Impurity Scattering in a d-Wave Superconductor

The influence of (non-magnetic and magnetic) impurities on the transition temperature of a d-wave superconductor is studied anew within the framework of BCS theory. Pairing interaction decreases linearly with the impurity concentration. Accordingly T_c suppression is proportional to the (potential or exchange) scattering rate, 1/τ, due to impurities. The initial slope versus 1/τ is found to depend on the superconductor contrary to Abrikosov–Gor'kov type theory. Near the critical impurity concentration T_c drops abruptly to zero. Because the potential scattering rate is generally much larger than the exchange scattering rate, magnetic impurities will also act as non-magnetic impurities as far as the T_c decrease is concerned. The implication for the impurity doping effect in high T_c superconductors is also discussed.