Axion physics in condensed-matter systems


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.

Key points

  • 3D insulators can be topologically characterized by the value of their bulk axion field.

  • Axion fields introduce additional terms in Maxwell’s equations for condensed-matter systems.

  • The microscopic expression for the axion field in a crystal is given by the non-Abelian Chern–Simons integral, which depends on the Berry connection matrix of the band structure.

  • In strong 3D topological insulators, a half-quantized surface Hall effect appears when the surface states are gapped, together with linear magnetoelectric coupling in their bulk.

  • The axion insulator state can be realized in antiferromagnetic insulators without external fields.

  • Materials with a non-trivial axion field can be used in dark-matter detectors and non-reciprocal thermal emitters.

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Fig. 1: Quantized responses in topological insulator–ferromagnet heterostructures.
Fig. 2: Material systems proposed to be axion insulators.
Fig. 3: Experimental set-ups to access topological responses.
Fig. 4: Signature of axionic charge-density wave in Ta2Se8I.


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The authors thank Y. Wang (Harvard) and S. Roychowdhury (Max Planck Institute) for input and discussions. This work was supported by the US Department of Energy ‘Photonics at Thermodynamic Limits’ Energy Frontier Research Center under grant DE-SC0019140, the Army Research Office MURI (Ab-Initio Solid-State Quantum Materials) grant no. W911NF-18-1-0431 and by the Science and Technology Center (STC) Center for Integrated Quantum Materials under US National Science Foundation (NSF) grant no. DMR-1231319. C.A.C.G. is supported by the NSF Graduate Research Fellowship Program under grant no. DGE-1745303. Financial support by the European Union (grant no. 742068) is gratefully acknowledged. P.N. is a Moore Inventor Fellow and gratefully acknowledges support through grant no. GBMF8048 from the Gordon and Betty Moore Foundation.

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\({{\mathbb{Z}}}_{2}\) invariant

Group of integers 0, 1 first introduced in 2D time-reversal-invariant systems to distinguish topological from trivial phases.

Chern number

Berry flux on a closed manifold, which becomes quantized in time-reversal-breaking topological insulators.

Berry connection

Gauge-dependent vector potential connected to the Berry phase.

Kramers degeneracy

In time-reversal-symmetric systems, every energy state is at least two-fold degenerate.

Casimir stress

Stress that results in Casimir forces inside inhomogeneous structures.

Shift current

Second-order optical effect that results in a d.c. current from incident monochromatic light.

Nesting vector

Vector connecting pockets of the Fermi surface, typically related to the formation of a density wave.

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Nenno, D.M., Garcia, C.A.C., Gooth, J. et al. Axion physics in condensed-matter systems. Nat Rev Phys 2, 682–696 (2020).

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