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Quantum Hall effects of graphene with multi orbitals: Topological numbers, Boltzmann conductance and Semi-classical quantization

Abstract

Hall conductance σxy\sigma_{xy} 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\sigma_{xy} coincides with a semi-classical result when magnetic field is sufficiently small. The Hall resistivity ρxy\rho_{xy} from the weak-field Boltzmann theory also explains the overall behaviour of the σxy\sigma_{xy} if the Fermi surface is composed of a single energy band. The plateaux of σxy\sigma_{xy} are explained from semi-classical quantization and necessary modification is proposed for the Dirac fermion regimes.Comment: 5pages, 3figure

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