Symmetric Vortex Solutions in the U(1) and SO(5) Ginzburg-Landau Models of Superconductivity

We present a summary of analytical and numerical results obtained with A. J. Berlinsky and T. Giorgi on the core structure of symmetric vortices in a Ginzburg-Landau model based on S. C. Zhang’s SO(5) theory of high temperature superconductivity and antiferromagnetism. We find that the usual superconducting vortices (with normal phase in the central core region) become unstable at a critical value of the chemical potential, giving rise to a new type of vortex profile with antiferromagnetic ordering in the core region. In the process we revisit the traditional U(1)-Ginzburg-Landau vortices and prove the uniqueness of symmetric solutions of degree d for κ ≥ |d|√2.