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

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

2008-10-14

arxiv.org/abs/0810.2377v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

5pages, 3figures

Scientific paper

10.1103/PhysRevB.79.075429

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

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