# Curvature-driven stability of defects in nematic textures over spherical disks

## TL;DR

This paper analytically investigates how curvature influences the stability and arrangement of defects in nematic liquid crystal textures on spherical disks, revealing phase-transition-like behavior and defect interactions driven by curvature effects.

## Contribution

It introduces a curvature-driven stability mechanism for nematic defects on spherical disks, showing how curvature affects defect positions and interactions without topological constraints.

## Key findings

- Curvature prevents +1 and +1/2 defects from forming boojum textures.
- A narrow area window causes +1 defect to move from boundary to center, showing phase transition behavior.
- Curvature induces alternating repulsive and attractive interactions between +1/2 defects.

## Abstract

Stabilizing defects in liquid-crystal systems is crucial for many physical processes and applications ranging from functionalizing liquid-crystal textures to recently reported command of chaotic behaviors of active matters. In this work, we perform analytical calculations to study the curvature driven stability mechanism of defects based on the isotropic nematic disk model that is free of any topological constraint. We show that in a growing spherical disk covering a sphere the accumulation of curvature effect can prevent typical +1 and +1/2 defects from forming boojum textures where the defects are repelled to the boundary of the disk. Our calculations reveal that the movement of the equilibrium position of the +1 defect from the boundary to the center of the spherical disk occurs in a very narrow window of the disk area, exhibiting the first-order phase-transition-like behavior. For the pair of +1/2 defects by splitting a +1 defect, we find the curvature driven alternating repulsive and attractive interactions between the two defects. With the growth of the spherical disk these two defects tend to approach and finally recombine towards a +1 defect texture. The sensitive response of defects to curvature and the curvature driven stability mechanism demonstrated in this work in nematic disk systems may have implications towards versatile control and engineering of liquid crystal textures in various applications.