Skyrmion

The skyrmion is a hypothetical particle related to baryons. It was described by Tony Skyrme and consists of a quantum superposition of baryons and resonance states.[1]

Skyrmions are homotopically non-trivial classical solutions of a nonlinear sigma model with a non-trivial target manifold topology - hence, they are topological solitons. An example occurs in chiral models of mesons, where the target manifold is a homogeneous space of the structure group

\( \left(\frac{SU(N)_L\times SU(N)_R}{SU(N)_\text{diag}}\right) \)

where SU(N)L and SU(N)R are the left and right copies, and SU(N)diag is the diagonal subgroup.

If spacetime has the topology S3×R, then classical configurations can be classified by an integral winding number because the third homotopy group

\( \pi_3\left(\frac{SU(N)_L\times SU(N)_R}{SU(N)_\text{diag}}\cong SU(N)\right) \)

is equivalent to the ring of integers, with the congruence sign referring to homeomorphism.

A topological term can be added to the chiral Lagrangian, whose integral depends only upon the homotopy class; this results in superselection sectors in the quantised model. A skyrmion can be approximated by a soliton of the Sine-Gordon equation; after quantisation by the Bethe ansatz or otherwise, it turns into a fermion interacting according to the massive Thirring model.

Skyrmions have been reported, but not conclusively proven, to be in Bose-Einstein condensates,[2] superconductors,[3] and thin magnetic films.[4]

An Introduction to Skyrmions

An Introduction to Skyrmions

References

^ Wong, Stephen (2002). "What exactly is a Skyrmion?". arXiv:hep-ph/0202250 [hep/ph].
^ Al Khawaja, Usama; Stoof, Henk (2001). "Skyrmions in a ferromagnetic Bose–Einstein condensate". Nature 411 (6840): 918–20. Bibcode 2001Natur.411..918A. doi:10.1038/35082010. PMID 11418849.
^ Baskaran, G. (2011). "Possibility of Skyrmion Superconductivity in Doped Antiferromagnet K$_2$Fe$_4$Se$_5$". arXiv:1108.3562 [cond-mat.supr-con].
^ 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.