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

Abstract

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 channel 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 ( ≃ 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 I 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.