LETTERS PUBLISHED ONLINE: 22 DECEMBER 2014 | DOI: 10.1038/NPHYS3194 Light-controlled topological charge in a nematic liquid crystal Maryam Nikkhou 1 , Miha Škarabot 1 , Simon Čopar 1,2 , Miha Ravnik 2 , Slobodan Žumer 1,2 and Igor Muševič 1,2 * 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 difficult—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 difficult 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 7–9 . 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 manipu- lation 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 parallel to the rubbing direction on the cell’s surfaces, whereas on the glass fibre they were perpendicularly aligned. We use the absorption of the focused beam of the laser tweezers to locally heat the NLC into the isotropic phase (Fig. 1a). This creates a 100 μm diameter island of a molten (isotropic) NLC, which is rapidly quenched by shutting off the light. With no fibre inserted (Fig. 1a and Supplementary Movie 1), the island undergoes a rapid phase transition that leaves behind the phase interfaces a dense tangle of defects through a process similar to the Kibble–Zurek mechanism of defect production in the early Universe 10,11,18 . In less than a second, this tangle annihilates back into the uniformly ordered ground state (vacuum state). However, there is a marked change in the outcome of the coarsening process when we perform the local melting experiment with the fibre inserted, because the connectedness of the quenching domain is changed (Fig. 1b and Supplementary Movie 2). After long times we observe two remnant topological defects, which are stabilized by the perpendicular alignment of molecules on the fibre, namely the Saturn ring 24 and the Saturn anti-ring, each having an opposite winding number and topological charge 1,2,17 , thereby preserving the charge neutrality. These rings are individually inherently stable, cannot be annihilated separately and can be arbitrarily moved with the tweezers. It should be noted that, in the absence of surface anchoring at the fibre walls, each defect would simply be allowed to pass through the NLC–fibre interface and annihilate. If left free, they slowly attract through elastic deformation of the NLC (Fig. 1c), slide towards each other along the fibre and annihilate into a non-uniform, defect-free vacuum state. By repeating the quench at different positions along the fibre, an arbitrary number of ring–anti-ring pairs can be created (Fig. 1f). The structures of the Saturn ring and anti-ring on a fibre are modelled using the Landau–de Gennes (LdG) theory 25 and shown in Fig. 1d. 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. As a reference charge, we use a small test particle (Fig. 1e), treated for perpendicular anchoring, which is by convention assigned a +1 charge for the particle and −1 charge for the accompanying Saturn ring. Such a particle induces an elastic distortion that repels the equally charged part of an elastic dipole and attracts the oppositely charged part (Supplementary Movie 3). 1 Condensed Matter Physics Department, Jožef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia. 2 Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia. *e-mail: igor.musevic@ijs.si NATURE PHYSICS | VOL 11 | FEBRUARY 2015 | www.nature.com/naturephysics 183 © 2015 Macmillan Publishers Limited. All rights reserved