Effect of vertex corrections on the correlation functions and the gap equation in the spin fluctuation-induced superconductors

Abstract

We calculate self-consistently the Green's function and dynamical spin susceptibility on the basis of the self-consistent renormalization (SCR) theory for the two-dimensional single-band Hubbard model near half-filling. Not only the vertex corrections to the susceptibility but also those to the self-energy are incorporated in our theory. The particle–particle irreducible vertex in the linearized gap equation is approximated by the maximally crossed diagrams generated by the bare interactions and the interactions resulting from the spin fluctuations. We find that the vertex corrections generally tend to enhance both antiferromagnetic fluctuations and the d-wave superconductivity.