Smectic Layering: Landau theory for a complex-tensor order parameter

TL;DR

This paper introduces a Landau theory based on a complex-tensor order parameter to model smectic liquid crystals, capturing their layered structure, defects, and elastic properties more comprehensively than previous scalar models.

Contribution

It develops a novel phenomenological Landau theory using a complex-tensor order parameter specifically for smectics, enabling detailed analysis of layering, defects, and elastic effects.

Findings

The model describes local lamellar order, layer displacement, and orientation.

It accounts for both parallel and perpendicular elastic contributions.

Reduces to previous smectic models and allows for complex geometries.

Abstract

Composed of microscopic layers that stack along one direction while maintaining fluid-like positional disorder within layers, smectics are excellent systems for exploring topology, defects and geometric memory in complex confining geometries. However, the coexistence of crystalline-like characteristics in one direction and fluid-like disorder within layers makes lamellar liquid crystals notoriously difficult to model - especially in the presence of defects and large distortions. Nematic properties of smectics can be comprehensively described by the Q-tensor but to capture the features of the smectic layering alone, we develop a phenomenological Landau theory for a complex-tensor order parameter E, which is capable of describing the local degree of lamellar ordering, layer displacement, and orientation of the layers. This theory can account for both parallel and perpendicular elastic contributions. In addition to resolving the potential ambiguities inherent to complex scalar order parameter models, this model reduces to previous employed models of simple smectics, and opens new possibilities for numerical studies on smectics possessing many defects, within complex geometries and under extreme confinement.