Pairing fluctuation theory of high Tc superconductivity in the presence of nonmagnetic impurities

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The pseudogap phenomena in the cuprate superconductors requires a theory beyond the mean field BCS level. A natural candidate is to include strong pairing fluctuations, and treat the two-particle and single particle Green's functions self-consistently. At the same time, impurities are present in even the cleanest samples of the cuprates. Some impurity effects can help reveal whether the pseudogap has a superconducting origin and thus test various theories. Here we extend the pairing fluctuation theory for a clean system [Phys. Rev. Lett. 81, 4708 (1998)] to the case with nonmagnetic impurities. Both the pairing and the impurity T matrices are included and treated self-consistently. We obtain a set of three equations for the chemical potential μ, Tc, the excitation gap Δ(Tc) at Tc, or μ, the order parameter Δsc, and the pseudogap Δpg at temperature T<Tc, and study the effects of impurity scattering on the density of states, Tc and the order parameter, and the pseudogap. Both Tc and the order parameter as well as the total excitation gap are suppressed, whereas the pseudogap is not for given T≤ Tc. Born scatterers are about twice as effective as unitary scatterers in suppressing Tc and the gap. In the strong pseudogap regime, pair excitations contribute a new T³/² term to the low T superfluid density. The initial rapid drop of the zero T superfluid density in the unitary limit as a function of impurity concentration nᵢ also agrees with experiment.