Field Theory of Superconductor and Charged Vortex

TL;DR

This paper develops an effective field theory for conventional superconductivity incorporating a complex scalar field, gauge field, and neutral scalar field, and finds finite-energy charged vortex solutions that classify superconductors into types I and II.

Contribution

It introduces a novel effective field theory framework with BPS charged vortex solutions that distinguish superconductor types based on nonperturbative bounds.

Findings

Charged vortex solutions with finite energy are found.

At critical couplings, vortices saturate the BPS bound.

The theory classifies superconductors into type I and II.

Abstract

A Lagrangian of a Schr\"{o}dinger 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.