Abstract
Domains of finite topological charge density can exist in chiral materials and chiral matter. Spatial and temporal variation of the average topological charge density, represented by the $\theta$-field, induces anomalous currents that are responsible for the chiral magnetic effect, the anomalous Hall effect and other phenomena that are intimately related to the chiral anomaly. We consider domains with constant average topological charge density. We argue that even though the Maxwell equations in the bulk are not altered, the chiral anomaly manifests itself by the way of the boundary conditions. This is illustrated by several examples. The first example deals with the refraction of plane electromagnetic wave on a surface of a constant-$\theta$ domain. We derive the modified Fresnel equations and discuss the effect of the chiral anomaly on the amplitude and polarization of the reflected and transmitted waves. In particular, we argue that the Brewster's angle is sensitive to the value of $\theta$. In the second example we compute the spectrum of the transition radiation at high frequencies and show that it is enhanced at finite $\theta$.
Highlights
The chiral anomaly [1,2] plays an important role in materials containing chiral fermions
The main goal of this paper is to use the macroscopic electrodynamics with anomalous boundary conditions to study electromagnetic wave refraction and the transition radiation by constant-θ domains
We observe that (i) the amplitudes of the transmitted and reflected waves do not depend on the angle of incidence, (ii) a material with finite θ reflects electromagnetic waves with the effective index of refraction neff = 1 − iθ [as can be realized by comparing (11) and (12)], and (iii) the polarization of the transmitted wave is the same as the polarization of the incident wave
Summary
The chiral anomaly [1,2] plays an important role in materials containing chiral fermions. It is worthwhile to study electrodynamics in the presence of domains with constant θ The main goal of this paper is to use the macroscopic electrodynamics with anomalous boundary conditions to study electromagnetic wave refraction and the transition radiation by constant-θ domains. We argue that these processes can be used as effective experimental tools to investigate the chiral matter/materials.
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