Artificial matter from knots: solitons and vortices in chiral media

Abstract: Topology is key for understanding properties of many natural material systems. Moreover, topology can be used as an important design principle to create artificial materials with properties not encountered in nature. This lecture will discuss how stable solitonic and vortex knots in chiral liquid crystals, colloids and magnets can exhibit atom-like behavior, including fusion, fission as well as self-assembly into various crystals and other forms of artificial matter [1-5]. The molecular and host medium's chirality play important roles in enabling stability of the spatially localized knotted solitons, the hopfions, and vortex structures, illustrating a hierarchical interplay of chirality effects. The unusual crystals of self-assembled knots exhibit giant electrostriction, facile reconfigurability of lattice symmetries and other properties never encountered in conventional forms of matter. These experimental demonstrations and theoretical/computational findings will let us revisit and admire the beautiful history of the early model of atoms by Kelvin, Maxwell and Tait, turning this model from a blunder to a new topological metamaterial design approach. I will then show that these vortices interact with light similar to what was previously predicted for the elusive cosmic strings, with knots and crystalline arrays of vortices allowing to spatially localize non-spreading laser beams into closed loops and knots, potentially paving the way to cosmology-inspired and knot-theory-guided optical engineering.

[1] D. Hall, J.-S. B. Tai, L. Kauffman and I. I. Smalyukh. Nature Physics doi.org/10.1038/s41567-025-03107-0 (2025). [2] J.-S. B. Tai and I. I. Smalyukh. Science 365, 1449-1453 (2019). [3] C. Meng, J.-S. Wu, and I. I. Smalyukh. Nature Materials 22, 64–72 (2023). [3] H. Zhao, J.-S. B. Tai, J.-S. Wu, and I. I. Smalyukh. Nature Physics 19, 451–459 (2023). [4] R. Voinescu, J.-S. B. Tai and I. I. Smalyukh. Phys Rev Lett 125, 057201 (2020). [5] P. J. Ackerman and I. I. Smalyukh. Nature Mater 16, 426-432 (2017).

geometric topology

Audience: researchers in the topic

GEOTOP-A seminar

Series comments: Web-seminar series on Applications of Geometry and Topology