The BCS-Bogoliubov gap equation with external magnetic field and the first-order phase transition
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916577221279744 |
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| author | Watanabe, Shuji |
| author_facet | Watanabe, Shuji |
| contents | We deal with a type I superconductor in a constant external magnetic field. We obtain the BCS-Bogoliubov gap equation with external magnetic field and apply the implicit function theorem to it. We show that there is a unique magnetic field (the critical magnetic field) given by a smooth function of the temperature and that there is also a unique nonnegative solution (the gap function) given by a smooth function of both the temperature and the external magnetic field. Using the grand potential, we show that the transition from the normal state to the superconducting state in a type I superconductor is of the first order. Moreover we obtain the explicit expression for the entropy gap. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12609 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The BCS-Bogoliubov gap equation with external magnetic field and the first-order phase transition Watanabe, Shuji Mathematical Physics Superconductivity We deal with a type I superconductor in a constant external magnetic field. We obtain the BCS-Bogoliubov gap equation with external magnetic field and apply the implicit function theorem to it. We show that there is a unique magnetic field (the critical magnetic field) given by a smooth function of the temperature and that there is also a unique nonnegative solution (the gap function) given by a smooth function of both the temperature and the external magnetic field. Using the grand potential, we show that the transition from the normal state to the superconducting state in a type I superconductor is of the first order. Moreover we obtain the explicit expression for the entropy gap. |
| title | The BCS-Bogoliubov gap equation with external magnetic field and the first-order phase transition |
| topic | Mathematical Physics Superconductivity |
| url | https://arxiv.org/abs/2501.12609 |