Axion crystals

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.

10 pages, 4 figures, version published in JHEP

References in corpus (2)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Chiral Soliton Lattice and Charged Pion Condensation in Strong Magnetic Fields

Cited by in corpus (11)

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• Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics
• Anomalous effects of dense matter under rotation
• Anomalous Casimir effect in axion electrodynamics
• Spontaneous symmetry breaking and Nambu-Goldstone modes in open classical and quantum systems
• Triangle anomalies and nonrelativistic Nambu-Goldstone modes of generalized global symmetries
• Anomalous low-temperature thermodynamics of QCD in strong magnetic fields
• Topological mass generation in gapless systems
• Optical helicity and Hertz vectors
• Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum
• Floquet vacuum engineering: Laser-driven chiral soliton lattice in the QCD vacuum