Exotic structures of a thin film of chiral liquid crystals: a numerical study based on the Landau–de Gennes theory

Chiral liquid crystals exhibit various intriguing ordered structures arising from helical distortions of the orientational order allowed by chirality. We present our numerical studies on such exotic structures of chiral liquid crystals, particularly focusing on those in a thin film whose thickness is on the order of or smaller than the characteristic helical pitch of the liquid crystal. We first review the Landau–de Gennes continuum theory we use in our calculations, in which the orientational order is described by a second-rank tensor (Formula presented.) and the free energy of a liquid crystal is given as a functional of (Formula presented.). We show that a thin film of a chiral liquid crystal can exhibit a diverse variety of ordered structures involving topological line defects (disclination lines), depending on film thickness, temperature, and type of surface anchoring (normal, planar, and planar degenerate). Such exotic structures include a hexagonal lattice of Skyrmions, a whirl-like localized structure that finds in its place in a wide variety of condensed matter systems. A thin film of a chiral liquid crystal thus provides an interesting platform for the investigation of exotic structures of orientational order arising from the frustration between the bulk ordering and the spatial confinement with surface anchoring.