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Hopf and Skyrme Solitons

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DNM - The mathematical design of new materials

Topologically nontrivial fields and vortices frequently arise in classical and quantum field theories, plasmas, optics, cosmology and atomic systems. On the other hand, condensed matter systems, such as colloids, magnets and liquid crystals, offer the complexity in degrees of freedom and symmetries that allow for probing topologically analogous phenomena on experimentally accessible scales. In my lecture, I will discuss Hopf and Skyrme solitons, continuous but topologically nontrivial knotted field configurations localized in three or two spatial dimensions. They emerge as static structures within the chiral condensed matter systems [1-4] and self-assemble into crystals, but can also exhibit emergent collective motions when powered by external stimuli [5]. I will show how such a synergistic interplay of topology and self-assembly paradigms can emerge as an exciting scientific frontier of condensed matter.
1. P. J. Ackerman and I. I. Smalyukh. Nature Mater 16, 426-432 (2017).
2. J.-S.B. Tai, P.J. Ackerman and I.I. Smalyukh. PNAS . 115, 921-926 (2018).
3. P. J. Ackerman and I. I. Smalyukh. Phys Rev X 7, 011006 (2017).
4. J.-S. B. Tai and I. I. Smalyukh. Phys Rev Lett 121, 187201 (2018). 5. H.R.O. Sohn, C.D. Liu and I.I. Smalyukh. (2019).



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