Twisted Superconducting Semilocal Strings

TL;DR

This paper constructs and analyzes a new class of twisted, current-carrying superconducting string solutions in an extended Abelian Higgs model, revealing multiple solution families with distinct energies and properties.

Contribution

It introduces a novel class of twisted superconducting strings with finite energy, characterized by a twist parameter and multiple solution families, expanding understanding of vortex solutions.

Findings

Multiple solution families with different energies for each winding number

Twisted vortices have lower energy than embedded ANO vortices in their rest frame

Solutions include a fundamental string and various excitations distinguished by polarization

Abstract

A new class of twisted, current carrying, stationary, straight string solutions having finite energy per unit length is constructed numerically in an extended Abelian Higgs model with global SU(2) symmetry. The new solutions correspond to deformations of the embedded Abrikosov-Nielsen-Olesen (ANO) vortices by a twist -- a relative coordinate dependent phase between the two Higgs fields. The twist induces a global current flowing through the string, and the deformed solutions bifurcate with the ANO vortices in the limit of vanishing current. For each value of the winding number $n=1,2...$ (determining the magnetic flux through the plane orthogonal to the string) there are $n$ distinct, two-parametric families of solutions. One of the continuously varying parameters is the twist, or the corresponding current, the other one can be chosen to be the momentum of the string. For fixed values of the momentum and twist, the $n$ distinct solutions have different energies and can be viewed as a lowest energy ``fundamental'' string and its $n-1$ ``excitations'' characterized by different values of their ``polarization''. The latter is defined as the ratio of the angular momentum of the vortex and its momentum. In their rest frame the twisted vortices have lower energy than the embedded ANO vortices and could be of considerable importance in various physical systems (from condensed matter to cosmic strings).