Cholesteric shells: two-dimensional blue fog and finite quasicrystals

TL;DR

This paper explores the unique topological phases of cholesteric liquid crystal shells on curved surfaces, revealing the emergence of quasicrystals, amorphous, and heterogeneous structures due to geometric frustration.

Contribution

It introduces the discovery of finite quasicrystals and amorphous phases in cholesteric shells, highlighting the effects of curvature on topological defect arrangements.

Findings

Finite quasicrystals observed on spherical shells.

Heterogeneous phases stabilized by local curvature on toroidal shells.

Geometric frustration prevents regular hexagonal tilings in curved geometries.

Abstract

We study the phase behaviour of a quasi-two dimensional cholesteric liquid crystal shell. We characterise 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 by mixtures of polygonal tessellations of half-skyrmions. 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 stabilises heterogeneous phases where cholesteric patterns coexist with hexagonal lattices of half-skyrmions. Quasicrystals, amorphous and heterogeneous structures could be sought experimentally by self assembling cholesteric shells on the surface of emulsion droplets.