Abstract
Topological order and phases represent an exciting research frontier [1], but knots in fields were postulated to behave like particles already starting from Gauss and Kelvin. Experimentally knots in order parameter fields were found only as transient features and could not self-assemble into three-dimensional crystals. I will describe energetically stable solitonic knots and knotted vortices that emerge in the physical fields of chiral liquid crystals and magnets [2,3]. While spatially localized and freely diffusing in all directions, they behave like colloidal particles and atoms, self-assembling into crystalline lattices with open and closed structures, as well as forming low-symmetry mesophases and gas- or liquid-like states [2,3]. A combination of energy-minimizing numerical modeling and nonlinear optical imaging uncovers the internal structure and topology of individual solitonic knots and the various hierarchical crystalline and other organizations that they form. These solitonic knots are robust [1-4] and topologically distinct from the host medium, though they can be morphed and reconfigured by weak stimuli like electric or magnetic fields. I will discuss their stability in molecular and colloidal liquid crystals of different symmetries [5-7] and will show how low-voltage electric fields can switch between the heliknoton [2,3] and hopfion [4] embodiments of such knot solitons while preserving their topology. Finally, I will discuss how this emergent paradigm of knotted solitonic matter could allow for imparting new designable material properties and for realizing phases of matter that so far could not be found in naturally occurring materials [5-7].
References
1) I. I. Smalyukh. Rep. Prog. Phys. 83, 106601 (2020).
2) J.-S. B. Tai and I. I. Smalyukh. Science 365, 1449 (2019).
3) R. Voinescu, J.-S. B. Tai and I. I. Smalyukh. Phys Rev lett 125, 057201 (2020)
4) P. J. Ackerman and I. I. Smalyukh. Nature Materials 16, 426 (2017)
5) G. Poy, A. Hess, A. Seracuse, S. Zumer, I.I Smalyukh. Nature Photonics 16, 454-461 (2022).
6) C. Meng, J.-S. Wu, and I. I. Smalyukh. Nature Materials 22, 64-72 (2023).
7) H. Zhao, J.-S. B. Tai, J.-S. Wu, and I. I. Smalyukh. Nature Physics 19, 451-459 (2023).
Please contact phweb@ust.hk should you have questions about the talk.
