Topological Metadefects: Tangles of Dislocations

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Topological Metadefects: Tangles of Dislocations

Pawel Pieranski, Mehdi Zeghal, Maria Helena Godinho, Patrick Judeinstein, Rémi Bouffet-Klein, Bastien Liagre, and Nicodème Rouger

Phys. Rev. Lett. 131, 128101 – Published 22 September 2023

See Focus story: Crystal Defects Interact to Form Intricate Structures

Abstract

The concept of topological defects is universal. In condensed matter, it applies to disclinations, dislocations, or vortices that are fingerprints of symmetry breaking during phase transitions. Using as a generic example the tangles of dislocations, we introduce the concept of topological metadefects, i.e., defects made of defects. We show that in cholesterics, dextrogyre and levogyre primary tangles are generated through the $D_{2} \to C_{2}$ symmetry breaking from the coplanar dislocation pair called Lehmann cluster submitted to a high enough tensile strain. The primary tangles can be wound up individually into double helices. They can also annihilate in pairs or associate into tangles of higher orders following simple algebraic rules.

Received 17 March 2023
Accepted 8 August 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.128101

Physics Subject Headings (PhySH)

Distortions & defects

Cholesteric liquid crystals Liquid crystals

Polymers & Soft Matter

Focus

Crystal Defects Interact to Form Intricate Structures

Published 22 September 2023

Two or more linear defects can twist around one another to form an entity that may affect the properties of a material.

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Authors & Affiliations

Pawel Pieranski ^* and Mehdi Zeghal

Université Paris-Saclay, Laboratoire de Physique des Solides, 91405 Orsay, France

Maria Helena Godinho

i3N/CENIMAT, Department of Materials Science, NOVA School of Science and Technology, NOVA University Lisbon, Campus de Caparica, Caparica 2829 - 516, Portugal

Patrick Judeinstein

Université Paris-Saclay, CEA, CNRS, LLB, 91191 Gif-sur-Yvette, France

Rémi Bouffet-Klein , Bastien Liagre , and Nicodème Rouger

ENS Paris-Saclay, 4 Avenue des Sciences, 91190 Gif-sur-Yvette, France

^*Corresponding author: pawel.pieranski@u-psud.fr

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Issue

Vol. 131, Iss. 12 — 22 September 2023

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Images

Figure 1
Generation of the Lehmann cluster. (a) Geometry of the experiment: a cholesteric droplet confined by capillarity between crossed cylindrical mica sheets (for a better visual readability, the thickness $h_{\min}$ of the gap is exaggerated). (b) Expanding coplanar dislocation loops. (c) Lehmann cluster resulting from the collision of the expanding loops. (d)–(g) Generation of the Lehmann cluster by collision of the expanding coplanar dislocation loops [0.87% $CB 15 / 5 CB$ , $N = 8$ , $p_{o} = 18 μ m$ , $h_{\min} = 9 p_{o}$ , point 2 in Fig. 2].
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Figure 2
Generation of one dextrogyre tangle of dislocations from the Lehmann cluster in a droplet with $N = 8$ cholesteric pitches. (a) Variation of the Peach-Koehler force with the thickness of the gap. (b)–(e) First overlapping instability occurring at $\tilde{h} = 10.3$ . (f) Cross section of the droplet with the Lehmann cluster. (g)–(i) Top views of the droplet during the generation of the tangle. (j),(k) Cross sections of the two types of $N + 2$ overlaps (0.87% $CB 15 / 5 CB$ , $N = 8$ , $p_{o} = 18 μ m$ ).
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Figure 3
Tensile strain-induced generation of the levogyre and dextrogyre tangles (labeled “lt” and “dt”) by the overlapping instability of the Lehmann cluster. (a) Temporal evolution as observed under a microscope (0.87% mixture of CB15 in 5CB, $p_{o} = 18 μ m$ ): (0 s) pair of coplanar dislocations associated into the Lehmann cluster; (0–81 s) the overlapping instability. (b)–(d) Schematic representation of the 3D motions of dislocations that break the coplanar configuration of the Lehmann cluster and lead to generation of the tangles. $C_{2 x}$ , $C_{2 y}$ , and $C_{2 z}$ are the twofold axes of the $D_{2}$ symmetry group of the Lehmann cluster shown in (b).
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Figure 4
Beginning of the winding of a double helix from the primary tangle. (a)–(d) Second overlapping instability (of a noncoplanar dislocations pair) occurring at $\tilde{h} = 11.2$ [points 4 in Fig. 2]. (e)–(h) Structure of the cholesteric droplet during the second overlapping instability.
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Figure 5
Winding of a dextrogyre double-helix tangle driven by a monotonic extension of the thickness $\tilde{h}$ . (a) Observations in a microscope (5.4% mixture of CB15 in 5CB, $p_{o} = 2.4 μ m$ ). (b) Spatiotemporal cross section extracted from a video along the octagonal dashed line defined in (a). Staircaselike trajectories of dislocations in the spatiotemporal cross section are due to the thresholds to overcome during the successive overlapping instabilities. (c) Growth of the reduced thickness in time. (d)–(h) Perspective view of the winding process.
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