Effect of anisotropic impurity scattering on the superfluid density and transition temperature in a d-wave superconductor

We study the effect of the anisotropic impurity scattering in a d-wave superconductor by taking into account the non-s-wave phase shifts of the impurity potential. We compute the transition temperature, superfluid density, and the residual density of states as a function of the impurity concentration. They depend strongly on the values of the phase shift. The inclusion of a non-s-wave component can make the suppression of the transition temperature weaker than the purely s-wave approximation when it is plotted against the zero-temperature value of the superfluid density. In the Ginzburg-Landau region we derive general expressions for the various physical quantities to discuss the effect of an arbitrary phase shift. [S0163-1829(99)09033-5].