On the structure of fractional degree vortices in a spinor Ginzburg–Landau model

We consider a Ginzburg–Landau functional for a complex vector order parameter Ψ=(ψ+,ψ−), whose minimizers exhibit vortices with half-integer degree. By studying the associated system of equations in R2 which describes the local structure of these vortices, we show some new and unconventional properties of these vortices. In particular, one component of the solution vanishes, but the other does not. We also prove the existence and uniqueness of equivariant entire solutions, and provide a second proof of uniqueness, valid for a large class of systems with variational structure.