Curvature potential unveiled topological defect attractors

Abstract

We consider the theoretical and positional assembling of topological defects (TDs) in effectively two-dimensional nematic liquid crystal films. We use a phenomenological Helfrich– Landau–de Gennes-type mesoscopic model in which geometric shapes and nematic orientational order are expressed in terms of a curvature tensor field and a nematic tensor order parameter field. Extrinsic, intrinsic, and total curvature potentials are introduced using the parallel transport concept. These potentials reveal curvature seeded TD attractors. To test ground configurations, we used axially symmetric nematic films exhibiting spherical topology.