Skyrmion States In Chiral Liquid Crystals

TL;DR

This paper investigates static skyrmion-like configurations in chiral liquid crystals using numerical and analytical methods within the Oseen-Frank framework, revealing how material parameters and boundary conditions influence their formation and stability.

Contribution

It provides the first detailed numerical and analytical analysis of localized skyrmion states in confined chiral liquid crystals, connecting experimental observations with theoretical models.

Findings

Numerical solutions describe skyrmion distortions in confined systems.

Analytical approximations elucidate stability conditions.

Relations with integrable equations help understand asymptotic behaviors.

Abstract

Within the framework of Oseen-Frank theory, we analyse the static configurations for chiral liquid crystals. In particular, we find numerical solutions for localised axisymmetric states in confined chiral liquid crystals with weak homeotropic anchoring at the boundaries. These solutions describe the distortions of two-dimensional skyrmions, known as either \textit{spherulites} or \textit{cholesteric bubbles}, which have been observed experimentally in these systems. Relations with nonlinear integrable equations have been outlined and are used to study asymptotic behaviors of the solutions. By using analytical methods, we build approximated solutions of the equilibrium equations and we analyse the generation and stabilization of these states in relation to the material parameters, the external fields and the anchoring boundary conditions.