Topological order and phasesrepresent an exciting researchfrontier , butknots in fieldswere postulatedto behave like particles already starting from Gauss and Kelvin.Experimentallythey were found only as transient features and could not self-assemble intothree-dimensional crystals. I will describe energetically stable solitonicknotsthat emerge in the physical fields of chiral liquid crystals and magnets [2,3].While spatially localized and freely diffusing in all directions, they behavelike colloidal particles and atoms, self-assembling into crystalline latticeswith open and closed structures, as well as forming low-symmetry mesophases andgas- or liquid-like states [2,3]. A combination of energy-minimizing numericalmodeling and nonlinear optical imaging uncovers the internal structure andtopology of individual solitonic knots and the various hierarchical crystallineand other organizations that they form.These solitonicknots are robust [1-4]and topologically distinct from the host medium, though they can be morphed andreconfigured by weak stimuli like electric or magnetic fields. I will discusstheir stability in molecular and colloidal liquid crystals of differentsymmetries [5,6]and will show how low-voltage electric fields canswitch between the heliknoton [2,3] and hopfion  embodiments of such knotsolitons while preserving their topology . Finally, I will discusshow thisemergentparadigm of knottedsolitonicmattercouldallow for impartingnew designable material propertiesand for realizing phasesof matter that so far could not be found in naturally occurring materials.
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2. J.-S. B. Tai and I. I. Smalyukh. Science365,1449 (2019).
3. R. Voinescu, J.-S. B. Tai and I.I. Smalyukh. Phys Rev lett125, 057201 (2020)
4. P. J. Ackerman and I. I. Smalyukh.Nature Materials16, 426 (2017)
5. H. Mundoor, S. Park, B. Senyuk, H. Wensink and I. I.Smalyukh. Science360, 768 (2018).
6. H. Mundoor, J.-S. Wu, H. Wensink and I.I. Smalyukh. Nature590,268 (2021).7. J.-S. B. Tai, J.-S. Wu and I. I. Smalyukh. Nature Commun.13,2986 (2022).