Zitterbewegung of nearly-free and tightly bound electrons in solids

Abstract

We show theoretically that nonrelativistic nearly-free electrons in solids should experience a trembling motion (Zitterbewegung, ZB) in absence of external fields, similarly to relativistic electrons in vacuum. The Zitterbewegung is directly related to the influence of periodic potential on the free electron motion. The frequency of ZB is $\omega \approx E_g/\hslash$, where $E_g$ is the energy gap. The amplitude of ZB is determined by the strength of periodic potential and the lattice period and it can be of the order of nanometers. We show that the amplitude of ZB does not depend much on the width of the wave packet representing an electron in real space. An analogue of the Foldy-Wouthuysen transformation, known from relativistic quantum mechanics, is introduced in order to decouple electron states in various bands. We demonstrate that, after the bands are decoupled, electrons should be treated as particles of a finite size. In contrast to nearly-free electrons we consider a two-band model of tightly bound electrons. We show that also in this case the electrons should experience the trembling motion. It is concluded that the phenomenon of Zitterbewegung of electrons in crystalline solids is a rule rather than an exception.

22 pages, 6 figures Published version, minor changes made

References in corpus (2)

• Zitterbewegung of electronic wave packets in semiconductor nanostructures
• Unified description of the Zitterbewegung for spintronic, graphene and superconducting systems

Cited by in corpus (11)

• Extremal transmission and beating effect of acoustic wave in two-dimensional sonic crystal
• Transient Zitterbewegung of charge carriers in graphene and carbon nanotubes
• Zitterbewegung (trembling motion) of electrons in semiconductors: a Review
• Wave packet dynamics in a monolayer graphene
• Cyclotron motion in graphene
• Magnetic focusing of charge carriers from spin-split bands: Semiclassics of a Zitterbewegung effect
• Cyclotron motion and magnetic focusing in semiconductor quantum wells with spin-orbit coupling
• Zitterbewegung of moiré excitons in twisted MoS${}_2$/WSe${}_2$ hetero-bilayers
• Effect of zitterbewegung on the propagation of wave packets in ABC-stacked multilayer graphene: an analytical and computational approach
• Revealing inherent quantum interference and entanglement of a Dirac particle
• Current Density of Majorana Bound States