Axion electrodynamics in topological materials

Abstract

One of the intriguing properties characteristic to three-dimensional topological materials is the topological magnetoelectric phenomena arising from a topological term called the θ term. Such magnetoelectric phenomena are often termed the axion electrodynamics since the θ 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 40 years ago to solve the so-called strong CP problem in quantum chromodynamics and is now considered 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 θ term.

Axion/hidden-photon dark matter conversion into condensed matter axion

“…The physics of CM axion is very rich and the CM axion in a different material may have a different microphysical origin [42,43,76]. It would be interesting to explore the physics of CM axion as a probe of DM in a broader class of materials.…”

“…[78] (arXiv version) and in section V. A of ref. [42], the CM axion dispersion relation is estimated by the one-loop calculation (or the random phase approximation), but it has been pointed out in ref. [77] that they incorrectly neglected the tree-level contribution to the CM axion mass and also took the wrong sign for the one-loop contribution.…”

“…We do not discuss in detail the detection method of generated magnons in this paper; they might be observed through the conversion into photons at the boundary of the material, which are then detected by single photon detectors [59], as demonstrated in ref. [39], or might be detected using some specific features for axionic insulators, such as the dynamical chiral magnetic effect [42]. For the estimation of the sensitivity, we just assume the noise rate for the detection dN noise /dt ∼ 10 −3 s −1 .…”

“…On the other hand, the axion-like excitation also appears in the condensed matter physics [40,41] (see refs. [42,43] for reviews). To distinguish it from the elementary particle axion or ALP, we call such an axion-like excitation in condensed matter context as "condensed matter axion (CM axion)".…”

Mirror Chern numbers in the hybrid Wannier representation

“…In brief, the isotropic part of the linear orbital magnetoelectric tensor is conveniently expressed in terms of the axion angle θ , which is defined only modulo 2π as a bulk property. In the presence of "axion-odd" symmetries that flip its sign, the axion angle can assume only two values: θ = 0 (trivial), and θ = π (topological) [3][4][5][6][7][8].…”