Skyrmion

This article is about the model in particle physics. For the vortex-like magnetic structure, see magnetic skyrmion.

In particle theory, the skyrmion (/ˈskɜːrmi.ɒn/) is a topologically stable field configuration of a certain class of non-linear sigma models. It was originally proposed as a model of the nucleon by (and named after) Tony Skyrme in 1961.[1][2][3][4] As a topological soliton in the pion field, it has the remarkable property of being able to model, with reasonable accuracy, multiple low-energy properties of the nucleon, simply by fixing the nucleon radius. It has since found application in solid-state physics, as well as having ties to certain areas of string theory.

Skyrmions as topological objects are important in solid-state physics, especially in the emerging technology of spintronics. A two-dimensional magnetic skyrmion, as a topological object, is formed, e.g., from a 3D effective-spin "hedgehog" (in the field of micromagnetics: out of a so-called "Bloch point" singularity of homotopy degree +1) by a stereographic projection, whereby the positive north-pole spin is mapped onto a far-off edge circle of a 2D-disk, while the negative south-pole spin is mapped onto the center of the disk. In a spinor field such as for example photonic or polariton fluids the skyrmion topology corresponds to a full Poincaré beam[5] (a spin vortex comprising all the states of polarization mapped by a stereographic projection of the Poincaré sphere to the real plane).[6] A dynamical pseudospin skyrmion results from the stereographic projection of a rotating polariton Bloch sphere in the case of dynamical full Bloch beams.[7][8]

Skyrmions have been reported, but not conclusively proven, to appear in Bose–Einstein condensates,[9] thin magnetic films,[10] and chiral nematic liquid crystals,[11] as well as in free-space optics.[12][13]

As a model of the nucleon, the topological stability of the skyrmion can be interpreted as a statement that the baryon number is conserved; i.e. that the proton does not decay. The Skyrme Lagrangian is essentially a one-parameter model of the nucleon. Fixing the parameter fixes the proton radius, and also fixes all other low-energy properties, which appear to be correct to about 30%, a significant level of predictive power.[14]

Hollowed-out skyrmions form the basis for the chiral bag model (Cheshire Cat model) of the nucleon. The exact results for the duality between the fermion spectrum and the topological winding number of the non-linear sigma model have been obtained by Dan Freed. This can be interpreted as a foundation for the duality between a quantum chromodynamics (QCD) description of the nucleon (but consisting only of quarks, and without gluons) and the Skyrme model for the nucleon.

The skyrmion can be quantized to form a quantum superposition of baryons and resonance states.[15] It could be predicted from some nuclear matter properties.[16]

  1. ^ Skyrme, T. H. R.; Schonland, Basil Ferdinand Jamieson (1961-02-07). "A non-linear field theory". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 260 (1300): 127–138. Bibcode:1961RSPSA.260..127S. doi:10.1098/rspa.1961.0018. S2CID 122604321.
  2. ^ Skyrme, T. (1962). "A unified field theory of mesons and baryons". Nuclear Physics. 31: 556–569. Bibcode:1962NucPh..31..556S. doi:10.1016/0029-5582(62)90775-7.
  3. ^ Tony Skyrme and Gerald E. Brown (1994). Selected Papers, with Commentary, of Tony Hilton Royle Skyrme. World Scientific. p. 456. ISBN 978-981-2795-9-22. Retrieved 4 July 2017.
  4. ^ Brown, G. E. (ed.) (1994) Selected Papers, with Commentary, of Tony Hilton Royle Skyrme. World Scientific Series in 20th Century Physics: Volume 3. ISBN 978-981-4502-43-6.
  5. ^ Beckley, A. M.; Brown, T. G.; Alonso, M. A. (2010). "Full Poincaré beams". Opt. Express. 18 (10): 10777–10785. Bibcode:2010OExpr..1810777B. doi:10.1364/OE.18.010777. PMID 20588931.
  6. ^ Donati, S.; Dominici, L.; Dagvadorj, G.; et al. (2016). "Twist of generalized skyrmions and spin vortices in a polariton superfluid". Proc. Natl. Acad. Sci. USA. 113 (52): 14926–14931. arXiv:1701.00157. Bibcode:2016PNAS..11314926D. doi:10.1073/pnas.1610123114. PMC 5206528. PMID 27965393.
  7. ^ Dominici; et al. (2021). "Full-Bloch beams and ultrafast Rabi-rotating vortices". Physical Review Research. 3 (1): 013007. arXiv:1801.02580. Bibcode:2021PhRvR...3a3007D. doi:10.1103/PhysRevResearch.3.013007.
  8. ^ Dominici, L.; Voronova, N.; Rahmani, A.; et al. (2023). "Coupled quantum vortex kinematics and Berry curvature in real space". Communications Physics. 6 (1): 197. arXiv:2202.13210. Bibcode:2023CmPhy...6..197D. doi:10.1038/s42005-023-01305-x.
  9. ^ Al Khawaja, Usama; Stoof, Henk (2001). "Skyrmions in a ferromagnetic Bose–Einstein condensate". Nature. 411 (6840): 918–920. arXiv:cond-mat/0011471. Bibcode:2001Natur.411..918A. doi:10.1038/35082010. hdl:1874/13699. PMID 11418849. S2CID 4415343.
  10. ^ Kiselev, N. S.; Bogdanov, A. N.; Schäfer, R.; Rößler, U. K. (2011). "Chiral skyrmions in thin magnetic films: New objects for magnetic storage technologies?". Journal of Physics D: Applied Physics. 44 (39): 392001. arXiv:1102.2726. Bibcode:2011JPhD...44M2001K. doi:10.1088/0022-3727/44/39/392001. S2CID 118433956.
  11. ^ Fukuda, J.-I.; Žumer, S. (2011). "Quasi-two-dimensional Skyrmion lattices in a chiral nematic liquid crystal". Nature Communications. 2: 246. Bibcode:2011NatCo...2..246F. doi:10.1038/ncomms1250. PMID 21427717.
  12. ^ Sugic, Danica; Droop, Ramon; Otte, Eileen; Ehrmanntraut, Daniel; Nori, Franco; Ruostekoski, Janne; Denz, Cornelia; Dennis, Mark R. (2021-11-22). "Particle-like topologies in light". Nature Communications. 12 (1): 6785. arXiv:2107.10810. Bibcode:2021NatCo..12.6785S. doi:10.1038/s41467-021-26171-5. ISSN 2041-1723. PMC 8608860. PMID 34811373.
  13. ^ Ehrmanntraut, Daniel; Droop, Ramon; Sugic, Danica; Otte, Eileen; Dennis, Mark R.; Denz, Cornelia (2023-06-20). "Optical second-order skyrmionic hopfion". Optica. 10 (6): 725. Bibcode:2023Optic..10..725E. doi:10.1364/OPTICA.487989. ISSN 2334-2536.
  14. ^ Adkins, Gregory S.; Nappi, Chiara R.; Witten, Edward (1983). "Static Properties of Nucleons in the Skyrme Model". Nucl. Phys. B. 228: 552. doi:10.1016/0550-3213(83)90559-X.
  15. ^ Wong, Stephen (2002). "What exactly is a Skyrmion?". arXiv:hep-ph/0202250.
  16. ^ Khoshbin-e-Khoshnazar, M. R. (2002). "Correlated Quasiskyrmions as Alpha Particles". Eur. Phys. J. A. 14 (2): 207–209. Bibcode:2002EPJA...14..207K. doi:10.1140/epja/i2001-10198-7. S2CID 121791891.