  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 $\theta$ 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 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.
