Scaling and spontaneous symmetry restoring of topological defect dynamics in liquid crystal.
Proc Natl Acad Sci U S A 2022;
119:e2207349119. [PMID:
36191224 PMCID:
PMC9565362 DOI:
10.1073/pnas.2207349119]
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Abstract
When order is formed, topological defects may appear generically, and as such, they are a key to characterize and control the order formation observed in different fields of physics and related disciplines. At the heart of such approaches is disentangling universal and nonuniversal aspects of topological defect dynamics. We do so by realizing direct observation of three-dimensional (3D) dynamics of liquid crystalline defects. Analyzing topological rearrangements called reconnections, on one hand, we establish the validity of the scaling law known for quantum fluid and two-dimensional (2D) liquid crystal; on the other hand, we reveal that the asymmetry present in 2D defect dynamics disappears in 3D. This finding is accounted for by a general mechanism that may hold beyond liquid crystal.
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.
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