Light-controlled topological charge in a nematic liquid crystal

Abstract

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...

Sensing surface morphology of biofibers by decorating spider silk and cellulosic filaments with nematic microdroplets

“…Being effectively elastic materials, the orientational order of nematics responds on long, typically micrometer scales (20)(21)(22), which results in a spatially varying birefringence that can be optically detected (23). Recently, it was demonstrated that glass fibers induce numerous defects in a well-aligned nematic liquid crystal cell and thus provide a simple illustration of topological phenomena (24). It is also known that liquid crystal droplets can considerably change their structure by the action of otherwise imperceptibly small external stimuli (21).…”

Direct mapping of local director field of nematic liquid crystals at the nanoscale

“…The defects, bearing quantized topological charge, resemble the defects in superconductors (16), soft ferromagnets (17), and even cosmic strings and monopoles (18). The fluidity of the phase and the weakly first-order nematic-isotropic phase transition allow for direct visualization of the creation/annihilation of defects via the Kibble-Zurek mechanism (19). Further, defects in a flat sheet of nematic gel or glass can be used to bend or twist local directors, inducing 3D shapes (20,21).…”

Electric field driven reconfigurable multistable topological defect patterns

“…Topological defects (TDs), in which the relevant order parameter field becomes ill-defined at a point, line, or surface [1], appear as a consequence of symmetry-breaking phase transitions. Since these structures generate complex order parameter patterns, TDs are of interest throughout the physical sciences, spanning such diverse areas as condensed materials [2][3][4][5] and cosmology [6], with TD-dominated physical properties exhibiting universal behavior independent of the systems' microscopic details [1].…”