Stability of highly-twisted Skyrmions from contact topology

TL;DR

This paper introduces a topological protection mechanism for highly-twisted 2D Skyrmions in systems with Dzyaloshinskii-Moriya coupling, demonstrating their stability via contact topology and extending applicability to various spin systems.

Contribution

It presents a novel topological protection mechanism for highly-twisted Skyrmions using contact topology, applicable across multiple 2D spin systems.

Findings

Highly-twisted Skyrmions have an N invariant due to twisting energy density.

Structural stability of Skyrmions is proven under arbitrary chirality-preserving distortions.

The mechanism applies to all 2D systems with Skyrmion excitations, including quantum Hall ferromagnets.

Abstract

We describe a topological protection mechanism for highly-twisted two-dimensional Skyrmions in systems with Dyloshinskii-Moriya (DM) coupling, where non-zero DM energy density (dubbed "twisting energy density") acts as a kind of band gap in real space, yielding an N invariant for highly twisted Skyrmions. We prove our result through the application of contact topology by extending our system along a fictitious third dimension, and further establish the structural stability of highly-twisted Skyrmions under arbitrary chirality-preserving distortions. Our results apply for all two-dimensional systems hosting Skyrmion excitations including spin-orbit coupled systems exhibiting quantum Hall ferromagnetism.