Field Theory of Superconductor and Charged Vortex
Abstract
A Lagrangian of a Schr\"odinger type complex scalar field of Cooper pair, a U(1) gauge field of electromagnetism, and a neutral scalar field of acoustic phonon with constant background charge density is proposed for an effective field theory of conventional superconductivity. We find static charged vortex solutions of finite energy and, for the critical couplings of the quartic self-interaction coupling of complex scalar field and the cubic Yukawa type coupling between neutral and complex scalar field, these charged vortices saturate the BPS (Bogomolny-Prasad-Sommerfield) bound, that guarantees the nonperturbative classification of type I and II superconductors.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.