Heat Kernel, Spectral Functions and Anomalies in Weyl Semimetals

TL;DR

This paper investigates the spectral geometry of Dirac operators in Weyl semimetals, focusing on anomalies and heat kernel methods, with implications for understanding chiral and parity anomalies in these materials.

Contribution

It introduces new computational techniques for spectral functions of Dirac operators with boundary conditions, and demonstrates independence of certain anomaly terms from the chiral phase.

Findings

Spectral functions are well-defined for the studied operators.

Anomaly terms involving electromagnetic potential are independent of the chiral phase.

Developed perturbation expansion methods for heat kernel calculations.

Abstract

Being motivated by applications to the physics of Weyl semimetals we study spectral geometry of Dirac operator with an abelian gauge field and an axial vector field. We impose chiral bag boundary conditions with variable chiral phase $\theta$ on the fermions. We establish main properties of the spectral functions which ensure applicability of the $\zeta$ function regularization and of the usual heat kernel formulae for chiral and parity anomalies. We develop computational methods, including a perturbation expansion for the heat kernel. We show that the terms in both anomalies which include electromagnetic potential are independent of $\theta$.