Stabilizing semilocal strings by polarization

TL;DR

This paper demonstrates that semilocal strings can be stabilized across all parameter regions, including type-II, by introducing an $SU(2)$ symmetry-breaking potential, and explores their phase diagram and polarization properties.

Contribution

It introduces a potential term breaking $SU(2)$ symmetry to stabilize semilocal strings throughout the parameter space, including the type-II region.

Findings

Vortices can be stabilized in the entire parameter region.

The phase diagram includes six distinct phases.

Polarized vortices form vortex molecules in certain phases.

Abstract

Semilocal strings are vortices in the extended Abelian-Higgs model with two complex Higgs scalar fields among which a global $SU(2)$ symmetry acts. They are known to be stable (unstable against expansion) in type-I (II) superconductors, in which gauge field is heavier (lighter) than the Higgs scalar field. In this paper, we find that vortices can be stabilized in the whole parameter region including the type-II region by adding a potential term breaking the $SU(2)$ symmetry. We construct numerical solutions in various parameters and determine the vortex phase diagram consisting of six phases. In two phases, a vortex is polarized, that is, split into two half-quantized vortices with a certain distance, to form a vortex molecule, while in the rests a vortex is identical to the conventional Abrikosov-Nielsen-Olesen vortex.