Abstract

We fabricate colloidal particles with nontrivial surface topology, including colloidal handlebodies, knots, links, Mobius strings, and Seifert surfaces. When introduced into a nematic liquid crystal with a uniform far-field director, these particles induce three-dimensional director fields and topological defects around them. We use director switching by electric fields, laser tweezing of defects, and local photothermal melting of the liquid crystal to promote transformations among many stable and metastable particle-induced director configurations and then explore them by means of a direct label-free three-dimensional nonlinear optical imaging. This reveals many peculiarities of the interplay between topologies of colloidal surfaces, director fields, and defects, which we find being in agreement with Gauss-Bonnet and Poincar-Hopf index theorems. The lecture will conclude with a brief discussion of how these findings may lay the groundwork for new types of topology-di ctated elastic self-assembly in liquid crystals and experimental study of low-dimensional topology.