A baby-Skyrme model with the anisotropic DM interaction: the compact skyrmions revisited

Abstract

We consider a baby-Skyrme model with a Dzyaloshinsikii-Moriya interaction (DMI) and two types of potential terms. The model has a close connection with the vacuum functional of fermions coupled with O(3) nonlinear n-fields and with a constant SU (2) gauge background. It can be derived from the heat-kernel expansion for the fermion determinant. The model possesses normal skyrmions with topological charge Q = 1. The restricted version of the model also possesses both weakcompacton (at the boundary, not continuously differentiable) and genuine-compacton (continuously differentiable). We also show that the model consists of only the Skyrme term and the DMI provides the soliton solutions, which are so-called skyrmions without a potential.