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=m2(1-φ3) and the easy plane potential V=12m2(φ1)2. In both models, the static energy functional is minimized over all two-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 being a perfect square (m2=1). In contrast, we observe that hexagonal crystal chunks in the standard model become the global minima for surprisingly large charges, B>954 (m2=0.1).