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

Abstract

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.

5pages, 3figures

References in corpus (5)

• Unconventional Integer Quantum Hall effect in graphene
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Quantum Hall Effect of Dirac Fermions in Graphene: Disorder Effect and Phase Diagram
• Chiral two-dimensional electron gas in a periodic magnetic field
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• Orbital Hall Effect Accompanying Quantum Hall Effect: Landau Levels Cause Orbital Polarized Edge Currents
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• Magnon Landau Levels and Spin Responses in Antiferromagnets
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• Numerical study of quantum Hall effect in two-dimensional multi-band system: single- and multi-layer graphene