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Pré-Publication, Document De Travail Année : 2024

Edge states for tight-binding operators with soft walls

Résumé

We study one- and two-dimensional periodic tight-binding models under the presence of a potential that grows to infinity in one direction, hence preventing the particles to escape in this direction (the soft wall). We prove that a spectral flow appears in these corresponding edge models, as the wall is shifted. We identity this flow as a number of Bloch bands, and provide a lower bound for the number of edge states appearing in such models.

Dates et versions

hal-04493074 , version 1 (06-03-2024)

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Camilo Gómez Araya, David Gontier, Hanne van Den Bosch. Edge states for tight-binding operators with soft walls. 2024. ⟨hal-04493074⟩
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