Edge states for tight-binding operators with soft walls
Mathematical Physics
2025-05-20 v3 Materials Science
math.MP
Spectral Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2403.02462,
title = {Edge states for tight-binding operators with soft walls},
author = {Camilo Gómez Araya and David Gontier and Hanne Van Den Bosch},
journal= {arXiv preprint arXiv:2403.02462},
year = {2025}
}