Scaling and spontaneous symmetry restoring of topological defect dynamics in liquid crystal

TL;DR

This study visualizes and analyzes the dynamics of topological defect lines in liquid crystals, revealing a universal symmetry-restoring mechanism during defect reconnections driven by energetic and topological considerations.

Contribution

It provides the first direct 3D observation of defect line reconnections in liquid crystals and uncovers a spontaneous symmetry restoring mechanism linked to topological and energetic factors.

Findings

Reconnection distance scales with the square root of time.

Reconnecting disclinations exhibit symmetric dynamics in a comoving frame.

Symmetric twist configurations are energetically favored during reconnections.

Abstract

Topological defects -- locations of local mismatch of order -- are a universal concept playing important roles in diverse systems studied in physics and beyond, including the universe, various condensed matter systems, and recently, even life phenomena. Among these, liquid crystal has been a platform for studying topological defects via visualization, yet it has been a challenge to resolve three-dimensional structures of dynamically evolving singular topological defects. Here, we report a direct confocal observation of nematic liquid crystalline defect lines, called disclinations, relaxing from an electrically driven turbulent state. We focus in particular on reconnections, characteristic of such line defects. We find a scaling law for in-plane reconnection events, by which the distance between reconnecting disclinations decreases by the square root of time to the reconnection. Moreover, we show that apparently asymmetric dynamics of reconnecting disclinations is actually symmetric in a comoving frame, in marked contrast to the two-dimensional counterpart whose asymmetry is established. We argue, with experimental supports, that this is because of energetically favorable symmetric twist configurations that disclinations take spontaneously, thanks to the topology that allows for rotation of the winding axis. Our work illustrates a general mechanism of such spontaneous symmetry restoring that may apply beyond liquid crystal, which can take place if topologically distinct asymmetric defects in lower dimensions become homeomorphic in higher dimensions and if the symmetric intermediate is energetically favorable.