Landau levels and quantum hall effect in graphene superlattices

Abstract

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,..., tunable by the potential strength and periodicity) with the corresponding Hall conductivity σxy showing a step of size 4(2N+1)e2/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. © 2009 The American Physical Society.