July 27 (Thu.) 14:00~
Yasuhiro Tada (ISSP, Tokyo University) 多田靖啓氏(東京大学物性研究所)
persistent current and U(1) symmetry in superconductors

Superconductivity is conventionally characterized by vanishing resistivity and Meissner effect. Although persistent currents can be expected from the vanishing resistivity, the textbook explanation is that the persistent current cannot be realized at equilibrium due to Bloch's theorem. On the other hand, the Meissner effect is usually discussed in terms of response to external magnetic field based on the BCS theory and Maxwell's equation. However, it is known that U(1) symmetry breaking cannot occur due to Elitzur's theorem if fluctuations of electromagnetic field are included. In this study, we have examined in detail Bloch's theorem and Elitzur's theorem for gauged fermion models with attractive interactions [1,2]. It is found that persistent currents flowing only near the surface in a toroidal sample cannot be ruled out by Bloch's theorem. By extending Elitzur's theorem to fixed gauge field configurations, we also show that the Cooper pair amplitude and corresponding long-range order vanish for almost all gauge fields. Furthermore, Cooper pair correlations are vanishing in the long range limit for models with a standard gauge fixing condition. In this seminar, we will explain the above results and consider the basic properties of superconductivity.

[1] Yasuhiro Tada and Tohru Koma, J. Stat. Phys. 165 (2016) 455.

[2] Yasuhiro Tada and Tohru Koma, arXiv:1612.00619.