Numerical Investigation of Single-Core to Split-Core Transitions in Nematic Liquid Crystals

TL;DR

This study uses numerical methods within the Landau-de Gennes framework to analyze the transition between single-core and split-core defects in nematic liquid crystals, revealing a temperature-dependent bifurcation and energy hierarchy.

Contribution

It provides a detailed numerical analysis of defect core transitions and their dependence on temperature and domain size in nematic liquid crystals.

Findings

Split-core defects have lower energy below the bifurcation temperature.

Above the bifurcation temperature, only single-core defects are stable.

Core sizes vary with temperature and domain size for both defect types.

Abstract

We analyze single-core and split-core defect structures in nematic liquid crystals within the Landau-de Gennes framework by studying minimizers of the associated energy functional. A bifurcation occurs at a critical temperature threshold, below which both split-core and single-core configurations are solutions to the Euler-Lagrange equation, with the split-core defect possessing lower energy. Above the threshold, the split-core configuration vanishes, leaving the single-core defect as the only stable solution. We analyze the dependence of such temperature threshold on the domain size and characterize the nature of the transition between the two defect types. We carry out a quantitative study of defect core sizes as functions of temperature and domain size for both single and split core defects.