Liquid Crystalline Half‐Skyrmions and Their Optical Properties

Abstract

AbstractLiquid crystals have intrigued physicists as a platform that facilitates direct visualization of topological concepts. Here, the theoretical and experimental studies demonstrating that a thin film of a chiral liquid crystal forms topological entities known as half‐Skyrmions, swirl‐like orientational order that spans the hemisphere of the order parameter space , are reviewed. They appear in the form of a hexagonal lattice or in an isolated manner, accompanied by topological line defects to satisfy topological constraints. Under an optical microscope, half‐Skyrmions appear as dark spots, and their hexagonal lattice yields a Kossel diagram comprising a hexagonal arrangement of circular arcs. These experimental observations are corroborated by numerical calculations of the orientational order based on the Landau‐de Gennes theory with an orientational order parameter of a second‐rank tensor, and construction of its optical images and Kossel diagrams by directly solving Maxwell equations for light wave. A thin film of a chiral liquid crystal thus provides an interesting system for the investigation of topological concepts, and spontaneous formation of a half‐Skyrmion lattice whose periodicity is of the order of the wavelength of visible light has a potential for photonics applications as well as poses a challenging problem on optics.