Ginzburg-Landau equations for a d-wave superconductor with paramagnetic impurities

Ginzburg-Landau (GL) equations for a d-wave superconductor with a repulsive s-wave interaction between electrons in the presence of paramagnetic impurities are microscopically derived based on the Born approximation. The diagrammatic relationships for the impurity-averaged product of Green's functions are algebraically established. The effect of paramagnetic impurities on the transition temperature and the London penetration depth are discussed. GL equations for a superconductor with both s-wave and d-wave pairing interactions are also examined. We show that the transition temperature for a superconductor with an s-wave symmetry is suppressed twice as rapidly as that with a d-wave symmetry in the dilute impurity limit if the strength of the spin-non-flip scattering is much weaker than the spin-flip interaction.