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 − ϕ 3 ) and the easy plane potential V = 1 2 m 2 (ϕ 1 ) 2 . In both models, the static energy functional is minimized over all 2dimensional 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).