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Exact higher-order bulk-boundary correspondence of corner-localized states

Exact higher-order bulk-boundary correspondence of corner-localized states

We demonstrate that the presence of a localized state at the corner of an insulating domain is not always a predictor of a certain non-trivial higher-order topological invariant, even though they appear to co-exist in the same Hamiltonian parameter space. Our analysis of $C^n$-symmetric crystalline insulators and their multi-layer stacks …