Electron dynamics in graphene with spin-orbit couplings and periodic potentials

Ranjani Seshadri, Diptiman Sen

Published 2016-07-20Version 1

We use both lattice and continuum models to study the energy-momentum dispersion and the dynamics of a wave packet for an electron moving in graphene in the presence of spin-orbit couplings and either a single potential barrier or a periodic array of potential barriers. Both Kane-Mele and Rashba spin-orbit couplings are considered. In the presence of a single potential barrier, we show that there are states localized along the barrier. When the Kane-Mele and Rashba couplings are equal in magnitude, we find that the dispersion consists of both massless Dirac and massive Dirac states. The two kinds of states respond differently to a potential barrier; the massless states Klein tunnel through the barrier at normal incidence while the massive states reflect from it. A periodic potential is known to generate additional Dirac points; we show that spin-orbit couplings generally open gaps at those points. Finally, we study the time evolution of a wave packet in the presence of a periodic potential. We discover special points in momentum space where there is almost no spreading of a wave packet; there are six such points in graphene when the spin-orbit couplings are absent.