$\textit{Zitterbewegung}$ near new Dirac points in graphene superlattice

Abstract

New Dirac points appear when periodic potentials are applied to graphene, and there are many interesting effects near these new Dirac points. Here we investigate the $\textit{Zitterbewegung}$ effect of fermions described by a Gaussian wave packet in graphene superlattice near new Dirac points. The $\textit{Zitterbewegung}$ near different Dirac points has similar characteristics, while Fermions near new Dirac points have different group velocities in both $x$- and $y$-direction, which causes the different properties of the $\textit{Zitterbewegung}$ near new Dirac points. We also investigate the $\textit{Zitterbewegung}$ effect influenced by all Dirac points, and get the evolution with changing potential. Our intensive results suggest that graphene superlattice may provide an appropriate system to study $\textit{Zitterbewegung}$ effect near new Dirac points experimentally.