Charged Vortex in Superconductor

TL;DR

This paper discovers charged vortex solutions in a superconductor model involving scalar fields, gauge fields, and phonons, revealing conditions for finite energy and BPS bounds that relate to superconductor types.

Contribution

It introduces a novel effective field theory with specific couplings that allow for regular, finite-energy charged vortices and explores their BPS properties at critical coupling.

Findings

Charged vortices have finite energy due to phonon-electromagnetic field cancellation.

Regular static vortex solutions exist only at a nonzero critical Yukawa coupling.

BPS bound saturation occurs at critical quartic coupling, indicating a borderline superconductor regime.

Abstract

We find the charged spinless vortices in the effective field theory of a Schr\"{o}dinger type complex scalar field of Cooper pair, a U(1) gauge field of electromagnetism, and a gapless neutral scalar field of acoustic phonon. We show that regular static vortex solutions are obtained only for the nonzero critical cubic Yukawa type coupling between neutral and complex scalar fields. Since the Coulombic electric field is exactly cancelled by the phonon, the obtained charged vortices have finite energy. When the quartic self-interaction coupling of complex scalar field has the critical value, the BPS (Bogomolny-Prasad-Sommerfield) bound is saturated for multiple charged vortices of arbitrary separations and hence the borderline of type I and II superconductors is achieved in nonperturbative regime.