Comment on “Chiral gauge field and axial anomaly in a Weyl semimetal”

In Liu et al. [Phys. Rev. B 87, 235306 (2013)], the authors obtain that the cross coupling between vector gauge field and chiral gauge field can lead to the anomaly of vector current. We demonstrate that this anomaly is not a physical effect. On one hand, it can be regulated out by the proper regulation. On the other hand, it leads to unjustifiable results, the breaking of the vector gauge symmetry and the ambiguous boundary current. Moreover, the effects associated with anomaly of vector current are understood by random phase approximation (RPA) in the paper we comment on. We point out that the RPA cannot describe the effects resulting from the quantum anomaly.