Topology of Ultralocalized Insulators and Superconductors
Phys. Rev. Lett. 136, 066601 – Published 9 February, 2026
DOI: https://doi.org/10.1103/37kd-thwq
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 ultralocalized. We derive the classification of such ultralocalized insulators in all symmetry classes and dimensions. We clarify their bulk-boundary correspondence and show that ultralocalized 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.
