Cholesteric Liquid Crystals: Defects and Topology

Abstract

This chapter reviews the basic static properties of defects in cholesteric liquid crystals. The elastic features of the cholesteric phase with deformations at short-range and long-range (as compared to the cholesteric pitch) scales are discussed. Spatial confinement, together with the relative smallness of the twist elastic constant, often leads to twisted and thus optically active structures even when the liquid crystal is composed of nonchiral molecules. The application of topological methods is illustrated using the models of twisted strips, closed DNA molecules, and defect lines--disclinations and dislocations. The homotopy classification of defects in cholesterics is similar to that in biaxial nematics, and predicts phenomena such as the topological entanglement of disclinations and the formation of nonsingular soliton configurations. The spatial confinement of ordered structures (represented, for example, by cholesteric droplets suspended in an isotropic matrix) imposes certain restrictions on the configurations of the order parameter and requires the appearance of topological defects in the ground state. The layered structure of cholesterics leads to the formation of large-scale defects such as focal conic domains and oily streaks.