Impurity effects in<i>d</i>-wave superconductors

Abstract

Impurity scattering will provide a crucial test for d-wave superconductor in high ${\mathit{T}}_{\mathit{c}}$ copper-oxides. Among other things we calculate the static spin susceptibility and find a simple relation between the susceptibility and superfluid density ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$(T)=[\ensuremath{\lambda}(0)/\ensuremath{\lambda}(T)${]}^{2}$ is broken in the presence of impurity scattering. Also we generalize Lee's universal conductivity at T=0 K. In the presence of a finite concentration of impurity, the order parameter ${\mathrm{\ensuremath{\Delta}}}_{00}$ in the conductivity has to be replaced by \ensuremath{\Delta}(\ensuremath{\Gamma},0) and \ensuremath{\Delta}(\ensuremath{\Gamma},0) is accessible through the tunneling experiment of the density of states.