Skyrmion States in Chiral Liquid Crystals

We analyze static configurations for chiral liquid crystals in the framework of the Oseen-Frank theory. In particular, we find numerical solutions for localized axisymmetric states in confined chiral liquid crystals with weak homeotropic anchoring at the boundaries. These solutions describe the distortions of twodimensional skyrmions, known as either spherulites or cholesteric bubbles, which have been observed experimentally in these systems. We outline relations to nonlinear integrable equations and use the relations to study the asymptotic behavior of the solutions. Using analytic methods, we build approximate solutions of the equilibrium equations and analyze the generation and stabilization of these states in relation to the material parameters, external fields, and anchoring boundary conditions.