Topology of ultra-localized insulators and superconductors

Abstract

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. As a consequence, we clarify which conventional topological phases are Wannierizable, and which topological phases cannot exist without delocalized states.

Version to appear in PRL

References in corpus (9)

• Anderson Transitions
• Topological Anderson Insulator
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Cited by in corpus (1)

• From quantum geometry to non-linear optics and gerbes: Recent advances in topological band theory