Structures of single vortex and vortex lattice in ad-wave superconductor

The structures of a single vortex and vortex lattice in a superconductor with $d_{x^2-y^2}$ symmetry are studied self-consistently employing a recently developed Ginzburg-Landau theory. Near a single vortex, we found that an $s$-wave component of the order parameter is always induced, and it causes the local magnetic-field distribution and the $d$-wave order parameter to have a fourfold anisotropy. It is shown that there is a strong correlation between the structure of a single vortex and the shape of the vortex lattice. Our numerical calculation indicates that the structure of the vortex lattice is always oblique except for temperatures very close to $T_c$ where it becomes triangular. The possible connection of the result with experiment is also discussed.