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Dynamical axion state with hidden pseudospin Chern numbers in MnBi$_{2}$Te$_{4}$-based heterostructures

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 effective theory of topological insulators and has attracted extensive attention in condensed matter physics. Time-reversal or inversion symmetry constrains the axion field $θ$ to be quantized. When both the time-reversal and inversion symmetries are broken by, say, an antiferromagnetic order, the axion field $θ$ 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 MnBi$_{2}$Te$_{4}$-family materials, we further show that such topological-insulator-based dynamical axion states can be hopefully achieved in MnBi$_{2}$Te$_{4}$-based heterostructures, which should greatly facilitate the study of axion electrodynamics in condensed matter physics.