Colloidal topological insulators

Topological insulators insulate in the bulk but exhibit robust conducting edge states protected by the topology of the bulk material. Here, we design a colloidal topological insulator and demonstrate experimentally the occurrence of edge states in a classical particle system. Magnetic colloidal particles travel along the edge of two distinct magnetic lattices. We drive the colloids with a uniform external magnetic field that performs a topologically non-trivial modulation loop. The loop induces closed orbits in the bulk of the magnetic lattices. At the edge, where both lattices merge, the colloids perform skipping orbits trajectories and hence edge-transport. We also observe paramagnetic and diamagnetic colloids moving in opposite directions along the edge between two inverted patterns; the analogue of a quantum spin Hall effect in topological insulators. We present a new, robust, and versatile way of transporting colloidal particles, enabling new pathways towards lab on a chip applications

Reconfigurable knots and links in chiral nematic colloids

Tying knots and linking microscopic loops of polymers, macromolecules, or defect lines in complex materials is a challenging task for material scientists. We demonstrate the knotting of microscopic topological defect lines in chiral nematic liquid crystal colloids into knots and links of arbitrary complexity by using laser tweezers as a micromanipulation tool. All knots and links with up to six crossings, including the Hopf link, the Star of David and the Borromean rings are demonstrated, stabilizing colloidal particles into an unusual soft matter. The knots in chiral nematic colloids are classified by the quantized self-linking number, a direct measure of the geometric, or Berry's, phase. Forming arbitrary microscopic knots and links in chiral nematic colloids is a demonstration of how relevant the topology can be for the material engineering of soft matter.Comment: 6 pages, 3 figure

Cellular solid behaviour of liquid crystal colloids. 1. Phase separation and morphology

We study the phase ordering colloids suspended in a thermotropic nematic liquid crystal below the clearing point Tni and the resulting aggregated structure. Small (150nm) PMMA particles are dispersed in a classical liquid crystal matrix, 5CB or MBBA. With the help of confocal microscopy we show that small colloid particles densely aggregate on thin interfaces surrounding large volumes of clean nematic liquid, thus forming an open cellular structure, with the characteristic size of 10-100 micron inversely proportional to the colloid concentration. A simple theoretical model, based on the Landau mean-field treatment, is developed to describe the continuous phase separation and the mechanism of cellular structure formation.Comment: Latex 2e (EPJ style) EPS figures included (poor quality to comply with space limitations

Point Defect Dynamics in Two-Dimensional Colloidal Crystals

We study the topological configurations and dynamics of individual point defect vacancies and interstitials in a two-dimensional colloidal crystal. Our Brownian dynamics simulations show that the diffusion mechanism for vacancy defects occurs in two phases. The defect can glide along the crystal lattice directions, and it can rotate during an excited topological transition configuration to assume a different direction for the next period of gliding. The results for the vacancy defects are in good agreement with recent experiments. For the interstitial point defects, which were not studied in the experiments, we find several of the same modes of motion as in the vacancy defect case along with two additional diffusion pathways. The interstitial defects are more mobile than the vacancy defects due to the more two-dimensional nature of the diffusion of the interstitial defects.Comment: 8 pages, 9 postscript figures. Version to appear in Phys. Rev.

Deck the Walls with Anisotropic Colloids in Nematic Liquid Crystals.

Nematic liquid crystals (NLCs) offer remarkable opportunities to direct colloids to form complex structures. The elastic energy field that dictates colloid interactions is determined by the NLC director field, which is sensitive to and can be controlled by boundaries including vessel walls and colloid surfaces. By molding the director field via liquid-crystal alignment on these surfaces, elastic energy landscapes can be defined to drive structure formation. We focus on colloids in otherwise defect-free director fields formed near undulating walls. Colloids can be driven along prescribed paths and directed to well-defined docking sites on such wavy boundaries. Colloids that impose strong alignment generate topologically required companion defects. Configurations for homeotropic colloids include a dipolar structure formed by the colloid and its companion hedgehog defect or a quadrupolar structure formed by the colloid and its companion Saturn ring. Adjacent to wavy walls with wavelengths larger than the colloid diameter, spherical particles are attracted to locations along the wall with distortions in the nematic director field that complement those from the colloid. This is the basis of lock-and-key interactions. Here, we study ellipsoidal colloids with homeotropic anchoring near complex undulating walls. The walls impose distortions that decay with distance from the wall to a uniform director in the far field. Ellipsoids form dipolar defect configurations with the colloid's major axis aligned with the far field director. Two distinct quadrupolar defect structures also form, stabilized by confinement; these include the Saturn I configuration with the ellipsoid's major axis aligned with the far field director and the Saturn II configuration with the major axis perpendicular to the far field director. The ellipsoid orientation varies only weakly in bulk and near undulating walls. All configurations are attracted to walls with long, shallow waves. However, for walls with wavelengths that are small compared to the colloid length, Saturn II is repelled, allowing selective docking of aligned objects. Deep, narrow wells prompt the insertion of a vertical ellipsoid. By introducing an opening at the bottom of such a deep well, we study colloids within pores that connect two domains. Ellipsoids with different aspect ratios find different equilibrium positions. An ellipsoid of the right dimension and aspect ratio can plug the pore, creating a class of 2D selective membranes