Chemical bonds of two vortex species with a generalized Josephson term and arbitrary charges

TL;DR

This paper studies vortex solutions in an Abelian-Higgs model with two scalar fields, arbitrary charges, and a generalized Josephson term, classifying minimal vortices and analyzing their magnetic flux and domain walls.

Contribution

It introduces a comprehensive classification of vortex solutions in a generalized Abelian-Higgs model with arbitrary charges and higher-order Josephson terms, including analytical and numerical results.

Findings

Finite-energy local vortices have rational fractional magnetic flux.

Global vortices can have arbitrary fractional flux and possess angular domain walls.

Numerical classification of minimal local vortices and vortex networks.

Abstract

We consider the Abelian-Higgs model with two complex scalar fields and arbitrary positive integer charges with the addition of a higher-order generalization of the Josephson term. The theory possesses vortices of both local and global variants. The only finite-energy configurations are shown to be the local vortices for which a certain combination of vortex numbers and electric charges -- called the global vortex number -- vanishes. The local vortices have rational fractional magnetic flux, as opposed to the global counterparts that can have an arbitrary fractional flux. The global vortices have angular domain walls, which we find good analytic approximate solutions for. Finally, we find a full classification of the minimal local vortices as well as a few nonminimal networks of vortices, using numerical methods.