Coexisting of Quantum Hall and Quantum Anomalous Hall phases in Disordered $\mathrm{MnBi_2Te_4}$

TL;DR

This paper explains the coexistence of quantum Hall and quantum anomalous Hall phases in disordered MnBi2Te4 using Anderson localization, supported by experimental and numerical results, and presents a phase diagram predicting multiple coexistence states.

Contribution

It introduces a physical picture based on Anderson localization to understand Hall plateaux in disordered MnBi2Te4, clarifying the nature of observed C=2 phases and predicting multiple coexistence states.

Findings

Bulk states are localized without magnetic field.

A QAH edge state with C=1 emerges in the absence of magnetic field.

A C=2 phase results from the coexistence of localized bulk states and QAH edge states under strong magnetic field.

Abstract

In most cases, to observe quantized Hall plateaux, an external magnetic field is applied in intrinsic magnetic topological insulators $\mathrm{MnBi_2Te_4}$. Nevertheless, whether the nonzero Chern number ($C\neq 0$) phase is a quantum anomalous Hall (QAH) state, or a quantum Hall (QH) state, or a mixing state of both is still a puzzle, especially for the recently observed $C=2$ phase [Deng \textit{et al}., Science \textbf{367}, 895 (2020)]. In this Letter, we propose a physical picture based on the Anderson localization to understand the observed Hall plateaux in disordered $\mathrm{MnBi_2Te_4}$. Rather good consistency between the experimental and numerical results confirms that the bulk states are localized in the absence of a magnetic field and a QAH edge state emerges with $C=1$. However, under a strong magnetic field, the lowest Landau band formed with the localized bulk states, survives disorder, together with the QAH edge state, leading to a $C=2$ phase. Eventually, we present a phase diagram of a disordered $\mathrm{MnBi_2Te_4}$ which indicates more coexistence states of QAH and QH to be verified by future experiments.