Mirror anomaly and anomalous Hall effect in type-I Dirac semimetals

TL;DR

This paper investigates the presence of mirror anomaly and anomalous Hall effect in type-I Dirac semimetals, finding that unlike type-II, they do not exhibit a singular Hall response at mirror symmetry, and the response can vanish under certain conditions.

Contribution

It clarifies that type-I Dirac semimetals lack the mirror anomaly in anomalous Hall response, contrasting with type-II, and explores conditions under which the Hall response vanishes.

Findings

Type-I Dirac semimetals do not exhibit a singular Hall response at mirror symmetry.

The anomalous Hall response in type-I semimetals approaches zero near mirror-symmetric angles.

Under certain conditions, the Hall response can vanish even with broken time-reversal symmetry.

Abstract

In addition to the well known chiral anomaly, Dirac semimetals have been argued to exhibit mirror anomaly, close analogue to the parity anomaly of ($2+1$)-dimensional massive Dirac fermions. The observable response of such anomaly is manifested in a singular step-like anomalous Hall response across the mirror-symmetric plane in the presence of a magnetic field. Although this result seems to be valid in type-II Dirac semimetals (strictly speaking, in the linearized theory), we find that type-I Dirac semimetals do not possess such an anomaly in anomalous Hall response even at the level of the linearized theory. In particular, we show that the anomalous Hall response continuously approaches zero as one approaches the mirror symmetric angle in a type-I Dirac semimetal as opposed to the singular Hall response in a type-II Dirac semimetal. Moreover, we show that, under certain condition, the anomalous Hall response may vanish in a linearized type-I Dirac semimetal, even in the presence of time reversal symmetry breaking.