Valley-dependent damping of Zitterbewegung in 2D structures based on Dirac crystals

The theory of increasing of the zitterbewegung duration by controlling of the mutual positions between the electron wave packet center and the valley in the band structure of the Dirac crystal is suggested. The Gaussian type of the electron wave packets is considered. The time of the zitterbewegung damping is shown to be increased by several orders as compared with that of massless Dirac electron if the wave packet is centered at the energy minimum or maximum of the dispersion law. To this end the different kinds of modifications of Dirac crystals such as semi-Dirac crystals, graphene with merging Dirac points and graphene superlattices are suggested to be used. In details the valley-dependent zitterbewegung in ac-driven Dirac crystals is studied. An increase in the duration of the zitterbewegung with the change of the ac-field power is explicitly demonstrated.