Mirror anomaly in Dirac semimetals

We demonstrate that, apart from the chiral anomaly, Dirac semimetals possess another quantum anomaly, which we call mirror anomaly, and which manifests in a singular response of the Dirac semimetal to an applied magnetic field. Namely, the anomalous Hall conductivity exhibits step-function singularities when the field is rotated. We show that this behavior may be understood as quantum mechanical violation of the mirror symmetry, which emerges near any Dirac point at a time reversal invariant momentum.