Consequences of average time-reversal symmetry in disordered antiferromagnetic topological insulators

Average symmetry protects the topological surface states of topological (crystalline) insulators with time-reversal symmetry from disorder-induced localization. However, the nature of such average symmetry for magnetic topological insulators and, in particular, its connection to surface transport await inspection. Here, we investigate the impact of imperfect magnetic order on an antiferromagnetic topological insulator, which is a solid with a bulk axion field $\ensuremath{\theta}=\ensuremath{\pi}$. We find that the disordered topological surfaces of an antiferromagnetic topological insulator can be generally gapped and localized. The behavior of topological surfaces is now controlled by a mesoscopic average time-reversal symmetry that requires a magnetically imperfect system to be divisible into finite and magnetically neutral slabs. In the presence of this mesoscopic average time-reversal symmetry, the topological surface states will be gapless in the thermodynamic limit and tend to delocalize at a single energy similar to the delocalization transition in the chiral universality class. The notion of average-symmetry-induced delocalization is thus extended to account for magnetic topological insulators, and the spectroscopic and transport signatures clarified herein are relevant to future experimental investigations.