The Topology of Dislocations in Smectic Liquid Crystals

TL;DR

This paper explores the unique topological defect structures in smectic liquid crystals, highlighting differences from superfluids and superconductors due to boundary conditions, and introduces topological invariants for dislocation loops.

Contribution

It reveals the topological distinctions of defects in smectic liquid crystals and introduces invariants that classify dislocation loops, advancing understanding of their defect topology.

Findings

Screw and edge defects are topologically distinguishable.

Boundary conditions lead to different defect topologies compared to superfluids.

Dislocation loops can be topologically linked using invariants.

Abstract

The order parameter of the smectic liquid crystal phase is the same as that of a superfluid or superconductor, namely a complex scalar field. We show that the essential difference in boundary conditions between these systems leads to a markedly different topological structure of the defects. Screw and edge defects can be distinguished topologically. This implies an invariant on an edge dislocation loop so that smectic defects can be topologically linked not unlike defects in ordered systems with non-Abelian fundamental groups.