Baby Skyrmion crystals

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, $B>954$ ($m^2=0.1$).