Study On The Stability Of Topological Defects In Two-Dimensional Spherical Nematic Liquid Crystal

An important frontier direction in the research and application of liquid crystal is the geometrically confined liquid crystal system.Various physical properties of liquid crystal are largely determined by the micro-orientation of the liquid crystal molecules,which are closely related to the distribution of topological defects in the liquid crystal.Therefore,topological defect structure in liquid crystal system plays an important role in many physical processes and applications.Experimental and theoretical studies show that defects can and must exist in a spherical liquid crystal,which is determined by the spherical topology.However,if topological constraints are removed,it is not clear if the liquid crystal defects are still stable.Based on the isotropic nematic liquid crystal disk model,we analytically study the stability mechanism of liquid crystal defects.We show that,in a growing spherical disk covering a sphere,the accumulation of curvature effect can prevent typical +1 and +1/2 defects from forming boojum textures.Driven by curvature,these defects will eventually move to the center of the disc and are stable.We also discuss the case where the +1 defect splits into two +1/2 defects and the curvature-driven alternating repulsive and attractive interactions between the two +1/2 defects.This study shows that curvature can drive the generation of topological defects in liquid crystal and ensure their stability,and can control the interaction between defects.The results of this work provide a geometric approach to stabilizing defects and may be instructive in engineering the use of defect-regulated geometrically constrained liquid crystal systems.