Curvature Potential Unveiled Topological Defect Attractors

Luka Mesarec,Epifanio G Virga,Aleš Iglič,Wojciech Góźdź,Samo Kralj,Veronika Kralj-Iglič

doi:10.3390/cryst11050539

Abstract

We consider the theoretical and positional assembling of topological defects (TDs) in effectively two-dimensional nematic liquid crystal films. We use a phenomenological Helfrich–Landau–de Gennes-type mesoscopic model in which geometric shapes and nematic orientational order are expressed in terms of a curvature tensor field and a nematic tensor order parameter field. Extrinsic, intrinsic, and total curvature potentials are introduced using the parallel transport concept. These potentials reveal curvature seeded TD attractors. To test ground configurations, we used axially symmetric nematic films exhibiting spherical topology.

Highlights

Topological defects (TDs) [1] refer to localized regions in an ordered manifold, where the local order is frustrated
We consider a more detailed model in which we focus on the impact of curvature on the position of TDs in nematic orientational order
We introduce the geometric potentials derived from the model free energy, which efficiently determine the location of TDs for a given manifold geometry

Summary

Introduction

Topological defects (TDs) [1] refer to localized regions in an ordered manifold, where the local order is frustrated. They are present in all branches of physics because the sole condition for their existence is symmetry breaking [2]. One commonly refers to TDs exhibiting m > 0 and m < 0 as defects and antidefects. TDs introduce local strong energetically expensive elastic distortions. For this reason, within defect cores, the ordering field is commonly melted or exhibits a qualitatively different structure with respect to bulk order [6]. It is of interest to find efficient mechanisms, which enable the creation, stabilization, and manipulation of TDs

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