Gate-Tunable Quantum Anomalous Hall Effects in MnBi$_2$Te$_4$ Thin Films

The quantum anomalous Hall (QAH) effect has recently been realized in thin films of intrinsic magnetic topological insulators (IMTIs) like MnBi$_2$Te$_4$. Here we point out that that the QAH gaps of these IMTIs can be optimized, and that both axion insulator/semimetal and Chern insulator/semimetal transitions can be driven by electrical gate fields on the $\sim 10$ meV/nm scale. This effect is described by combining a simplified coupled-Dirac-cone model of multilayer thin films with Schr{\"o}dinger-Poisson self-consistent-field equations.