Analysis of Nematic Liquid Crystals with Disclination Lines

TL;DR

This paper analyzes the formation of disclination lines in nematic liquid crystals using a tensor model, revealing the limiting uniaxial textures and defect degrees as elasticity tends to zero.

Contribution

It provides a rigorous mathematical proof of the limiting behavior of nematic liquid crystal textures with defects, extending to related models like the Chern-Simons-Higgs.

Findings

Limiting uniaxial textures form with defects of degree ±1/2.

Disclination lines correspond to finite defect numbers.

Results apply as elasticity constant approaches zero.

Abstract

We investigate the structure of nematic liquid crystal thin films described by the Landau--de Gennes tensor-valued order parameter with Dirichlet boundary conditions of nonzero degree. We prove that as the elasticity constant goes to zero a limiting uniaxial texture forms with disclination lines corresponding to a finite number of defects, all of degree 1/2 or all of degree -1/2. We also state a result on the limiting behavior of minimizers of the Chern-Simons-Higgs model without magnetic field that follows from a similar proof.