Evolution of Berry curvature and reentrant quantum anomalous Hall effect in an intrinsic magnetic topological insulator

Recently, the magnetic topological insulator MnBi$_2$Te$_4$ emerged as a competitive platform to realize quantum anomalous Hall (QAH) states. We report a Berry-curvature splitting mechanism to realize the QAH effect in the disordered magnetic TI multilayers when switching from an antiferromagnetic order to a ferromagnetic order. We reveal that the splitting of spin-resolved Berry curvature, originating from the separation of the mobility edge during the magnetic switching, can give rise to a QAH insulator even \emph{without} closing the band gap. We present a global phase diagram, and also provide a phenomenological picture to elucidate the Berry curvature splitting mechanism by the evolution of topological charges. At last, we predict that the Berry curvature splitting mechanism will lead to a reentrant QAH effect, which can be detected by tuning gate voltage. Our theory will be instructive for the studies of the QAH effect in MnBi$_2$Te$_4$ in future experiments.