Survival of the quantum anomalous Hall effect in orbital magnetic fields as a consequence of the parity anomaly
2019
Recent experimental progress in condensed matter physics gives the prospect to observe the parity anomaly in two-dimensional Dirac-like materials. Using effective field theories and analyzing band structures in external out-of-plane magnetic fields (orbital fields), we show that topological properties of quantum anomalous Hall (QAH) insulators are related to the parity anomaly. We demonstrate that the QAH phase survives in orbital fields, violates Onsager relations, and can be therefore distinguished from a quantum Hall (QH) phase. As a fingerprint of the QAH phase in increasing orbital fields, we predict a transition from a quantized Hall plateau with $\sigma_\mathrm{xy}= -\mathrm{e}^2/\mathrm{h}$ to a not perfectly quantized plateau, caused by scattering processes between counterpropagating QH and QAH edge states. This transition could be especially important in paramagnetic QAH insulators, such as $\mathrm{Hg}_{1-y}\mathrm{Mn}_y\mathrm{Te}$/CdTe quantum wells, where exchange interaction and orbital fields compete.
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