On the role of Lifshitz invariants in liquid crystals

TL;DR

This paper explores how Lifshitz invariants influence the behavior of liquid crystals, especially under external electric fields and confinement, using a Landau-Ginzburg framework and case studies on nematic cells.

Contribution

It analyzes the role of Lifshitz coupling terms in liquid crystals, extending concepts from magnetic materials to nematic liquid crystal configurations.

Findings

Lifshitz invariants induce undulations in director configurations.

External fields and confinement significantly affect liquid crystal arrangements.

Theoretical framework applicable to various cell geometries.

Abstract

The interaction between an external action and the order parameter, via a dependence described by a so-called Lifshitz invariant, is very important to determine the final configuration of the liquid crystal cells. The external action can be an electric field applied to the bulk or the confinement due to free surfaces or cell walls. The Lifshitz invariant includes the order parameter in the form of an elastic strain. This coupling between elastic strains and fields, inserted in a Landau-Ginzburg formalism, is well known and give rise to striction effects causing undulations in the director configuration. We want to discuss here the role of Lifshitz coupling terms, following an approach similar to that introduced by Dzyaloshinskii for magnetic materials. Case studies on nematics in planar and cylindrical cells are also proposed.