Recent experimental progress in condensed matter physics enables the observation of signatures of 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 the Onsager relation, 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 σxy = −e 2 /h to a not perfectly quantized plateau, caused by scattering processes between counterpropagating QH and QAH edge states. This transition can be especially important in paramagnetic QAH insulators, such as (Hg,Mn)Te/CdTe quantum wells, in which exchange interaction and orbital fields compete.
The breaking of parity and time-reversal symmetry in two-dimensional Fermi liquids gives rise to non-dissipative transport features characterized by the Hall viscosity. In magnetic fields, the Hall viscous force directly competes with the Lorentz force, since both mechanisms contribute to the Hall voltage. In this work, we present a channel geometry that allows us to uniquely distinguish these two contributions and derive, for the first time, their functional dependency on all external parameters. We show that the ratio of the Hall viscous to the Lorentz force contribution is negative and that its modulus decreases with increasing width, slip-length and carrier density, while it increases with the electron-electron mean free path of our channel. In typical materials such as GaAs the Hall viscous contribution can dominate the Lorentz signal up to a few tens of millitesla until the total Hall voltage vanishes and subsequently is overcome by the Lorentz contribution. Moreover, we prove that the total Hall electric field is parabolic due to Lorentz effects, whereas the offset of this parabola is characterized by the Hall viscosity. Hence, our results pave the way to measure and identify the Hall viscosity via both global and local voltage measurements. arXiv:1905.03269v3 [cond-mat.mes-hall]
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