Axion Electrodynamics in Topological Materials

TL;DR

This paper reviews theoretical and experimental advances in axion electrodynamics within topological materials, highlighting phenomena like topological magnetoelectric effects, axion insulators, Weyl semimetals, and topological superconductors.

Contribution

It provides a comprehensive overview of axion electrodynamics in various topological phases, connecting concepts from particle physics to condensed matter systems.

Findings

Topological magnetoelectric effect in topological insulators

Electromagnetic responses of Weyl semimetals related to chiral anomaly

Responses of topological superconductors described by gravitational topological terms

Abstract

One of the intriguing properties characteristic to three-dimensional topological materials is the topological magnetoelectric phenomena arising from a topological term called the $\theta$ term. Such magnetoelectric phenomena are often termed the axion electrodynamics, since the $\theta$ term has exactly the same form as the action describing the coupling between a hypothetical elementary particle, axion, and a photon. The axion was proposed about forty years ago to solve the so-called strong CP problem in quantum chromodynamics, and is now considered as a candidate for dark matter. In this tutorial, we overview theoretical and experimental studies on the axion electrodynamics in three-dimensional topological materials. Starting from the topological magnetoelectric effect in three-dimensional time-reversal invariant topological insulators, we describe the basic properties of static and dynamical axion insulators whose realizations require magnetic orderings. We also discuss the electromagnetic responses of Weyl semimetals with a focus on the chiral anomaly. We extend the concept of the axion electrodynamics in condensed matter to topological superconductors, whose responses to external fields can be described by a gravitational topological term analogous to the $\theta$ term.