Nature of electron Zitterbewegung in crystalline solids

TL;DR

This paper clarifies that electron Zitterbewegung in crystalline solids is a velocity oscillation ensuring energy conservation, differing from relativistic electrons, and shows it can be observed experimentally using the two-band k.p model.

Contribution

It provides a classical and quantum mechanical analysis of electron Zitterbewegung in solids, revealing its true nature and demonstrating its observability, contrasting with previous relativistic interpretations.

Findings

Electron Zitterbewegung is velocity oscillation conserving energy.

Two-band k.p model accurately describes ZB in solids.

ZB in solids is experimentally observable.

Abstract

We demonstrate both classically and quantum mechanically that the Zitterbewegung (ZB, the trembling motion) of electrons in crystalline solids is nothing else, but oscillations of velocity assuring the energy conservation when the electron moves in a periodic potential. This means that the nature of electron ZB in a solid is completely different from that of relativistic electrons in a vacuum, as proposed by Schrodinger. Still, we show that the two-band {\bf k.p} model of electronic band structure, formally similar to the Dirac equation for electrons in a vacuum, gives a very good description of ZB in solids. Our results indicate unambiguously that the trembling motion of electrons in solids should be observable.