Reinterpretation of chiral anomaly on a lattice

Abstract

Chiral anomalies are a quantum mechanical effect for massless Dirac fermions in both particle physics and condensed matter physics. Here we present a set of effective models for single massless Dirac fermions in one and three dimensions in the whole Brillouin zone from higher-dimensional Chern insulators, which uniquely capture both the chiral fermion behavior near the Dirac point and high-energy states at Brillouin zone boundaries. In the presence of electromagnetic fields, the chiral coefficient C5 is found to be chemical potential dependent in general but quantized precisely at the Fermi surface where chiral symmetry is preserved. This result provides an alternative interpretation of a chiral anomaly on a lattice: The anomaly is caused by symmetry-broken states far below the Fermi surface and protected by the local chiral symmetry. Our analysis here might provide a potential theoretical foundation for applying the concept of chiral anomalies in condensed matter physics.