Mirror Anomaly in Dirac Semimetals

TL;DR

This paper uncovers a new mirror anomaly in Dirac semimetals, showing a singular response in Hall conductivity to magnetic field rotation, analogous to the parity anomaly but related to mirror symmetry.

Contribution

It introduces the concept of mirror anomaly in Dirac semimetals and links it to mirror symmetry near Dirac points, expanding understanding of quantum anomalies in these materials.

Findings

Hall conductivity exhibits step-function singularities with magnetic field rotation

Mirror anomaly is analogous to the parity anomaly in (2+1)D Dirac fermions

Mirror symmetry replaces parity symmetry near Dirac points

Abstract

We demonstrate that, apart from the chiral anomaly, Dirac semimetals possess another quantum anomaly, which we call the 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 phenomenon is closely analogous to the parity anomaly of (2+1)-dimensional Dirac fermions, but with mirror symmetry, which we demonstrate emerges near any Dirac point at a time reversal invariant momentum, replacing the parity symmetry.