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Abstract

In addition to the well-known chiral anomaly, Dirac semimetals have been argued to exhibit a mirror anomaly, a close analog to the parity anomaly of (2 + 1)-dimensional massive Dirac fermions. The observable response of such anomaly is manifested in a singular steplike 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 Hamiltonian), we find that type-I Dirac semimetals do not possess such an anomaly in anomalous Hall response even at the level of the linearized Hamiltonian. 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 conditions, the anomalous Hall response may vanish in a linearized type-I Dirac semimetal, even in the presence of time-reversal symmetry breaking.