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

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.

References in corpus (12)

• The Chiral Magnetic Effect
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Topological response in Weyl semimetals and the chiral anomaly
• Quantum transport evidence for a three-dimensional Dirac semimetal phase in Cd3As2
• Anomalous Hall Effect in Weyl Metals
• Discovery of Weyl fermion semimetals and topological Fermi arc states
• Weyl Semimetals, Fermi Arcs and Chiral Anomalies (A Short Review)
• Chiral anomaly, Charge Density Waves, and Axion Strings from Weyl Semimetals
• Discovery of a new type of topological Weyl fermion semimetal state in Mo${}_x$W${}_{1-x}$Te${}_2$
• Resolution of the Abraham-Minkowski Controversy
• Constructing a Weyl semimetal by stacking one dimensional topological phases

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• Electromagnetic Radiation in chiral matter: the Cherenkov case
• Optical properties and energy propagation in a dielectric medium supporting magnetic current
• Rotatory power reversal induced by magnetic-current in bi-isotropic media
• Nonreciprocal Weyl semimetal waveguide
• Optical reflection signature of an axion dielectric with magnetic current
• Double rotatory power reversal, continuous Kerr angle, and enhanced reflectance in bi-isotropic media with anomalous Hall current
• Fermions in $(1+2)$-dimensions modified by nonminimal coupling and its applications to condensed matter physics
• Probing emergent axion electrodynamics with waveguide apparatus
• Nonlocal transport phenomena in Weyl metals beyond the mesoscopic scale