Demonstrates the first intrinsic statistical topological insulator: a disordered ensemble with an average axion angle theta-bar = pi protected by an average C4T symmetry satisfying (C4T)^4 = 1, which has no clean band-insulator counterpart because a symmetric clean system with that symmetry cannot realize theta = pi. A disordered lattice model and finite-size scaling of the localization length map a phase diagram in which the axion STI is separated from band insulators and trivial Anderson insulators by an unavoidable metallic phase.
A statistical topological insulator (STI) is an ensemble of disordered insulators whose boundary states are protected from localization by a symmetry that holds only on average, rather than in every …