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

Abstract

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 $\ensuremath{\kappa}$ 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 $\ensuremath{\kappa},$ 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 $(g\ensuremath{\approx}0.25)$ which is essentially independent of $\ensuremath{\kappa}$ for large $\ensuremath{\kappa}.$ 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.