Edge states for tight-binding operators with soft walls
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910948506206208 |
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| author | Araya, Camilo Gómez Gontier, David Bosch, Hanne Van Den |
| author_facet | Araya, Camilo Gómez Gontier, David Bosch, Hanne Van Den |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02462 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Edge states for tight-binding operators with soft walls Araya, Camilo Gómez Gontier, David Bosch, Hanne Van Den Mathematical Physics Materials Science Spectral Theory 81Q10, 58J30, 47A13, 35J10 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. |
| title | Edge states for tight-binding operators with soft walls |
| topic | Mathematical Physics Materials Science Spectral Theory 81Q10, 58J30, 47A13, 35J10 |
| url | https://arxiv.org/abs/2403.02462 |