Unveiling the chirality of the quantum anomalous Hall effect

The ordinary and quantum Hall effects with fixed carrier types, electron or hole, exhibit well-defined chirality under external magnetic fields, but the analogous chirality of the quantum anomalous Hall effect (QAHE) remains little explored. Here, for the electronic structures of intrinsic QAHE systems, we show that the local Berry curvature is linked with the angular-momentum difference ${l}_{\ensuremath{\delta}z}$ of the inverted bands. In the presence of rotation symmetries, the value of ${l}_{\ensuremath{\delta}z}$ will be quantized and set as the Chern number. The quantized ${l}_{\ensuremath{\delta}z}$ will also give rise to a unique quantized magnetic circular dichroism effect in the case of resonance absorption. By ${l}_{\ensuremath{\delta}z}$, we find that the chiral flow-direction of an electron in the QAHE is not explicitly related to the intrinsic spin axis, thereby enabling the spin-momentum-unlocking edge states in an antiferromagnetic QAHE system. The validity of our theory is confirmed through rigorous examinations using perturbation theory, $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ modeling, tight-binding modeling, and first-principle calculations, which predicts exotic behavior in experimentally accessible quantum materials.