Quantized Anomalous Hall Effect in Two-Dimensional Ferromagnets - Quantum Hall Effect from Metal -

TL;DR

This paper demonstrates that in two-dimensional ferromagnets, the anomalous Hall effect can become quantized due to disorder-induced localization, extending the quantum Hall effect to metallic systems without a magnetic field.

Contribution

It shows that Pruisken's two-parameter scaling theory applies to disordered metallic ferromagnets, establishing conditions for quantized anomalous Hall effect without a gap.

Findings

Quantized AHE occurs in disordered 2D ferromagnets.

Pruisken's scaling theory applies beyond gapped systems.

Quantization depends on Hall conductivity magnitude.

Abstract

We study the effect of disorder on the anomalous Hall effect (AHE) in two-dimensional ferromagnets. The topological nature of AHE leads to the integer quantum Hall effect from a metal, i.e., the quantization of $\sigma_{xy}$ induced by the localization except for the few extended states carrying Chern number. Extensive numerical study on a model reveals that Pruisken's two-parameter scaling theory holds even when the system has no gap with the overlapping multibands and without the uniform magnetic field. Therefore the condition for the quantized AHE is given only by the Hall conductivity $\sigma_{xy}$ without the quantum correction, i.e., $|\sigma_{xy}| > e^2/(2h)$.