Statistical topological insulators

We define a class of insulators with gapless surface states protected from localization due to the statistical properties of a disordered ensemble, namely, due to the ensemble's invariance under a certain symmetry. We show that these insulators are topological, and are protected by a Z(2) invariant. Finally, we prove that every topological insulator gives rise to an infinite number of classes of statistical topological insulators in higher dimensions. Our conclusions are confirmed by numerical simulations.