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arXiv · 2407.07957

Topology of ultra-localized insulators and superconductors

Bastien Lapierre·Luka Trifunovic·Titus Neupert·Piet W. Brouwer
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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.

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Bastien Lapierre, Luka Trifunovic, Titus Neupert, Piet W. Brouwer. 2024-07-10. Topology of ultra-localized insulators and superconductors. https://doi.org/10.1103/37kd-thwq

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