Influence of Electron-Phonon Interaction on Spin Fluctuation Induced Superconductivity

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We investigate the interplay of the electron-phonon and the spin fluctuation interaction for the superconducting state of YBa₂Cu₃O₇. The spin fluctuations are described within the nearly antiferromagnetic Fermi liquid theory, whereas 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. Taking into account both interactions we get a superconducting state with dₓ₂₋y₂-symmetry, whose origin are antiferromagnetic spin fluctuations. The investigation of all phonon modes of the system shows that the phononic contribution to the d-wave pairing interaction is attractive. This is a necessary prerequisite for 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, which is always of s-wave character, is possible.