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When two parallel coplanar dislocations with opposite Burgers vectors are brought by action of a stress into a collision in solid crystals, they annihilate each other (see the picture on the left). In cholesterics with the pitch p, in certain conditions, colliding dislocations with Burgers vectors b=p and b=-p are immune against annihilation and form stable twin-like pairs known as Lehmann clusters as well as skyrmion tubes embedded in a helicoidal background (see pictures on the right).
Annihilation of dislocations in solid crystals.
Occurrence of Lehmann clusters. a) As crossings of b = p dislocations. b) Spanned between the b = p and b = p/2 dislocations. c) Spanned between two b = p/2 dislocations. d) As a closed worm-like loop equivalent to a skyrmion tube.
Structure of Lehmann clusters. a) Junction between a Lehmann cluster and a p/2 dislocation loop. b) Close-up of the junction. c) Defect-free variant of the director field in the (x,z) cross section of the Lehmann cluster.
Immunity against annihilation of Lehmann clusters. a) Mapping on the unit sphere of director fields shown in (b) and (c). No matter what is the distance δ between the dislocations, the whole unit sphere is covered completely because the angle θ varies always from 0 to 2π.
Controlled generation of Lehmann clusters. a) Experimental setup. b) Eight Lehmann clusters spanned between circular b = p/2 dislocations loops. N is the number of full cholesteric pitches located between the mica sheets. c) Dense skein of dislocations generated locally by the sequence of phase transitions: cholesteric → isotropic → cholesteric. d) After relaxation, a new Lehmann cluster appears. Like the initial eight ones, it is spanned between two b = p/2 loop
Generation of a Lehmann cluster by local melting into the isotropic phase.
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