Boundary Superconductivity in the BCS Model
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866917622225829888 |
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| author | Hainzl, Christian Roos, Barbara Seiringer, Robert |
| author_facet | Hainzl, Christian Roos, Barbara Seiringer, Robert |
| contents | We consider the linear BCS equation, determining the BCS critical temperature, in the presence of a boundary, where Dirichlet boundary conditions are imposed. In the one-dimensional case with point interactions, we prove that the critical temperature is strictly larger than the bulk value, at least at weak coupling. In particular, the Cooper-pair wave function localizes near the boundary, an effect that cannot be modeled by effective Neumann boundary conditions on the order parameter as often imposed in Ginzburg-Landau theory. We also show that the relative shift in critical temperature vanishes if the coupling constant either goes to zero or to infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_08090 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Boundary Superconductivity in the BCS Model Hainzl, Christian Roos, Barbara Seiringer, Robert Mathematical Physics Superconductivity We consider the linear BCS equation, determining the BCS critical temperature, in the presence of a boundary, where Dirichlet boundary conditions are imposed. In the one-dimensional case with point interactions, we prove that the critical temperature is strictly larger than the bulk value, at least at weak coupling. In particular, the Cooper-pair wave function localizes near the boundary, an effect that cannot be modeled by effective Neumann boundary conditions on the order parameter as often imposed in Ginzburg-Landau theory. We also show that the relative shift in critical temperature vanishes if the coupling constant either goes to zero or to infinity. |
| title | Boundary Superconductivity in the BCS Model |
| topic | Mathematical Physics Superconductivity |
| url | https://arxiv.org/abs/2201.08090 |