Parity and time-reversal anomaly in a semiconductor

The physics of a parity anomaly, potentially observable in a narrow-gap semiconductor, is revisited. Fradkin, Dagotto, and Boyanovsky have suggested [Phys. Rev. Lett. 57, 2967 (1986)] that a Hall current of anomalous parity can be induced by a Peierls distortion on a domain wall. I argue that a perturbation inducing the parity anomaly must break the time-reversal symmetry, which rules out the Peierls distortion as a potential cause. I list all possible perturbations that can generate the anomaly.