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Topological metadefects: tangles of dislocations
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 D2 -> C2 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.
Published in Physical Review Letters 131 (2023) 128101
Generation of a Lehmann cluster by collision of coplanar dislocations
Generation of a 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 hmin 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% CB15=5CB, N =8, po = 18 μm, hmin= 9po, point 2 infigure below.
Generation of the primary tangle by the overlapping instability of the Lehmann cluster submitted to a dilation strain
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 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% CB15=5CB, N= 8, po = 18 μm).
Generation of a Lehmann cluster by collision of two coplanar dislocations
Generation of a tangle by instability of a Lehmann cluster submitted to a dilation strain
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