Tying knots in liquid crystals

The topological nature of knots in fields has fascinated physicists and mathematicians. Experimentally they had been found only as transient features or required complex boundary conditions to exist until recently [1]. Here we present energetically stable, micrometer-sized knots in the chiral background of liquid crystals. These knots are spatially localized and diffusing in all directions. They self-assemble into crystalline lattices with open and closed structures, resembling colloidal particles and atomic nuclei. These knots are robust and topologically distinct from the host medium and can be morphed and reconfigured by weak stimuli under conditions such as those in displays. We use a combination of energy-minimizing numerical modeling and optical imaging to uncover the internal structure and topology of individual knots and the various hierarchical crystalline organizations they form. We further explore the effects of elastic anisotropy and external fields on the stability of these knots.

[1] Jung-Shen B. Tai, Ivan I. Smalyukh, Three-dimensional crystals of adaptive knots, Science 365, 1449-1453 (2019).