The BCS-Bogoliubov gap equation with external magnetic field and the first-order phase transition

2025/01/22 by Shuji Watanabe · 1 voice
Physics and Astronomy · #math-ph #cond-mat.supr-con

paper · pdf · doi:10.1088/1751-8121/ada743

Abstract

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.

Discussions

• Shuji Watanabe: The BCS-Bogoliubov gap equation with external magnetic field and the first-order phase transition https://arxiv.org/abs/2501.12609 https://arxiv.org/pdf/2501.12609 https://arxiv.org/ht [bsky, 0 points, 1 comments]

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