Exploring self-consistency of the equations of axion electrodynamics in Weyl semimetals

TL;DR

This paper investigates the self-consistency of axion electrodynamics equations in Weyl semimetals, revealing conditions under which solutions exist and predicting significant magnetic field magnification as an experimental signature.

Contribution

It compares three versions of axion electrodynamics in Weyl semimetals, analyzing their self-consistency and physical implications for different theoretical assumptions.

Findings

Self-consistent solutions exist for non-dynamical axions with linear chiral magnetic terms.

Dynamical axions yield solutions only when the chiral magnetic term vanishes.

No solutions are found for nonlinear chiral magnetic terms except in special cases.

Abstract

Recent works have provided evidence that an axial anomaly can arise in Weyl semimetals. If this is the case, then the electromagnetic response of Weyl semimetals should be governed by the equations of axion electrodynamics. These equations capture both the chiral magnetic and anomalous Hall effects in the limit of linear response, while at higher orders their solutions can provide detectable electromagnetic signatures of the anomaly. In this work, we consider three versions of axion electrodynamics that have been proposed in the Weyl semimetal literature. These versions differ in the form of the chiral magnetic term and in whether or not the axion is treated as a dynamical field. In each case, we look for solutions to these equations for simple sample geometries subject to applied external fields. We find that in the case of a linear chiral magnetic term generated by a non-dynamical axion, self-consistent solutions can generally be obtained. In this case, the magnetic field inside of the Weyl semimetal can be magnified significantly, providing a testable signature for experiments. Self-consistent solutions can also be obtained for dynamical axions, but only in cases where the chiral magnetic term vanishes identically. Finally, for a nonlinear form of the chiral magnetic term frequently considered in the literature, we find that there are no self-consistent solutions aside from a few special cases.