Nature of electron Zitterbewegung in crystalline solids

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. We show that the two-band 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 unambiguously indicate that the trembling motion is the basic way of electron propagation in periodic potentials and, as such, it is certainly observable. A recent experimental simulation of ZB with the use of trapped ions is in good agreement with our calculations.