Topological solitons in anisotropic superconductors

Superconductors subjected to a magnetic field can host topological solitons called "vortices", spatially localized tubes of magnetic flux and energy that cannot dissipate for topological reasons. Their dynamics and properties are key to understanding many important effects in superconductivity. 

The conventional mathematical model of superconductivity treats vortices as solutions of a nonlinear field theory, called Ginzburg-Landau theory, that is homogeneous and isotropic in space, with a single field (or "order parameter") representing a single condensate of electron pairs. However, real superconductors often have highly anisotropic crystal structures, and can support electron condensates in more that one pairing state, so a more realistic model should have several fields and be spatially anisotropic. The behaviour of vortices (and domain walls, and Skyrmions) in these anisotropic multicomponent Ginzburg-Landau models is more richer and less well understood than in the simpler, conventional model. 

The purpose of this project is to study the properties of these various topological solitons in multicomponent Ginzburg-Landau theory, guided by a mixture of computer simulation, analytic approximation and geometry.