Coupling topological defect phase to extrinsic curvature in nematic shells

TL;DR

This paper investigates how the extrinsic curvature of a cylindrical surface influences the phase and structure of topological defects in nematic liquid crystals, revealing a coupling dependent on distortion energies and bistability phenomena.

Contribution

It introduces the coupling between defect phase and extrinsic curvature in nematic shells, highlighting the role of distortion energies and identifying defect phase bistability.

Findings

Defect phase couples to cylinder orientation due to extrinsic curvature.

Bistability occurs in defect phase when twist distortions dominate.

Similar effects observed for integer charge defects.

Abstract

In two dimensional nematics, topological defects are point like singularities with both a charge and a phase. We study topological defects within curved nematic textures on the surface of a cylinder. This allows us to isolate the effect of extrinsic curvature on the structure of the topological defect. By minimizing the energy associated with distortions in the nematic director around the core of a defect we show that the phase of the topological defect is coupled to the orientation of the cylinder. This coupling depends on the relative energetic cost associated with splay, bend and twist distortions of the nematic director. We identify a bistability in the phase of the defects when twist deformations dominate. Finally, we show a similar effect for integer charge topological defects.