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A theory of nonmagnetic impurities in an anisotropic superconductor including the effect of anisotropic (momentum-dependent) impurity scattering is given. It is shown that for a strongly anisotropic scattering the reduction of the pair-breaking effect of the impurities is large. For a significant overlap between the anisotropy functions of the scattering potential and that of the pair potential and for a large amount of anisotropic scattering rate in impurity potential the superconductivity becomes robust vis a vis impurity concentration. The implications of our result for YBCO high-temperature superconductor are discussed. The experimental data of electron irradiationinduced T c suppression (Phys. Rev. B50, 15967 (1994)) is understood quantitatively and a good qualitative agreement with the ion (N e + ) damage and P r substitution-induced T c decrease data (Phys. Rev. B50, 3266 (1994)) is obtained. 74.62.Dh Typeset using REVT E X 1

We discuss the weak-coupling BCS theory of a superconductor with the impurities, accounting for their anisotropic momentum-dependent potential.The impurity scattering process is considered in the t-matrix approximation and its influence on the superconducting critical temperature T c is studied in the Born and unitary limit for a d x 2 −y 2 -and (d x 2 −y 2 + s)-wave superconductors. We observe a significant dependence of the pair-breaking strength on the symmetry of the scattering potential and classify the impurity potentials according to their ability to alter T c . A good agreement with the experimental data for Zn doping and oxygen irradiation in the overdoped cuprates is found.

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We present a theory of combined nonmagnetic and magnetic impurity scattering in anisotropic superconductors accounting for the momentum-dependent impurity potential. Applying the model to the d-wave superconducting state, we obtain a quantitative agreement with the initial suppression of the critical temperature due to Zn and Ni substitutions as well as electron irradiation defects in the cuprates. We suggest, that the unequal pair-breaking effect of Zn and Ni may be related to a different nature of the magnetic moments induced by these impurities.Comment: 5 pages, 3 tables, RevTex, to be published in Phys. Rev.