Abrikosov clusters in chiral liquid crystal droplets.

Self-organizing triangular lattices of topological vortices have been observed in type-II superconductors, Bose-Einstein condensates, and chiral magnets under external forcing. Liquid crystals exhibit vortex self-organization in dissipative media. In this study, we experimentally investigate the formation of vortex clusters, analogous to Abrikosov lattices, in temperature-driven chiral liquid crystal droplets. Based on a Ginzburg-Landau-like equation, we derive the interaction laws underlying the formation of these Abrikosov clusters of chiral domains. The origin of these is elucidated due to the competition between the repulsive interaction and the spatial effect of the confinement within the droplet. Our results advance the theoretical understanding of localized vortex self-organization in liquid crystals and open up possibilities for controlling the clustering of these topological defects.