Exploring self-consistency of the equations of axion electrodynamics

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 nondynamical 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.

Automated summary

Recent works suggest that an axial anomaly can occur in Weyl semimetals, leading to the electromagnetic response being governed by axion electrodynamics. Different versions of axion electrodynamics were considered, with consistent solutions found for certain conditions, particularly amplification of the magnetic field providing a detectable signature for experiments. Solutions were generally obtained for non-dynamical axions with linear chiral magnetic terms, while dynamical axions had consistent solutions only when the chiral magnetic term vanished. Nonlinear forms of the chiral magnetic term presented challenges in finding self-consistent solutions, with few special cases producing results.