Skyrmion

In <a href="/facts/Particle_theory/YgIuyj2t">particle theory</a>, the skyrmion is a topologically stable field configuration of a certain class of non-linear <a href="/facts/Sigma_model/jPexPMcr">sigma models</a>. It was originally proposed as a model of the <a href="/facts/Nucleon/6fguU9Xk">nucleon</a> by (and named after) <a href="/facts/Tony_Skyrme/5tzyD2IS">Tony Skyrme</a> in 1961. As a <a href="/facts/Topological_soliton/Hqrvx2Lj">topological soliton</a> in the <a href="/facts/Pion/x5HamzG3">pion</a> <a href="/facts/Field_theory_(physics)/FJdAKeRA">field</a>, 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 <a href="/facts/Solid-state_physics/Cmc6hvyR">solid-state physics</a>, as well as having ties to certain areas of <a href="/facts/String_theory/HUJFIPYH">string theory</a>.
Skyrmions as topological objects are important in <a href="/facts/Solid-state_physics/Cmc6hvyR">solid-state physics</a>, especially in the emerging technology of <a href="/facts/Spintronics/dAWl8rcI">spintronics</a>. A two-dimensional <a href="/facts/Magnetic_skyrmion/KVLjJpxX">magnetic skyrmion</a>, as a topological object, is formed, e.g., from a 3D effective-spin "hedgehog" (in the field of <a href="/facts/Micromagnetics/ssksKTWS">micromagnetics</a>: out of a so-called "<a href="/facts/Bloch_sphere/CvgaFMNf">Bloch point</a>" singularity of homotopy degree +1) by a <a href="/facts/Stereographic_projection/oVyMrWqR">stereographic projection</a>, 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 <a href="/facts/Spinor_field/z88hf7ps">spinor field</a> such as for example <a href="/facts/Photon/mFNhAEzA">photonic</a> or <a href="/facts/Exciton-polaritons/qkpq8YFe">polariton fluids</a> the skyrmion topology corresponds to a full Poincaré beam (a <a href="/facts/Spin_(physics)/4Jvp7e8P">spin</a> <a href="/facts/Quantum_vortex/0Tzjncgk">vortex</a> comprising all the states of <a href="/facts/Polarization_(waves)/fP33m0eD">polarization</a> mapped by a stereographic projection of the <a href="/facts/Poincar%C3%A9_sphere_(optics)/fP33m0eD">Poincaré sphere</a> to the real plane). A dynamical pseudospin skyrmion results from the stereographic projection of a rotating polariton Bloch sphere in the case of dynamical full Bloch beams.
Skyrmions have been reported, but not conclusively proven, to appear in <a href="/facts/Bose%E2%80%93Einstein_condensate/76peCwfW">Bose–Einstein condensates</a>, thin magnetic films, and chiral nematic <a href="/facts/Liquid_crystals/ehCCST89">liquid crystals</a>, as well as in free-space optics.
As a model of the <a href="/facts/Nucleon/6fguU9Xk">nucleon</a>, the topological stability of the skyrmion can be interpreted as a statement that the baryon number is conserved; i.e. that the <a href="/facts/Proton/clCjepXP">proton</a> 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.
Hollowed-out skyrmions form the basis for the <a href="/facts/Chiral_bag_model/6fguU9Xk">chiral bag model</a> (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 <a href="/facts/Dan_Freed/5EF4xX8G">Dan Freed</a>. This can be interpreted as a foundation for the duality between a <a href="/facts/Quantum_chromodynamics/3cA2ctyb">quantum chromodynamics</a> (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 <a href="/facts/Quantum_superposition/4z1UJg9o">quantum superposition</a> of baryons and resonance states. It could be predicted from some nuclear matter properties.

Skyrmion open-in-new

Skyrmion