Fractional vortex molecules and vortex polygons in a baby Skyrme model

TL;DR

This paper constructs and analyzes fractional vortex molecules in a baby Skyrme model, revealing stable and metastable polygonal arrangements with broken rotational symmetry and calculating their binding energies.

Contribution

It introduces novel fractional vortex molecule configurations in a baby Skyrme model, including regular polygons and arrays, with detailed stability and energy analysis.

Findings

Vortex molecules form regular polygons with 2Q vertices for topological charge Q.

Stable and metastable configurations depend on the value of Q.

Binding energies are calculated for all configurations.

Abstract

We construct a molecule of fractional vortices with fractional topological lump charges as a baby Skyrmion with the unit topological lump charge in the anti-ferromagnetic (or XY) baby Skyrme model, that is, an O(3) sigma model with a four derivative term and an anti-ferromagnetic or XY-type potential term quadratic in fields. We further construct configurations with topological lump charges Q <= 7 and find that bound states of vortex molecules constitute regular polygons with 2Q vertices as vortices, where the rotational symmetry SO(2) in real space is spontaneously broken into a discrete subgroup Z_Q. We also find metastable and arrayed bound states of fractional vortices for Q=5,6. On the other hand, we find for Q=7 that the regular polygon is metastable and the arrayed bound state is stable. We calculate binding energies of all configurations.