ar X iv : c on d - m at / 9 51 11 30 v 1 2 7 N ov 1 99 5 Superconducting state properties of a d - wave superconductor with mass anisotropy

YBa 2 Cu 3 O 7 (YBCO) exhibits a large anisotropy between the a and b axes in the CuO 2 planes because of the presence of CuO chains. In order to account for such an anisotropy we develop a Ginzburg-Landau (GL) theory for an anisotropic d-wave superconductor in an external magnetic field, based on an anisotropic effective mass approximation within CuO 2 planes. The anisotropic parameter λ = m x /m y , where m x (m y) is the effective mass in the x (y) direction, is found to have significant physical consequences: In the bulk case, there exist both the sand d-wave order parameters with the same transition temperature, as long as λ = 1. The GL equations are also solved both analytically and numerically for the vortex state, and it is shown that both the sand d-wave components show a twofold symmetry, in contrast to the four-fold symmetry around the vortex, as expected for the purely d-wave vortex. With the deviation of λ from unity, the opposite winding between the sand d-wave components observed in the purely d-wave case is gradually taken over by the same winding number. The vortex lattice is found to have oblique structure in a wide temperature range with the precise shape depending on the anisotropy.