PHONON-MEDIATED UNCONVENTIONAL SUPERCONDUCTIVITY IN STRONGLY CORRELATED SYSTEMS

We propose an adiabatic approach for Hubbard models in the Fermi-liqui d regime coupled to phonons. The Hubbard parameters are associated wit h the bandwidth W via an interpolation formula between the trivial for W strong-and weak-coupling limits of Hubbard models. Phonons are intr oduced via an adiabatic random-phase approximation scheme. We obtain s imple conditions for phonon-driven instabilities in a Fermi liquid wit h short-ranged interactions. We report phonon-driven instabilities wit hout nesting and describe the elimination of the Peierls instability i n a nested system by Coulomb correlations. We also report the possibil ity for a phonon-driven phase separation (PS) instability as well as t he strong enhancement of forward processes in the effective electron-p honon scattering near the phase separation instability. We show that t he proximity to PS induces momentum decoupling (MD) in superconductivi ty which implies a tendency for decorrelation between the physics in t he different regions of the Fermi surface. MD could induce anisotropic superconductivity with unconventional gap symmetry such as d wave. Wh ether anisotropy in the high-T-c oxides is driven by MD or by anisotro pic scattering (for example with spin fluctuations) becomes a crucial question. We discuss some qualitative implications of MD that explain puzzling qualitative aspects of superconductivity in the oxides and co uld advocate that MD is at the origin of anisotropies. Such effects ar e the marginality of the superconducting gap symmetry for the condensa tion free energy and the resulting possibility of gap symmetry transit ions with the doping, the temperature dependence of the shape of the a nisotropy, and the behavior of the anomalous dip above the gap in the density of states. Pie also show that in the MD regime the orthorhombi c distortion of the CuO2 planes in YBa2Cu3O7 could be sufficient ro ex plain the mixing of s-gap components in the dominantly d-wave gap. On the other hand, if spin fluctuations mediate the pairing in YBa2Cu3O7, at least 25% of the condensate must be located in the chains. Our ana lysis could rehabilitate phonons as potential mediators of the pairing in all ''unconventional'' superconductors including heavy-fermion and organic compounds.