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Register a new userCoexisting of Quantum Hall and Quantum Anomalous Hall phases in Disordered $mathrm{MnBi_2Te_4}$
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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 ($C eq 0$) 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.
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