An axion is a hypothetical elementary particle which was initially postulated to solve the charge conjugation-parity problem in particle physics. Interestingly, the axion state has emerged in the effective theory of topological insulators and has attracted extensive attention in condensed matter physics. Time-reversal or inversion symmetry constrains the axion field $\theta$ to be quantized. When both the time-reversal and inversion symmetries are broken by, say, an antiferromagnetic order, the axion field $\theta$ could become unquantized and dynamical along with magnetic fluctuations, which is termed the dynamical axion field. Here, we reveal that a wide class of topological-insulator-based dynamical axion states could be distinguished from the normal-insulator-based ones by a hidden quantity derived from the pseudospin Chern number. Motivated by recent research on the ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ family of materials, we further show that such topological-insulator-based dynamical axion states can be hopefully achieved in ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$-based heterostructures, which should greatly facilitate the study of axion electrodynamics in condensed matter physics.

• Received 9 November 2019
• Accepted 4 February 2020

DOI:https://doi.org/10.1103/PhysRevB.101.081109