Zitterbewegung (trembling motion) of electrons in narrow-gap semiconductors

The theory of trembling motion (Zitterbewegung (ZB)) of charge carriers in various narrow-gap materials is reviewed. Nearly free electrons in a periodic potential, InSb-type semiconductors, bilayer graphene, monolayer graphene and carbon nanotubes are considered. General features of ZB are emphasized. It is shown that, when the charge carriers are prepared in the form of Gaussian wavepackets, ZB has a transient character with a decay time of femtoseconds in graphene and picoseconds in nanotubes. Zitterbewegung of electrons in graphene in the presence of an external magnetic field is mentioned. A similarity of ZB in semiconductors to that of relativistic electrons in a vacuum is stressed. Possible ways of observing trembling motion in solids are mentioned.