The classic Thouless-Kohmoto-Nightingale-Nijs theorem dictates that a single electron band of a lattice can only harbor an integer quantum Hall conductance as a multiple of $e^2/h$, while recent studies have pointed to the emergence of half-quantum anomalous Hall (HQAH) effect, though the underlying microscopic mechanisms remain controversial. Here we propose an ideal platform of $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4/{\mathrm{Sb}}_2{\mathrm{Te}}_3$ that allows one to not only realize the HQAH effect at much higher temperatures, but also to critically assess the different contributions of the gapped and gapless Dirac bands. We first show that the top surface bands of the ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ film become gapped, while the bottom surface bands remain gapless due to proximity coupling with the $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$ overlayer. Next we show that such a semimagnetic topological insulator harbors the HQAH effect at ∼20 K, with Cr doping enhancing it to as high as 67 K, driven by large magnetic anisotropy and strong magnetic coupling constants that raise the Curie temperature. Our detailed Berry curvature analysis further helps to reveal that, although the gapped surface bands can contribute to the Hall conductance when the chemical potential is tuned to overlap with the bands, these bands have no net contribution when the chemical potential is in the gapped region, leaving the gapless bands to be the sole contributor to the HQAH conductance. Counterintuitively, the part of the gapless bands within the gapped region of the top surface bands has no net contribution, thereby ensuring the plateau nature of the Hall conductance.

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• Anomalous Hall effect
• Magnetic anisotropy
• Quantum transport
• Topological insulators
• Ferromagnets
• Heterostructures
• Topological materials
• Density functional theory
• Wannier function methods