Skyrmion formation and organization on a shell*

Blue phases (BPs) arise spontaneously in chiral liquid crystals (ChLCs) as the result of minimizing the global free energy, by forming networks of defects with specific cubic symmetry. Confining cuboidal phases to a channel smaller than the molecular pitch results in frustrating the full development of a BP cell, creating skyrmions that pack with hexagonal order. Beyond confinement in a channel, here, we consider the effect of curvature by confining a ChLC in spherical shells. The equilibrium configurations are obtained following a theoretically-informed Monte Carlo relaxation and a Ginzburg-Landau relaxation of the free energy functional, described within the Landau-de Gennes formalism, and solved numerically through finite element discretization. By considering homeotropic and planar anchoring, we stabilize half and full skyrmions. When stabilized in a shell, the hexagonal packing becomes imperfect, to accommodate for the closed surface, resulting in the creation of 5-7 pairs of skyrmions on the surface of the shell. The control over the formation and packing of the skyrmions offers opportunities for pattern design and engineering 2D ordered nanoparticle assemblies.