Phonon-induced and phonon-free superconductivity in correlated systems: Eliashberg equations for the two-dimensional Hubbard model

The problem of phonon-induced and phonon-free superconductivity in the two-dimensional Hubbard model has been addressed. We have generalized the Eliashberg equations to account for both on-site and intersite pairing and consider the electron-electron and electron-phonon channels on an equal footing. This approach allows for the discussion of pairing and depairing properties of the local repulsive interaction. We demonstrate the possibility of cooperation between electron-phonon and electron-electron interaction in the stabilization of the d-wave superconductivity, in particular close to the experimental value of optimal doping (δ ≅ 0.15). We have also discussed the problem of phonon-induced superconductivity in the two-dimensional Hubbard model close to the metal-insulator transition. Here, the Coulomb correlations have been incorporated within the Hubbard 1 approximation whereas the superconductivity is treated by the Eliashberg scheme. The results support the view that a d-wave component dominates in the gap function. (author)