Predictions for impurity-induced Tc suppression in the high-temperature superconductors.

We address the question of whether anisotropic superconductivity is compatible with the evidently weak sensitivity of the critical temperature Tc to sample quality in the high-Tc copper oxides. We examine this issue quantitatively by solving the strongcoupling Eliashberg equations numerically as well as analytically for s-wave impurity scattering within the second Born approximation. For pairing interactions with a characteristically low energy scale, we find an approximately universal dependence of the d-wave superconducting transition temperature on the planar residual resistivity which is independent of the details of the microscopic pairing. These results, in conjunction with future systematic experiments, should help elucidate the symmetry of the order parameter in the cuprates.