Fundamental aspects of skyrmions in condensed matter systems
Skyrmions as topological multidimensional solitons are exceptional, as explained by the Derrick theorem that forbids existence of non-linear, smooth, and localized textures in generic continuum models of ordered states.
I will discuss three known ways to overcome this limitation in condensed matter to create particle-like states:
(i) Skyrmions as elementary composite excitations in two-dimensional electron systems
(ii) The Skyrme models employing higher-order gradient terms in a classical field theory.
(iii) Dzyaloshinskii models in the framework of Landau-Ginzburg free energy functionals with chiral Lifshitz invariants.
The realizations of the different types of skyrmions in magnetic systems and their properties will be presented along with some of their connections to other systems, ranging from non-centrosymmetric superconductors via mesophases in chiral liquid crystals to dense nuclear matter.