Numerical study of quantum Hall effect in two-dimensional multi-band system: single- and multi-layer graphene

TL;DR

This paper numerically investigates the quantum Hall effect in single- and multi-layer graphene, analyzing Chern numbers and quantized Hall conductance across energy ranges, including effects at van-Hove singularities.

Contribution

It provides a detailed numerical analysis of Chern numbers and Hall conductance in multi-band graphene systems, highlighting behavior at singularities and in various energy regimes.

Findings

Quantized Hall conductance occurs across the entire energy range.

Large jumps in Chern numbers at van-Hove singularities.

Discussion of Hall plateaux from semi-classical quantization.

Abstract

The Chern numbers which correspond to quantized Hall conductance $\sigma_{xy}$ were calculated for single- and bi-layer honeycomb lattices. The quantization of $\sigma_{xy}$ occurs in entire energy range. Several large jumps of Chern numbers appear at van-Hove singularities of energy bands without magnetic fields. The plateauxof $\sigma_{xy}$ are discussed from semi-classical quantization.