Superconductivity of Strongly Correlated Electrons on a Square Lattice: Vertex Corrections to Eliashberg Equations

The two-dimensional Hubbard model coupled to phonons has been considered in the U→ ∞ limit. We have introduced fluctuations of the auxiliary boson fields over their mean-field value to allow for the phonon-free pairing mechanism. Vertex corrections to the Eliashberg equations in electron–boson and electron–phonon channels have been taken into account. The superconducting transition temperature Tchas been evaluated as a function of the occupation number. It has been found that phonon-mediated and correlation-mediated pairing mechanisms cooperate in the formation of a d-wave superconducting state for physically interesting concentrations of holes. It is vertex corrections in the electron–phonon channel that causes vanishing of Tcwhen approaching half-filling. Vertex corrections in the electron–boson channel are of minor importance in the underdoped region. However, they suppress the superconducting transition temperature at optimal doping and in the overdoped region causing the occupation number dependence of Tcto become similar to the experimentally observer behavior.