Coexistence of Quantum Hall and Quantum Anomalous Hall Phases in Disordered MnBi_{2}Te_{4}

In most cases, to observe quantized Hall plateaus, an external magnetic field is applied in intrinsic magnetic topological insulators MnBi_{2}Te_{4}. Nevertheless, whether the nonzero Chern number (C≠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)SCIEAS0036-807510.1126/science.aax8156]. In this Letter, we propose a physical picture based on the Anderson localization to understand the observed Hall plateaus in disordered MnBi_{2}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 MnBi_{2}Te_{4} which indicates more coexistence states of QAH and QH to be verified by future experiments.