Localization corrections and small-q phonon-mediated unconventional superconductivity in the cuprates

Taking into account the first localization corrections in the electron-impurity self-energy we study the effect of non-magnetic impurities on unconventional superconductivity (SC) mediated by small-q electron-phonon scattering. We show that when van Hove singularities are close to the Fermi level making the electronic system anisotropic as in the high-$T_c$ oxides, both the d-wave and s-wave states are sensitive to non-magnetic impurities and beyond a critical impurity concentration SC disappears in {\it both gap symmetry channels}. Impurity doping may induce a first order transition from d-wave to s-wave SC, but no saturation of the impuruty effect is reported due to the intrinsically anisotropic character of the localization corrections in this context.