. JETP 71, 550 (1990).

[4] S.D. Ganichev, E.L. Ivchenko, V.V. Bel’kov, S.A. Tarasenko, M. Sollinger, D. Weiss, W. Wegscheider, and W. Prettl, Spin-galvanic effect, Nature 417, 153 (2002).

S. A. Tarasenko, A. V. Poshakinskiy, E. L. Ivchenko, I. Stepanov,

M. Ersfeld, M. Lepsa, and B. Beschoten

JETP Letters 108, issue 5 (2018)