The quantum anomalous Hall (QAH) effect has recently been realized in thin films of intrinsic magnetic topological insulators (IMTIs) like $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$. Here we point out 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 Schrödinger-Poisson self-consistent-field equations.

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• Quantum anomalous Hall effect
• Topological insulators
• Density functional theory
• k dot p method