Aspects of Defect Topology in Smectic Liquid Crystals

TL;DR

This paper provides a topological classification of defects in smectic liquid crystals, revealing how broken translational symmetry affects defect interactions and classifications in two and three dimensions.

Contribution

It introduces a comprehensive topological framework for classifying smectic defects and explains the path dependence in defect combination rules due to broken translational symmetry.

Findings

Classified smectic point defects and disclination lines topologically

Described defect combination rules and path dependence

Highlighted the impact of broken translational symmetry

Abstract

We study the topology of smectic defects in two and three dimensions. We give a topological classification of smectic point defects and disclination lines in three dimensions. In addition we describe the combination rules for smectic point defects in two and three dimensions, showing how the broken translational symmetry of the smectic confers a path dependence on the result of defect addition.