Vortex state in a d-wave superconductor

We discuss the physics of the vortex state in a d-wave superconductor, using the phenomenological Ginzburg-Landau theory, where many unusual phenomena arise from the small admixture of the s-wave component induced by spatial variations in the dominant d wave. Properties of an isolated vortex and of the Abrikosov vortex lattice are studied by means of analytic and numerical methods. An isolated vortex has a considerable structure, with four ''extra'' nodes in the s-wave order parameter symmerically placed around the core and an amplitude forming a four-lobe profile decaying as 1/r(2) at large distances. The supercurrent and magnetic-field distributions are also calculated. The Abrikosov lattice is in general oblique with the precise shape determined by the magnetic field and s-d mixing parameter epsilon(upsilon). The magnetic-field distribution in the Abrikosov state has two nonequivalent saddle points resulting in the prediction of a double peak line shape in mu SR and NMR experiments as a test of a d-wave symmetry. Detailed comparison is made with existing experimental data and experiments are proposed to test for the predicted effects.