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

نویسندگان

چکیده

We demonstrate that the presence of a localized state at corner an insulating domain is not always predictor certain non-trivial higher-order topological invariant, even though they appear to co-exist in same Hamiltonian parameter space. Our analysis $C^n$-symmetric crystalline insulators and their multi-layer stacks reveals states are necessarily correlated with other well-established boundary observables, such as fractional charge or filling anomaly. In $C^3$-symmetric breathing Kagome lattice, for example, we show bulk polarization, which successfully predicts anomaly, fails be relevant invariant zero-energy states; instead, these can exactly explained by decoration edges. Also, while $C^4$-symmetric have long been conjectured result polarization quarter-filling, correct this misconception introducing proper half-filling establishing precise bulk-corner correspondence. By refining several correspondences two-dimensional insulators, our work motivates further development rigorous theoretical grounds associating existence topology host materials.

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ژورنال

عنوان ژورنال: Physical review

سال: 2021

ISSN: ['0556-2813', '1538-4497', '1089-490X']

DOI: https://doi.org/10.1103/physrevb.104.195437