Fractional vortex molecules and vortex polygons in a baby Skyrme model

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.

21 pages, 5 figures

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• Relations among topological solitons
• Fractional Skyrmions and their molecules
• Instantons in Chiral Magnets
• Skyrmions confined as beads on a vortex ring
• Vortex molecules in Bose-Einstein condensates
• Stable $Z$-strings with topological polarization in two Higgs doublet model
• Broken planar Skyrmions -- statics and dynamics
• Fractional Skyrmion molecules in a $\mathbb{C}{P}^{N-1}$ model
• Baby Skyrmion crystals
• Potentials and the vortex solutions in the $C{P}^N$ Skyrme-Faddeev model
• Gauged BPS baby Skyrmions with quantised magnetic flux
• Topological invariants of vortices, merons, skyrmions, and their combinations in continuous and discrete systems
• Gauged merons
• Superconductors that do not expel magnetic flux
• Magnetic Hopfions in the Faddeev-Skyrme-Maxwell model
• Stabilizing semilocal strings by polarization
• "Half a proton" in the Bogomol'nyi-Prasad-Sommerfield Skyrme model