Topological defects in dispersed words and worlds around liquid crystals, or liquid crystal drops

Lavrentovich, Oleg D.

doi:10.1080/026782998207640

Cited by 282 publications

(308 citation statements)

References 19 publications

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“…Topological defects in liquid crystals 16,17 are the carriers of topological charge, which are produced as transients by a rapid pressure or temperature quench 18,19 and made stable either by colloidal inclusions 20,21 , or by confining the liquid crystal to cavities of various geometries and surface properties. One such example is liquid-crystalline droplets 22,23 .Full control over the topological charge creation and manipulation in a nematic liquid crystal (NLC) is achieved by using laser tweezers to induce a thermal microquench of the NLC around an inserted thin fibre (a few µm in diameter). We use a focused laser beam to locally 'melt' and quench the NLC, which leaves behind isolated topological defects that are stabilized by the fibre.…”

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confidence: 99%

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“…Whereas the structure of the Saturn ring (with winding number −1/2 and topological charge −1 is well known 17,24 , the Saturn anti-ring with the opposite winding and topological charge is not stable around a sphere. A single Saturn anti-ring is stable inside a nematic droplet 22,23 , or in a carefully designed confinement geometry 26 . The sign of the topological charge of the two rings can be determined by probing the elastic deformation field around the fibre, as opposite topological charges generally attract.…”

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Light-controlled topological charge in a nematic liquid crystal

et al. 2014

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Creating, imaging, and transforming the topological charge 1,2 in a superconductor 3 , a superfluid 4,5 , a system of cold atoms 6 , or a soft ferromagnet 7-9 is a di cult-if not impossible-task because of the shortness of the length scales and lack of control. The length scale and softness of defects in liquid crystals allow the easy observation of charges, but it is di cult to control charge creation. Here we demonstrate full control over the creation, manipulation and analysis of topological charges that are pinned to a microfibre in a nematic liquid crystal. Oppositely charged pairs are created through the Kibble-Zurek mechanism 10,11 by applying a laser-induced local temperature quench in the presence of symmetry-breaking boundaries. The pairs are long-lived, oppositely charged rings or points that either attract and annihilate, or form a long-lived, charge-neutral loop made of two segments with a fractional topological charge.Topological charge 1,2 is a conserved quantity that is associated with point, string or loop-like topological singularities of physical fields. It is assigned to topological defects in systems of various natures and length scales, such as Abrikosov vortices in type-II superconductors 3 , superfluid vortices 4,5 in 3 He and Bose-Einstein condensates 6 , quasiparticles in the fractional quantum Hall effect 12 , cold fermionic atoms in optical lattices 13 , and in field theories 14 . Integer or fractional topological charge is important for magnetization switching in soft ferromagnets [7][8][9] . In optical vortex beams the topological charge is a measure of the phase singularities of the optical field, and describes the orbital angular momentum of light 15 . Topological defects in liquid crystals 16,17 are the carriers of topological charge, which are produced as transients by a rapid pressure or temperature quench 18,19 and made stable either by colloidal inclusions 20,21 , or by confining the liquid crystal to cavities of various geometries and surface properties. One such example is liquid-crystalline droplets 22,23 .Full control over the topological charge creation and manipulation in a nematic liquid crystal (NLC) is achieved by using laser tweezers to induce a thermal microquench of the NLC around an inserted thin fibre (a few µm in diameter). We use a focused laser beam to locally 'melt' and quench the NLC, which leaves behind isolated topological defects that are stabilized by the fibre. The defects appear in the form of singular points or closed loops, which can be drawn, manipulated, cut and fused together with a laser under an optical microscope. We demonstrate a direct measurement of the topological charge using the charge-induced colloidal forces. This makes inclusions in nematic liquid crystals an ideal system for studying topological charge in soft matter.The experiments were performed on a glass fibre, a few µm in diameter, that was immersed in a thin layer of pentylcyanobiphenyl (5CB) NLC, sandwiched between two glass plates. The NLC molecules were aligned uniformly par...

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Light-controlled topological charge in a nematic liquid crystal

et al. 2014

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“…The continuum theory of liquid crystals [1] is a prototypical nonlinear field theory in which topological considerations play a fundamental role [2,3,4], both in equilibrium (eg [5,6]) and dynamical phenomena (eg [7]). Nematic liquid crystals are represented by a director field n(r), which describes the mean local orientation of the constituent rod-like molecules.…”

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Elastic energy of liquid crystals in convex polyhedra

Majumdar¹,

Robbins²,

Zyskin³

2004

J. Phys. A: Math. Gen.

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We consider nematic liquid crystals in a bounded, convex polyhedron described by a director field n(r) subject to tangent boundary conditions. We derive lower bounds for the one-constant elastic energy in terms of topological invariants. For a right rectangular prism and a large class of topologies, we derive upper bounds by introducing test configurations constructed from local conformal solutions of the Euler-Lagrange equation. The ratio of the upper and lower bounds depends only on the aspect ratios of the prism. As the aspect ratio is varied, the minimum-energy conformal state undergoes a sharp transition from being smooth to having singularities on the edges.

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“…If the pitch, p, is on the order of visible light wavelengths, the selective reflection gives these short-pitch CLCs striking iridescent colours. While liquid crystals were studied in spherical shape very soon after their discovery [2], with a number of seminal works published also in the 1970s-1990s [3][4][5][6][7][8][9][10], not least in connection to polymer-dispersed liquid crystals [11], the success of liquid crystals in the flat panel display industry has for a quite long time set a paradigm in which liquid crystals are studied primarily in a flat sample geometry. This is today changing and curved geometries like droplets, cylinders or shells are now drawing more attention [12,13] (and references therein), due to the many interesting effects arising from confinement within one (droplet) or two (shell) self-closing surfaces.…”

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Elucidating the fine details of cholesteric liquid crystal shell reflection patterns

et al. 2017

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Clusters of planar-aligned short-pitch cholesteric liquid crystal spheres generate dynamic colourful patterns due to multiple selective reflections from the radially oriented cholesteric helices in neighbour shells at varying distances. These photonic communication patterns were widely investigated for the cases of both droplets and shells, demonstrating not only intriguing optical phenomena but also potential for applications as new optical elements for photonics, sensing or security pattern generation. However, the optics of these clusters is truly complex and until now only the strongest and most fundamental reflections have been analysed and explained. In this report, we elucidate the origin of a number of more subtle reflections and we explain the extension in space of various spots as well as their internal colour variations. ARTICLE HISTORY

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Topological defects in dispersed words and worlds around liquid crystals, or liquid crystal drops

Cited by 282 publications

References 19 publications

Light-controlled topological charge in a nematic liquid crystal

Light-controlled topological charge in a nematic liquid crystal

Elastic energy of liquid crystals in convex polyhedra

Elucidating the fine details of cholesteric liquid crystal shell reflection patterns

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