Baby Skyrmion crystals

TL;DR

This paper models baby Skyrme crystal chunks with different potentials, revealing distinct lattice structures and identifying conditions under which hexagonal or square crystals are energetically favored at various charges.

Contribution

It introduces a model for baby Skyrme crystals with arbitrary potentials, analyzing their minimal energy lattice structures and charge-dependent stability.

Findings

Hexagonal lattice for standard potential

Square lattice for easy plane potential

Hexagonal crystals dominate at very high charges (B>954)

Abstract

This paper describes a model for baby Skyrme crystal chunks with arbitrary potential by considering energy contributions from the bulk and surface of a crystal chunk. We focus on two potentials which yield distinct Skyrme lattices: the standard potential $V=m^2(1-\varphi^3)$ and the easy plane potential $V=\frac{1}{2}m^2 (\varphi^1)^2$. In both models, the static energy functional is minimized over all $2$-dimensional period lattices, yielding the minimal energy crystal structure(s). For the standard potential, the Skyrmions form a hexagonal crystal structure, whereas, for the easy plane potential, the minimal energy crystal structure is a square lattice of half-charge lumps. We find that square crystal chunks are the global minima in the easy plane model for charges $B>6$ with $2B$ a perfect square ($m^2=1$). In contrast, we observe that hexagonal crystal chunks in the standard model become the global minima for surprisingly large charges, $B>954$ ($m^2=0.1$).