Magnetic Vortices in the Abelian Higgs Model with Derivative Interactions

TL;DR

This paper investigates magnetic vortex solutions and lattice structures in a generalized Abelian Higgs model with derivative interactions, revealing that the vortex lattice remains hexagonal and providing insights into their energetic properties.

Contribution

It introduces derivative interactions into the Abelian Higgs model and analyzes their effects on vortex solutions and lattice structures, extending the understanding of such systems.

Findings

Vortex solutions exhibit modified asymptotic behavior due to derivative interactions.

Vortex lattice remains hexagonal near the upper critical field.

Condensation energy of vortex lattices is quantified.

Abstract

We study the properties of a single magnetic vortex and magnetic vortex lattices in a generalization of the Abelian Higgs model containing the simplest derivative interaction that preserves the $U(1)$ gauge symmetry of the original model. The paper is motivated by the study of finite isospin chiral perturbation theory in a uniform, external : since pions are Goldstone bosons of QCD (due to chiral symmetry breaking by the QCD vacuum), they interact through momentum dependent terms. We introduce a uniform external magnetic field and find the asymptotic properties of single vortex solutions and compare them to the well-known solutions of the standard Abelian Higgs Model. Furthermore, we study the vortex lattice solutions near the upper critical field using the method of successive approximations, which was originally used by Abrikosov in his seminal paper on type-II superconductors. We find the vortex lattice structure, which remains hexagonal as in the standard Abelian Higgs model, and condensation energy of the vortex lattices relative to the normal vacuum (in a uniform magnetic field).