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

TL;DR

This paper investigates the quantum Hall effects in graphene with multiple orbitals, calculating topological invariants and conductance, and compares quantum and semi-classical approaches for different magnetic field regimes.

Contribution

It provides a detailed analysis of the topological and semi-classical descriptions of Hall conductance in multi-orbital graphene, including modifications for Dirac fermion regimes.

Findings

Hall conductance matches semi-classical results at low magnetic fields.

Boltzmann theory explains overall Hall resistivity behavior for single-band Fermi surfaces.

Semi-classical quantization accounts for Hall plateaux, with modifications for Dirac regimes.

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.