Skyrmion-vortex pairing from duality

TL;DR

Problem: Understand the interplay of ferromagnetic and superconducting order in two dimensions and the dynamics of Skyrmion–vortex composites. Approach: formulate a dual description using a CP^1 spin representation and a direct spin–superconductor coupling that yields an emergent gauge field mediating the interaction. Key contributions: derive a dual action with Skyrmion–vortex currents coupled to a massive gauge field, predicting a screened attractive potential V(r) ∝ K0(tilde m r) with tilde m = sqrt(q^2 rho_s / m) and bound pairs of size ~ 1/tilde m; discuss possible BKT-like unbinding transitions and experimental signatures. Significance: extends particle–vortex duality to Skyrmion–vortex composites and offers a framework for analyzing coupled topological textures and transport in ferromagnetic superconductors.

Abstract

An interaction between ferromagnetic and superconducting order, to be realized in a 2d ferromagnetic superconductor, is proposed obeying necessary symmetry principles. This interaction allow us to formulate a duality, similar to the Boson-vortex duality in 2+1 dimensional superfluid. In the dual theory Skyrmion and vortex excitations interact with each other via an emergent gauge field. The static interaction potential is attractive for a Skyrmion and a vortex with opposite topological charges. This interaction can lead to formation of bound pairs of the mentioned topological excitations.