Landau Levels and Quantum Hall Effect in Graphene Superlattices

We show that, when graphene is subjected to an appropriate one-dimensional external periodic potential, additional branches of massless fermions are generated with nearly the same electron-hole crossing energy as that at the original Dirac point of graphene. Because of these new zero-energy branches, the Landau levels at charge neutral filling become $4(2N+1)$-fold degenerate (with $N=0,1,2,\dots$, tunable by the potential strength and periodicity) with the corresponding Hall conductivity ${\sigma }_{xy}$ showing a step of size $4(2N+1)e^2/h$. These theoretical findings are robust against variations in the details of the external potential and provide measurable signatures of the unusual electronic structure of graphene superlattices.