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 $V=V_{0}cos(2\pi y/a_0)$ with $a_0$ as its period, in the presence of a perpendicular magnetic field $B$ and of a weak sinusoidal electric field $E_z=E_{0}cos(2\pi y/b_0)$, 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.

• Received 16 May 2014
• Revised 3 September 2014

DOI:https://doi.org/10.1103/PhysRevB.90.125444