Walls and chains of planar skyrmions

TL;DR

This paper investigates linear structures in planar skyrmion systems, showing that the existence of walls or chains depends on the potential and boundary conditions, with single-vacuum systems supporting chains and double-vacuum systems supporting walls.

Contribution

It clarifies the conditions under which walls or chains of skyrmions can exist, highlighting the role of vacuum structure and boundary conditions in these solutions.

Findings

Single-vacuum systems admit chain solutions.

Double-vacuum systems support stable wall solutions.

Walls can be primary objects, with skyrmions built from them.

Abstract

In planar (baby) Skyrme systems, there may be extended linear structures which resemble either domain walls or chains of skyrmions, depending on the choice of potential and boundary conditions. We show that systems with a single vacuum, for example with potential V=1-phi_3, admit chain solutions, whereas walls are ruled out by the uniqueness of the vacuum. On the other hand, in double-vacuum systems such as V=1/2*(1-phi_3^2), one has stable wall solutions, but there are no stable chains; the walls may be viewed as the primary objects in such systems, with skyrmions being made out of them.