Abstract
The intrinsic anomalous Hall conductance of a minimal model of the twodimensional disordered Chern insulator is investigated in the framework of Kubo quantum theory of linear response. The electron momentum relaxation is assumed to be due to electron scattering by Gaussian white-noise potential. The explicit expressions for the density of states and are obtained in the self-consistent Born approximation. The numerical analysis of these expressions at the different values of parameters of the considered model shows that calculated takes a quantized value e2/4πħ when the Fermi level lies within the energy gap. This gap is narrowed as disorder increases that leads to decreasing of the Hall plateau width.
Highlights
In the last years, a widespread interest was attracted to investigation of the quantum anomalousHall effect (QAHE) in the topological nontrivial materials [1,2,3]
The numerical analysis of these expressions at the different values of parameters of the considered model shows that calculated σxinyt takes a quantized value e2/4π when the Fermi level lies within the energy gap
As can be seen from this figure, the quantization of the anomalous Hall conductance is protected against perturbation due to disorder, if the Fermi level lies within the energy gap
Summary
A widespread interest was attracted to investigation of the quantum anomalousHall effect (QAHE) in the topological nontrivial materials [1,2,3]. The numerical analysis of these expressions at the different values of parameters of the considered model shows that calculated σxinyt takes a quantized value e2/4π when the Fermi level lies within the energy gap. This effect was first discovered experimentally by Chang with coworkers [9] in the thin films of the bismuth based topological insulator doped by Cr. According to [5] the anomalous Hall conductance σxy of a two-dimensional magnetic topological insulator takes quantized value, when the Fermi level lies within the gap between the bulk energy bands.
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