Coupling the topological defect phase to the extrinsic curvature in nematic shells

In two dimensional nematics, topological defects are point like singularities with both a charge and a phase. We study the 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.