Effect of antiferromagnetic spin fluctuations on the phonon-mediated pair interaction in high-T _c superconductors

Abstract

We investigate the effect of electronic correlations on the phonon-mediated part of the pair interaction by including the effect of an exchange interaction U between the electrons in the calculation of the phonon frequencies and the electron-phonon vertices. We employ two RPA models: the first, consisting of a direct Coulomb interaction in addition to U, leads to softer phonons and an enhanced attractive s-wave phonon-induced electron-electron interaction while the second, a pure Hubbard model, yields the opposite effect. The weak-coupling selfconsistency equation for the order parameter in the 2D first Brillouin zone is solved for a tight-binding band. The change of T_c arises primarily from the change of the phonon frequencies rather than from the vertex renormalization.