Quantum Hall effects of graphene with multiorbitals: Topological numbers, Boltzmann conductance, and semiclassical quantization

Abstract

Hall conductance σxy as the Chern numbers of the Berry connection in the magnetic Brillouin zone is calculated for a realistic multi band tight-band model of graphene with non-orthogonal basis. It is confirmed that the envelope of σxy coincides with a semi-classical result when magnetic field is sufficiently small. The Hall resistivity ρxy from the weak-field Boltzmann theory also explains the overall behaviour of the σxy if the Fermi surface is composed of a single energy band. The plateaux of σxy are explained from semi-classical quantization and necessary modification is proposed for the Dirac fermion regimes