The topology of an insulator can be defined even when all eigenstates of the system are localized - an extreme case of Anderson insulators that we call ultra-localized. We derive the classification of such ultra-localized insulators in all symmetry classes and dimensions. We clarify their bulk-boundary correspondence and show that ultra-localized systems are in many instances phases of matter not described by the known classification of topological insulators and superconductors.
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Lapierre et al. (2024) studied this question.
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