Anomalous Edge Transport in the Quantum Anomalous Hall State

TL;DR

This paper predicts the coexistence of chiral and non-chiral edge states in magnetic topological insulator thin films, explaining dissipative transport in the quantum anomalous Hall state and proposing experiments to detect these states.

Contribution

It introduces the presence of gapless non-chiral edge states coexisting with chiral states in Cr-doped (Bi,Sb)$_2$Te$_3$ films, advancing understanding of dissipative QAH transport.

Findings

Non-chiral edge states coexist with chiral states in the system.

Longitudinal resistance is nonzero but Hall resistance remains quantized.

Adding a floating probe reduces longitudinal resistance without affecting Hall quantization.

Abstract

We predict by first-principles calculations that thin films of Cr-doped (Bi,Sb)$_2$Te$_3$ magnetic topological insulator have gapless non-chiral edge states coexisting with the chiral edge state. Such gapless non-chiral states are not immune to backscattering, which would explain dissipative transport in the quantum anomalous Hall (QAH) state observed in this system experimentally. Here we study the edge transport with both chiral and non-chiral states by Landaur-B\"{u}ttiker formalism, and find that the longitudinal resistance is nonzero whereas Hall resistance is quantized to $h/e^2$. In particular, the longitudinal resistance can be greatly reduced by adding an extra floating probe even if it is not used, while the Hall resistance remains at the quantized value. We propose several transport experiments to detect the dissipative non-chiral edge channels. These results will facilitate the realization of pure dissipationless transport of QAH states in magnetic topological insulators.