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Recently, the magnetic topological insulator MnBi$_2$Te$_4$ emerged as acompetitive platform to realize quantum anomalous Hall (QAH) states. We reporta Berry-curvature splitting mechanism to realize the QAH effect in thedisordered magnetic TI multilayers when switching from an antiferromagneticorder to a ferromagnetic order. We reveal that the splitting of spin-resolvedBerry curvature, originating from the separation of the mobility edge duringthe 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 aphenomenological picture to elucidate the Berry curvature splitting mechanismby the evolution of topological charges. At last, we predict that the Berrycurvature splitting mechanism will lead to a reentrant QAH effect, which can bedetected by tuning gate voltage. Our theory will be instructive for the studiesof the QAH effect in MnBi$_2$Te$_4$ in future experiments.

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