# Composite Dislocations in Smectic Liquid Crystals

## TL;DR

This paper investigates the complex core structures of dislocations in smectic liquid crystals, revealing how topological constraints lead to composite dislocation cores involving disclinations and localized higher-order singularities.

## Contribution

It provides a detailed topological analysis of composite dislocation cores in smectics, highlighting the geometric transitions constrained by the material's inability to twist.

## Key findings

- Large charge dislocations break into disclinations
- Transitions between disclination geometries are constrained
- Higher-order point singularities localize dislocation core transformations

## Abstract

Smectic liquid crystals are charcterized by layers that have a preferred uniform spacing and vanishing curvature in their ground state. Dislocations in the smectics play an important role in phase nucleation, layer reorientation, and dynamics. Typically modeled as possessing one line singularity, the layer structure of a dislocation leads to a diverging compression strain as one approaches the defect center, suggesting a large, elastically determined melted core. However, it has been observed that for large charge dislocations, the defect breaks up into two disclinations [C. E. Williams, Philos. Mag. 32, 313 (1975)]. Here we investigate the topology of the composite core. Because the smectic cannot twist, transformations between different disclination geometries are highly constrained. We demonstrate the geometric route between them and show that despite enjoying precisely the topological rules of the three-dimensional nematic, the additional structure of line disclinations in three-dimensional smectics localizes transitions to higher-order point singularities.