Linear Criterion for an Upper Bound on the Bardeen-Cooper-Schrieffer Critical Temperature
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913660408954880 |
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| author | Roos, Barbara |
| author_facet | Roos, Barbara |
| contents | Since Bardeen-Cooper-Schrieffer theory of superconductivity is non-linear, it is difficult to study superconducting properties analytically. There is a more tractable linear criterion which determines a temperature $T_l$ below which the system is superconducting. Here, we observe that there is a similar linear criterion which gives a temperature $T_u$ above which no superconductivity occurs. We provide examples of translation invariant systems where $T_u>T_l$ as well as systems where $T_u=T_l$. Furthermore, we estimate $T_u$ for half-spaces and show that it is exponentially small in the weak coupling limit, exhibiting the same asymptotics as the critical temperature for full space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00796 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear Criterion for an Upper Bound on the Bardeen-Cooper-Schrieffer Critical Temperature Roos, Barbara Mathematical Physics Superconductivity 81Q10 (Primary) 46N50, 82D55 (Secondary) Since Bardeen-Cooper-Schrieffer theory of superconductivity is non-linear, it is difficult to study superconducting properties analytically. There is a more tractable linear criterion which determines a temperature $T_l$ below which the system is superconducting. Here, we observe that there is a similar linear criterion which gives a temperature $T_u$ above which no superconductivity occurs. We provide examples of translation invariant systems where $T_u>T_l$ as well as systems where $T_u=T_l$. Furthermore, we estimate $T_u$ for half-spaces and show that it is exponentially small in the weak coupling limit, exhibiting the same asymptotics as the critical temperature for full space. |
| title | Linear Criterion for an Upper Bound on the Bardeen-Cooper-Schrieffer Critical Temperature |
| topic | Mathematical Physics Superconductivity 81Q10 (Primary) 46N50, 82D55 (Secondary) |
| url | https://arxiv.org/abs/2407.00796 |