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The pseudogap phenomena in the cuprate superconductors requires a theorybeyond the mean field BCS level. A natural candidate is to include strongpairing fluctuations, and treat the two-particle and single particle Green'sfunctions self-consistently. At the same time, impurities are present in eventhe cleanest samples of the cuprates. Some impurity effects can help revealwhether the pseudogap has a superconducting origin and thus test varioustheories. 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 treatedself-consistently. We obtain a set of three equations for the chemicalpotential $\mu$, $T_c$, the excitation gap $\Delta(T_c)$ at $T_c$, or $\mu$,the order parameter $\Delta_{sc}$, and the pseudogap $\Delta_{pg}$ attemperature $T<T_c$, and study the effects of impurity scattering on thedensity of states, $T_c$ and the order parameter, and the pseudogap. Both $T_c$and the order parameter as well as the total excitation gap are suppressed,whereas the pseudogap is not for given $T\le T_c$. Born scatterers are abouttwice as effective as unitary scatterers in suppressing $T_c$ and the gap. Inthe strong pseudogap regime, pair excitations contribute a new $T^{3/2}$ termto 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$n_i$ also agrees with experiment.Comment: 16 journal pages with 20 figures embedded, formatted using REVTeX

physical review. b, condensed matter

Pairing fluctuation theory of high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>superconductivity in the presence of nonmagnetic impurities

Pairing fluctuation theory of high-Tcsuperconductivity in the presence of nonmagnetic impurities