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, ..., 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.