Smectic layering: Landau theory for a complex-tensor order parameter
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.
History
School
- Science
Department
- Mathematical Sciences
Published in
Journal of Physics A: Mathematical and TheoreticalVolume
55Issue
35Publisher
IOP PublishingVersion
- VoR (Version of Record)
Rights holder
© The Author(s)Publisher statement
This is an Open Access Article. It is published by IOP Publishing under the Creative Commons Attribution 4.0 International Licence (CC BY). Full details of this licence are available at: https://creativecommons.org/licenses/by/4.0/Acceptance date
2022-07-13Publication date
2022-08-10Copyright date
2022ISSN
1751-8113eISSN
1751-8121Publisher version
Language
- en