Skyrmion States in Chiral Liquid Crystals

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 spherulites or 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.

Waveguiding by helicoids in confined chiral nematics

“…Among the vast variety of liquid crystals, nematics have played a fundamental role in display and non-display optical applications for decades, since their behavior is the simplest and the most deeply understood. However, in last years the interest in chiral liquid crystals, also called cholesterics or chiral nematics, has known a sharp growth since they have been discovered to be possibly hosts of a pletora of configurations, which show the features of well-known topological solitons, when frustrated by geometric confinement and/or external fields [10][11][12][13][14][15][16][17][18].…”

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

“…where κ 4 is a positive constant. The baby-skyrmions have their applications in the quantum Hall effects [14][15][16][17][18], the nematic crystals [19][20][21][22][23][24], the superconducting materials [25], and the brane-world scenarios [26][27][28][29], so on. The baby-Skyrme model without the kinetic term, named the restricted baby-Skyrme model [30][31][32] has a significant feature; it possesses analytical Bogomol'nyi-Prasad-Sommerfield (BPS) solutions.…”

Non-uniform localised distortions in generalised elasticity for liquid crystals

“…All of them show interesting new properties and phase transitions when frustrated by geometric confinement and/or external fields [1][2][3][5][6][7]. In particular, in recent years it has been demonstrated that chiral nematics can be host for a pletora of new topological and non topological solitonic structures, i. e. skyrmions, helicoids, merons and hopfions [8][9][10][11][12][13]. Furthermore, skyrmion clusters with mutually orthogonal orientations of the constituent isolated skyrmions have been observed and studied in frustrated chiral liquid crystals [14,15].…”