Abstract
We investigate emergent Dirac fermions and topological phases in magnetic topological insulator (TI) films. By presenting an exact lattice solution for a TI film, we show that its low‑energy physics is fully captured by a pair of gapless Dirac fermions accompanied by gapped bulk modes. For a mirror‑symmetric film, we find that the two gapless fermions carry opposite half‑integer topological invariants, leading to a half‑quantized Z₂ phase—the half‑quantum mirror Hall effect (HQMHE). Upon introducing magnetism, our unified framework not only reproduces the known quantum anomalous Hall, axion insulator, and half‑quantum Hall effects, but also predicts a new metallic quantized anomalous Hall phase (MQAHE) with quantized conductance but no chiral edge modes.
Collaborated with first‑principles calculations, we demonstrate the half‑quantum Hall effect in MnBi₂Te₄/Sb₂Te₃ heterostructures at elevated temperatures. We also study antiferromagnetic polar-stacking bilayer MnBi₂Te₄, for which we propose a minimal model describing its ferroelectricity. Remarkably, when proximitized with an s‑wave superconductor, the system hosts a single Majorana zero mode (MZM) at the boundary, with its chirality controlled by ferroelectric polarization—offering a controllable platform for topological quantum computation. Our work advances the understanding of symmetry‑topology interplay and paves the way for future quantum devices.
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