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

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