Cholesteric Shells: Two-Dimensional Blue Fog and Finite Quasicrystals

We study the phase behavior of a quasi-two-dimensional cholesteric liquid crystal shell. We characterize the topological phases arising close to the isotropic-cholesteric transition and show that they differ in a fundamental way from those observed on a flat geometry. For spherical shells, we discover two types of quasi-two-dimensional topological phases: finite quasicrystals and amorphous structures, both made up of mixtures of polygonal tessellations of half-skynnions. These structures generically emerge instead of regular double twist lattices because of geometric frustration, which disallows a regular hexagonal tiling of curved space. For toroidal shells, the variations in the local curvature of the surface stabilizes heterogeneous phases where cholesteric patterns coexist with hexagonal lattices of half-skyrmions. Quasicrystals and amorphous and heterogeneous structures could be sought experimentally by self-assembling cholesteric shells on the surface of emulsion droplets.

Automated summary

This study investigates the phase behavior of quasi-two-dimensional cholesteric liquid crystal shells and discovers novel topological phases that differ from those observed on flat geometries. For spherical shells, finite quasicrystals and amorphous structures are identified, which are made up of mixtures of polygonal tessellations of half-skynnions. For toroidal shells, variations in local curvature lead to the stabilization of heterogeneous phases where cholesteric patterns coexist with hexagonal lattices of half-skyrmions. These findings provide important insights for experimental self-assembling of cholesteric shells.