Liquid Crystalline Half‐Skyrmions and Their Optical Properties

Liquid 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 S2/Z2$S^2/Z_2$, 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. A thin film of a chiral liquid crystal is shown to exhibit localized excitations called half‐Skyrmions, non‐singular swirl‐like orientational order that spans the hemisphere of the orientational order parameter space. Combination of the results of various experimental observations and numerical calculations reveals their spontaneous formation both in the form of a hexagonal lattice or in an isolated manner.