In most cases, to observe quantized Hall plateaus, an external magnetic field is applied in intrinsic magnetic topological insulators ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. Nevertheless, whether the nonzero Chern number ($C\ne 0$) 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 et al., Science 367, 895 (2020)]. In this Letter, we propose a physical picture based on the Anderson localization to understand the observed Hall plateaus in disordered ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. 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 ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ which indicates more coexistence states of QAH and QH to be verified by future experiments.

中文翻译：

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无序MnBi2Te4中量子霍尔相和量子反常霍尔相的共存

在大多数情况下，为了观察量化霍尔平台，在本征磁拓扑绝缘体中施加外部磁场 ${\mathrm{锰铋}}_2{特}_4$. 尽管如此，无论是非零陈数（$C\ne 0$) 相是量子反常霍尔 (QAH) 态，还是量子霍尔 (QH) 态，或两者的混合态仍然是一个谜，尤其是对于最近观察到的 $C=2$阶段 [Deng et al. ,科学 367 , 895 (2020)]。在这封信中，我们提出了一个基于安德森定域的物理图片，以了解观察到的无序霍尔高原${\mathrm{锰铋}}_2{特}_4$. 实验和数值结果之间相当好的一致性证实，体态在没有磁场的情况下是局部的，并且 QAH 边缘态出现在$C=1$. 然而，在强磁场下，由局部体态形成的最低朗道带与 QAH 边缘态一起在无序中幸存下来，导致$C=2$阶段。最后，我们展示了一个无序的相图${\mathrm{锰铋}}_2{特}_4$ 这表明 QAH 和 QH 的更多共存状态有待未来实验验证。