Topologically nontrivial fields and vortices frequently arise in superstring and quantum field theories, plasmas, optics, elementary particles, cosmology, condensed matter and atomic systems, etc. Their complex structures are expected to follow predictions of topological theorems and mathematical theories, such as the knot theory, but are rarely accessible to direct experimental visualization. On the other hand, soft condensed matter systems, such as colloids and liquid crystals, offer complexity in degrees of freedom and symmetries that allow for probing analogous phenomena on completely different scales, ranging from kinetics of atoms in glasses to cosmic strings in the early Universe. In my lecture, I will show examples of how we extend these possibilities by developing soft matter model systems to probe the interplay of topologies of surfaces, fields, and defects [1-7]. This combination of topology and self-assembly paradigms emerges as an interdisciplinary scientific frontier of topological soft matter, potentially enabling scalable fabrication of composite materials with unusual properties .
. A. Martinez, L. Hermosillo, M. Tasinkevych, and I.I. Smalyukh. “Linked topological colloids in a nematic host.” Proc. Natl. Acad. Sci. U.S.A. 112, 4546-4551 (2015).
. Y. Yuan and I. I. Smalyukh. “Topological nanocolloids with facile electric switching of plasmonic properties.” Optics Letters 40, 5630-5633 (2015).
. A. Martinez, M. Ravnik, B. Lucero, R. Visvanathan, S. Žumer, and I. I. Smalyukh. “Mutually tangled colloidal knots and induced defect loops in nematic fields.” Nature Materials 13, 258–263 (2014).
. M. Campbell, M. Tasinkevych, and I.I. Smalyukh. “Topological polymer dispersed liquid crystals with bulk nematic defect lines pinned to handlebody surfaces” Phys. Rev. Lett. 112, 197801 (2014).
. M. Tasinkevych, M. Campbell, and I.I. Smalyukh. “Splitting, linking, knotting, and solitonic escape of topological defects in homeotropic nematic drops with handles”, Procs. Natl. Acad. Sci. USA 111, 16268–16273 (2014).
. B. Senyuk, Q. Liu, S. He, R. D. Kamien, R. B. Kusner, T. C. Lubensky, & I. I. Smalyukh. ”Topological colloids.” Nature 493, 200-205 (2013).
. Q. Liu, B. Senyuk, M. Tasinkevych, and I. I. Smalyukh. “Nematic liquid crystal boojums with handles on colloidal handlebodies,” Proc. Natl. Acad. Sci. U.S.A. 110, 9231 (2013).