Formation of Abrikosov cluster in chiral liquid crystal droplets: repulsive interaction of vortices

Chiral liquid crystals exhibit self-organization of topological vortices into triangular lattices within dissipative media. Similar to Abrikosov lattices observed in conservative systems such as type-II superconductors, Bose–Einstein condensates, and chiral magnets. The formation of Abrikosov clusters in liquid crystal droplets has recently been reported. These structures arise from the interplay between the repulsive interactions of chiral domains and confinement effects. In this work, we present a detailed derivation of the kinematic repulsion law governing the interactions between chiral domains based on a Ginzburg-Landau-like amplitude equation.