Dynamics of topological monopoles annihilation on a fibre in a thick and thin nematic layer.

We study topological defect annihilation on a glass fibre with homeotropic surface anchoring of nematic liquid crystal molecules. The fibre is set parallel to the nematic director of a planar cell with variable thickness and we create pairs of Saturn ring and Saturn anti-ring using the laser tweezers. In thick cells we observe in the whole region of defect separation a Coulomb-like pair attraction with no background force, [Formula: see text] with [Formula: see text]. In cells with thickness comparable to glass fibre diameter, we observe the Coulomb-like attraction only at small separations of the defect pair. For separations larger than the fibre diameter, the pair interaction force is independent of separation. This string-like force is attributed to the formation of defect lines, connecting both monopoles and are indeed visible only on extremely confined fibre, where the fibre diameter is practically equal to the nematic layer thickness. Numerical simulations confirm the formation of defect lines connecting both rings.

Chirality screening and metastable states in chiral nematic colloids.

We show that forces between two colloidal particles in a thin layer of a chiral nematic liquid crystal strongly depend on the chirality of the liquid crystal. The observed pair potentials are attractive, but are oscillatory functions of colloidal separation. The number and the position of local energy minima increase with increasing chirality. The pair interaction is the strongest for the pitch equal to the colloidal diameter and decreases with increasing chirality. We show that the chirality of the medium is responsible for this oscillatory nature and screening of the colloidal interaction in the far and near field. The measurements are in agreement with numerical calculations using Landau-de Gennes theory.

Spherical microparticles with Saturn ring defects and their self-assembly across the nematic to smectic-A phase transition.

We report experimental studies on the Saturn ring defect associated with a spherical microparticle across the nematic (N) to smectic-A (SmA) phase transition. We observe that the director distortion around the microparticle changes rapidly with temperature. The equilibrium interparticle separation and the angle between two quadrupolar particles in the N phase are larger than those of the SmA phase. They are almost independent of the temperature in both phases, except for a discontinuous jump at the transition. We assembled a few particles using a laser tweezer to form a two-dimensional colloidal crystal in the N phase. The lattice structure of the crystal dissolves irreversibly across the N-SmA phase transition. The results on the pretransitional behavior of the defect are supported by the Landau-de Gennes Q-tensor modeling.

Topological defect transformation and structural transition of two-dimensional colloidal crystals across the nematic to smectic-A phase transition.

We observe that topological defects in nematic colloids are strongly influenced by the elasticity and onset of smectic layering across the nematic (N) to smectic-A (SmA) phase transition. When approaching the SmA phase from above, the nematic hyperbolic hedgehog defect that accompanies a spherical colloidal inclusion is transformed into a focal conic line in the SmA phase. This phase transformation has a strong influence on the pairwise colloidal interaction and is responsible for a structural transition of two-dimensional colloidal crystals. The pretransitional behavior of the point defect is supported by Landau-de Gennes Q-tensor modeling accounting for the increasing elastic anisotropy.

Self-assembly of skyrmion-dressed chiral nematic colloids with tangential anchoring.

We describe dipolar nematic colloids comprising mutually bound solid microspheres, three-dimensional skyrmions, and point defects in a molecular alignment field of chiral nematic liquid crystals. Nonlinear optical imaging and numerical modeling based on minimization of Landau-de Gennes free energy reveal that the particle-induced skyrmions resemble torons and hopfions, while matching surface boundary conditions at the interfaces of liquid crystal and colloidal spheres. Laser tweezers and videomicroscopy reveal that the skyrmion-colloidal hybrids exhibit purely repulsive elastic pair interactions in the case of parallel dipoles and an unexpected reversal of interaction forces from repulsive to attractive as the center-to-center distance decreases for antiparallel dipoles. The ensuing elastic self-assembly gives rise to colloidal chains of antiparallel dipoles with particles entangled by skyrmions.

Topological switching and orbiting dynamics of colloidal spheres dressed with chiral nematic solitons.

Metastable configurations formed by defects, inclusions, elastic deformations and topological solitons in liquid crystals are a promising choice for building photonic crystals and metamaterials with a potential for new optical applications. Local optical modification of the director or introduction of colloidal inclusions into a moderately chiral nematic liquid crystal confined to a homeotropic cell creates localized multistable chiral solitons. Here we induce solitons that "dress" the dispersed spherical particles treated for tangential degenerate boundary conditions, and perform controlled switching of their state using focused optical beams. Two optically switchable distinct metastable states, toron and hopfion, bound to colloidal spheres into structures with different topological charges are investigated. Their structures are examined using Q-tensor based numerical simulations and compared to the profiles reconstructed from the experiments. A topological explanation of observed multistability is constructed.

Colloidal entanglement in highly twisted chiral nematic colloids: twisted loops, Hopf links, and trefoil knots.

The topology and geometry of closed defect loops is studied in chiral nematic colloids with variable chirality. The colloidal particles with perpendicular surface anchoring of liquid crystalline molecules are inserted in a twisted nematic cell with the thickness that is only slightly larger than the diameter of the colloidal particle. The total twist of the chiral nematic structure in cells with parallel boundary conditions is set to 0, π, 2π, and 3π, respectively. We use the laser tweezers to discern the number and the topology of the -1/2 defect loops entangling colloidal particles. For a single colloidal particle, we observe that a single defect loop is winding around the particle, with the winding pattern being more complex in cells with higher total twist. We observe that colloidal dimers and colloidal clusters are always entangled by one or several -1/2 defect loops. For colloidal pairs in π-twisted cells, we identify at least 17 different entangled structures, some of them exhibiting linked defect loops-Hopf link. Colloidal entanglement is even richer with a higher number of colloidal particles, where we observe not only linked, but also colloidal clusters knotted into the trefoil knot. The experiments are in good agreement with numerical modeling using Landau-de Gennes theory coupled with geometrical and topological considerations using the method of tetrahedral rotation.