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Abstract

Axion fields provide a unique way to understand large quantized electromagnetic responses in topological insulators and dynamics in Weyl semimetals. This Review discusses the theory of axion fields in condensed matter, their experimental realization and their application in next-generation devices.
Axions are hypothetical particles that were proposed to solve the strong charge-parity problem in high-energy physics. Although they have long been known in quantum field theory, axions have so far not been observed as elementary particles in nature. Yet, in condensed-matter systems, axions can also emerge as quasiparticles in certain materials such as strong topological insulators. The corresponding axion field is expected to lead to exciting physical phenomena in condensed-matter systems, such as a fractional quantum anomalous Hall effect, the chiral anomaly, exotic Casimir-Lifshitz repulsion and a linear magnetoelectric response quantized in units of the fine-structure constant. First signatures of electronic states that permit axion dynamics have been reported in condensed-matter systems. In this Review, we explore the concepts that introduce axion fields in condensed-matter systems and present experimental findings. We discuss predicted and realized material systems, the prospects of using axion electrodynamics for next-generation devices and the search for axions as a possible constituent of dark matter.