Anomalous Chiral Fermi Surface

TL;DR

This paper explores how Berry curvature on a Fermi surface leads to a Wess-Zumino-Witten term, resulting in chiral anomalies and anomalous currents, with implications for low-temperature fermionic fluids and gravitational anomalies.

Contribution

It provides a geometric derivation of the WZW term for Fermi surfaces with Berry curvature and links it to chiral anomalies and anomalous transport phenomena.

Findings

WZW term emerges for Fermi surfaces with Berry curvature

Chiral anomalies appear at the Fermi surface edge in external fields

Temperature corrections relate to gravitational anomalies

Abstract

We provide a geometrical argument for the emergence of a Wess-Zumino-Witten (WZW) term for a Fermi surface threaded by a Berry curvature. In the presence of external fields, the gauged WZW term yields a chiral (triangle) anomaly for the fermionic current at the edge of the Fermi surface. Fermion number is conserved though since the Berry curvatures occur always in pairs with opposite (monopole) charge. The anomalous vector and axial currents for a a fermionic fluid at low temperature threaded by pairs of Berry curvatures are discussed. The leading temperature correction to the chiral vortical effect in a slowly rotating Fermi surface threaded by a Berry curvature maybe tied to the gravitational anomaly.