GINZBURG-LANDAU EQUATIONS FOR A D-WAVE SUPERCONDUCTOR WITH APPLICATIONS TO VORTEX STRUCTURE AND SURFACE PROBLEMS

The properties of a d (x2-y2)-wave superconductor in an external magne tic held are investigated on the basis of Gorkov's theory of weakly co upled superconductors. The Ginzburg-Landau (GL) equations, which gover n the spatial variations of the order parameter and the supercurrent, are microscopically derived. The single vortex structure and surface p roblems in such a superconductor are studied using these equations. It is shown that the d-wave vortex structure is very different from the conventional s-wave vortex: the s-wave and d-wave components, with the opposite winding numbers, are found to coexist in the region near the vortex core. The supercurrent and local magnetic field around the vor tex are calculated. Far away from the vortex core, both of them exhibi t a fourfold symmetry, in contrast to an s-wave superconductor. The su rface problem in a d-wave superconductor is also studied by solving th e GL equations. The total order parameter near the surface is always a real combination of s- and d-wave components, which means that the pr oximity effect cannot induce a time-reversal symmetry-breaking state a t the surface.