Chiral edge state coupling theory of transport in quantum anomalous Hall insulators

TL;DR

This paper introduces a theory explaining the discrepancy between quantized Hall resistance and non-quantized Hall conductance in quantum anomalous Hall insulators by considering chiral edge state coupling, aligning well with experimental observations.

Contribution

It proposes a novel chiral edge state coupling theory that accounts for experimental anomalies in quantum anomalous Hall insulators, which previous models did not fully explain.

Findings

Chiral edge state coupling hinders Hall conductance quantization.

The theory explains the universal exponential decay of longitudinal resistance.

Results align with experiments in magnetic topological insulators and moiré superlattices.

Abstract

Theoretically, the quantum anomalous Hall effect is characterized by a quantized Hall conductance. However, many experiments only reported the quantization of the Hall resistance, which is accompanied by a non-vanishing longitudinal resistance, resulting in a non-quantized Hall conductance. Meanwhile, the non-vanishing longitudinal resistance features a universal exponential decay with the increase in magnetic field. Such a discrepancy obviously challenges the understanding of the quantum anomalous Hall effect. To this end, we propose that the coupling of chiral edge states, which has not been properly evaluated in the previous theories, hinders the quantization of the Hall conductance, while it maintains the quantization of the Hall resistance. The coupling between the chiral edges states along the opposite boundaries can be assisted by magnetic domains or defects inside the sample bulk, which has been already identified in recent experiments. We demonstrate that the chiral edge state coupling theory works rather well to explain the experimental results in both magnetic topological insulator and moir\'e superlattice systems.