Ginzburg-Landau Equations and Vortex Structure of adx2−y2Superconductor

We derive microscopically the Ginzburg-Landau equations of a superconductor with $d_{x^2{-y}^2}$ symmetry. The structure of a single vortex in such a superconductor is determined by solving these equations. The most interesting feature of the vortex structure is the opposite winding $s$-wave component induced near the vortex core. Far away from the center of the vortex core, the winding of the $s$-wave component becomes more complicated and the magnitude shows strong anisotropy. The distributions of supercurrent and local magnetic field also show anisotropic behaviors.