Cholesteric fingers from a magnetic perspective: Topology, energetics, and interactions

Chiral liquid crystals and chiral magnets host a wide variety of topological solitons governed by closely related continuum theories, namely the Frank-Oseen model for liquid crystals and the Dzyaloshinskii model for chiral magnets. Here we exploit this correspondence to develop a unified theoretical 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, internal structure, interactions, and collective states of the two principal finger varieties, CF-1 and CF-2. We show that cholesteric fingers can be interpreted as composite chiral solitons built from meronic constituents. In particular, CF-2 corresponds to a bimeron with unit topological charge, whereas CF-1 represents a topologically trivial composite object formed by two merons with identical vorticities. From a homotopic viewpoint these textures correspond to skyrmions and droplets, respectively. Strong homeotropic surface anchoring induces pronounced confinement effects that reshape the meron structure and redistribute the topological charge across the film thickness. Despite their composite nature, isolated fingers embedded in the homogeneous state interact repulsively and behave as particle-like objects. Periodic finger phases emerge when the eigenenergy of an isolated finger becomes negative, giving rise to nucleation-type phase transitions with a diverging lattice period. The coexistence of several energetically degenerate finger varieties allows the formation of mixed periodic sequences whose number grows combinatorially and can be classified analogously to stacking polytypes in close-packed crystals. In contrast, when embedded in the conical background the interaction between fingers becomes attractive due to the overlap of distortion regions. Finally, we demonstrate that the film thickness strongly controls the stability and internal structure of cholesteric fingers. At small thickness the solitons collapse at a critical point where their internal topological structure disappears, whereas at large thickness isolated bimerons exhibit bistability between surface-stabilized and bulklike configurations. These results establish cholesteric fingers as experimentally accessible realizations of composite chiral solitons and highlight the deep correspondence between topological textures in chiral liquid crystals and chiral magnets.