Waltzing route toward double-helix formation in cholesteric shells

Significance Droplets of chiral liquid crystals, or cholesterics, typically exhibit an intriguing radial defect which results from frustrations in the molecular order. This configuration shows a fascinating analogy to the Dirac monopole, a hypothetical magnetic charge, and plays a crucial role in the droplet optical properties, recently exploited to produce microlasers. Despite its evident interest, the nature of this disclination remains uncertain. We experimentally show, by studying spherical cholesteric shells, that it is composed of two line defects that wrap around each other on a double-helix structure. By tuning the system chirality, we can make this configuration dissociate into two independent stacks of disclination rings. The transition between configurations is reversible and entails an unexpected defect waltz dynamics. Liquid crystals, when confined to a spherical shell, offer fascinating possibilities for producing artificial mesoscopic atoms, which could then self-assemble into materials structured at a nanoscale, such as photonic crystals or metamaterials. The spherical curvature of the shell imposes topological constraints in the molecular ordering of the liquid crystal, resulting in the formation of defects. Controlling the number of defects, that is, the shell valency, and their positions, is a key success factor for the realization of those materials. Liquid crystals with helical cholesteric order offer a promising, yet unexplored way of controlling the shell defect configuration. In this paper, we study cholesteric shells with monovalent and bivalent defect configurations. By bringing together experiments and numerical simulations, we show that the defects appearing in these two configurations have a complex inner structure, as recently reported for simulated droplets. Bivalent shells possess two highly structured defects, which are composed of a number of smaller defect rings that pile up through the shell. Monovalent shells have a single radial defect, which is composed of two nonsingular defect lines that wind around each other in a double-helix structure. The stability of the bivalent configuration against the monovalent one is controlled by c = h/p, where h is the shell thickness and p the cholesteric helical pitch. By playing with the shell geometry, we can trigger the transition between the two configurations. This transition involves a fascinating waltz dynamics, where the two defects come closer while turning around each other.