Vortices with antiferromagnetic cores in the SO(5) model of high-temperature superconductivity

We consider the problem of superconducting Ginzburg-Landau (GL) vortices with antiferromagnetic cores which arise in Zhang’s SO(5) model of antiferromagnetism (AF) and high-temperature superconductivity (SC). This problem was previously considered by Arovas et al. who constructed approximate “variational” solutions, in the large $\kappa$ limit, to estimate the domain of stability of such vortices in the temperature-chemical potential phase diagram. By solving the GL equations numerically for general $\kappa ,$ we show that the amplitude of the antiferromagnetic component at the vortex core decreases to zero continuously at a critical value of the AF-SC anisotropy $(g\approx 0.25)$ which is essentially independent of $\kappa$ for large $\kappa .$ The magnetic field profile, the vortex line energy and the value of the B field at the center of the vortex core, as functions of anisotropy are also presented.