Cholesteric Shells: Two-Dimensional Blue Fog and Finite Quasicrystals

• Published in: Physical review letters 2022-01, Vol.128 (2), p.027801-027801, Article 027801
• Main Authors: Carenza, L N, Gonnella, G, Marenduzzo, D, Negro, G, Orlandini, E
• Format: Article
• Language: English
• ISSN: 0031-9007; 1079-7114
• DOI: 10.1103/PhysRevLett.128.027801

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-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 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.