Smectics: Symmetry Breaking, Singularities, and Surfaces

TL;DR

This paper develops a new topological framework for understanding defects in smectic liquid crystals, emphasizing the role of rotational symmetry and providing a 3D model that clarifies defect topology.

Contribution

It introduces an alternative approach to defect classification in smectics, accounting for translation-rotation interactions and extending the theory to higher dimensions.

Findings

Dislocations linked to phase branch points

Disclinations as critical points and singularities

A 3D model clarifies defect topology without compatibility conditions

Abstract

The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood in terms of the lack of rotational Goldstone modes in such systems and provide an alternate approach that correctly accounts for the interaction between translations and rotations. Dislocations are associated, as usual, with branch points in a phase field, while disclinations arise as critical points and singularities in the phase field. We introduce a three-dimensional model for two-dimensional smectics that clarifies the topology of disclinations and geometrically captures known results without the need for compatibility conditions. Our work suggests natural generalizations of the two-dimensional smectic theory to higher dimensions and to crystals.