Cholesteric Shells: Two-Dimensional Blue Fog and Finite Quasicrystals

Area of Science:

• Materials Science
• Condensed Matter Physics
• Soft Matter Physics

Background:

• Cholesteric liquid crystals exhibit complex phase behaviors.
• Topological defects in confined geometries are crucial for material properties.
• Understanding phase transitions in quasi-two-dimensional systems is an active research area.

Purpose of the Study:

• To investigate the topological phases of quasi-two-dimensional cholesteric liquid crystal shells near the isotropic-cholesteric transition.
• To compare the phase behavior on curved surfaces with that on flat geometries.
• To identify novel topological structures and their formation mechanisms.

Main Methods:

• Theoretical study of phase behavior.
• Characterization of topological phases using concepts from geometry and topology.
• Analysis of defect structures (half-skyrmions) and their arrangement.

Main Results:

• Discovered two novel quasi-two-dimensional topological phases on spherical shells: finite quasicrystals and amorphous structures.
• These structures are composed of polygonal tessellations of half-skyrmions, driven by geometric frustration.
• On toroidal shells, heterogeneous phases with coexisting cholesteric patterns and hexagonal lattices of half-skyrmions were observed due to local curvature variations.

Conclusions:

• The phase behavior of cholesteric liquid crystal shells fundamentally differs from flat geometries due to curvature.
• Geometric frustration on curved surfaces leads to the formation of quasicrystalline and amorphous structures instead of regular lattices.
• Experimental realization may be achieved by self-assembling cholesteric shells on emulsion droplets.