Axion crystals

TL;DR

This paper introduces axion crystals, a new class of photonic crystals with periodic theta parameters, revealing unique properties like helicity-dependent gaps and nonrelativistic dispersion, with potential realizations in condensed matter and high-energy physics.

Contribution

It proposes and analyzes the concept of axion crystals with periodic theta, highlighting their novel photonic properties not seen in traditional photonic crystals.

Findings

Helicity-dependent mass gap in photon band structure

Nonrelativistic gapless dispersion at small momentum

Potential realizations in condensed matter and high-energy physics

Abstract

The low-energy effective theories for gapped insulators are classified by three parameters: permittivity $\epsilon$, permeability $\mu$, and theta angle $\theta$. Crystals with periodic $\epsilon$ are known as photonic crystals. We here study the band structure of photons in a new type of crystals with periodic $\theta$ (modulo $2\pi$) in space, which we call the axion crystals. We find that the axion crystals have a number of new properties that the usual photonic crystals do not possess, such as the helicity-dependent mass gap and nonrelativistic gapless dispersion relation at small momentum. We briefly discuss possible realizations of axion crystals in condensed matter systems and high-energy physics.