Influence of Electron-Phonon Interaction on Spin Fluctuation Induced Superconductivity

Abstract

We investigate the interplay of the electron-phonon and the spin fluctuation interaction for the superconducting state of YBa${}_2$Cu${}_3$O${}_7$. 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 ${\epsilon }_{\infty }$ and by holes within the CuO${}_2$ planes. Taking into account both interactions we get a superconducting state with $d_{x^2-y^2}$-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.

11 pages, 12 figures

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