| I will introduce 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. These insulators are topological, and are protected by a Z2 invariant. I will show that every topological insulator gives rise to an infinite number of classes of statistical topological insulators in higher dimensions, and will show a general construction of statistical topological insulators with mirror symmetry. |
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