Spin- and valley-dependent magnetotransport in periodically modulated silicene

Abstract

The low-energy physics of silicene is described by Dirac fermions with a strong spin-orbit interaction and its band structure can be controlled by an external perpendicular electric field ${E}_{z}$. We investigate the commensurability oscillations in silicene modulated by a weak periodic potential $V={V}_{0}cos(2\ensuremath{\pi}y/{a}_{0})$ with ${a}_{0}$ as its period, in the presence of a perpendicular magnetic field $B$ and of a weak sinusoidal electric field ${E}_{z}={E}_{0}cos(2\ensuremath{\pi}y/{b}_{0})$, where ${b}_{0}$ is its period. We show that the spin and valley degeneracy of the Landau levels is lifted, due to the modulation, and that the interplay between the strong spin-orbit interaction and the potential and electric field modulations can result in spin- and valley-resolved magnetotransport. At very weak magnetic fields the commensurability oscillations induced by a weak potential modulation can exhibit a beating pattern depending on the strength of the homogenous electric field ${E}_{z}$ but this is not the case when only ${E}_{z}$ is modulated. The Hall conductivity plateaus acquire a step structure, due to spin and valley intra-Landau-level transitions, that is absent in unmodulated silicene. The results are critically contrasted with those for graphene and the two-dimensional electron gas.