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

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

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