Influence of electron-phonon interaction on spin-fluctuation-induced superconductivity

We investigate the interplay of the electron-phonon and the spin-fluctuation interaction in the superconducting state of YBa₂Cu₃O₇. The spin fluctuations are described within the nearly antiferromagnetic Fermi-liquid theory and the phonons are treated using a shell-model calculation of all phonon branches. The electron-phonon coupling is calculated using rigidly displaced ionic potentials screened by a background dielectric constant ε_∞ and by holes within the CuO₂ planes. We get a superconducting state with d_x²-y² symmetry whose origin is antiferromagnetic spin fluctuations. The phononic contribution of all phonon modes of the system to the d-wave pairing interaction is attractive. This gives a positive isotope effect. The size of the isotope exponent depends strongly on the relative strength of the electron-phonon and spin-fluctuation coupling. Due to the strong electronic correlations no phononic induced superconducting state of s-wave character, is possible.