Chiral pair of Fermi arcs, anomaly cancellation, and spin or valley Hall effects in Weyl metals with broken inversion symmetry

Abstract

Anomaly cancelation has been shown to occur in time-reversal symmetry-broken Weyl metals, which explains the existence of a Fermi arc. We extend this result in the case of inversion symmetry-broken Weyl metals. Constructing a minimal model that takes a double pair of Weyl points, we demonstrate the anomaly cancelation explicitly. This demonstration explains why a chiral pair of Fermi arcs appear in inversion symmetry-broken Weyl metals. In particular, we find that this pair of Fermi arcs gives rise to either "quantized" spin Hall or valley Hall effects, which corresponds to the "quantized" version of the charge Hall effect in time-reversal symmetry-broken Weyl metals.