Cholesteric Fingers from a Magnetic Perspective: Topology, Energetics, and Interactions

Chiral liquid crystals and chiral magnets host a wide variety of topological solitons described by closely related continuum theories, namely the Frank-Oseen and Dzyaloshinskii models. Exploiting this correspondence, we develop a unified description of cholesteric fingers in confined liquid crystals and their magnetic counterparts. Within a continuum framework including bulk and surface anisotropies, we analyze the topology, structure, interactions, and collective states of the two main finger types, CF-1 and CF-2. We show that cholesteric fingers are composite chiral solitons built from merons. CF-2 corresponds to a bimeron with unit topological charge, while CF-1 is a topologically trivial composite of two merons with identical vorticities. From a homotopic viewpoint these textures correspond to skyrmions and droplets. Strong homeotropic anchoring induces confinement effects that reshape the meron structure and redistribute topological charge across the film thickness. Isolated fingers in the homogeneous state interact repulsively and behave as particle-like objects. Periodic phases emerge when the energy of an isolated finger becomes negative, leading to nucleation-type transitions with a diverging lattice period. Degenerate finger types allow mixed periodic sequences, analogous to stacking polytypes. In a conical background, interactions become attractive due to overlap of distortion regions. Film thickness controls stability and structure: at small thickness solitons collapse, while at large thickness bimerons exhibit bistability between surface-stabilized and bulk-like states.