RENORMALIZATION OF THE ELECTRON-PHONON INTERACTION BY STRONG ELECTRONIC CORRELATIONS IN HIGH-T-C SUPERCONDUCTORS

The renormalization of the electron-phonon interaction by strong elect ronic correlations is studied using a one-band Hubbard model with infi nite repulsion and nearest (t model) and nearest and second-nearest (t t' model) neighbor hopping terms and an on-site electron-phonon coupli ng. Using Hubbard's X operators and an extension from 2 to N degrees o f freedom for the electrons the leading contributions for the electron self-energy and the vertex function in 1/N and the electron-phonon co upling constant are given and numerically evaluated for a square latti ce. We find that the momentum dependence of the vertex function depend s strongly on doping: For large dopings it is rather weak, with decrea sing doping it becomes more and more pronounced leading to a strong re duction of the vertex at larger momentum transfers until, for very sma ll dopings, the vertex essentially consists of a forward scattering pe ak with a width proportional to the doping. This behavior occurs both in the t and the tt' models and also in one dimension where analytic e xpressions are derived. Correlation effects also change alpha(2)F in g eneral: The full-symmetric component alpha(2)F(1) is in the t model so mewhat, in the tt' model rather strongly suppressed, especially near h alf-filling; the other symmetry components alpha(2)F(i) with i=2,...,5 increase strongly with decreasing doping and are of similar magnitude as alpha(2)F(1) near half-filling. Including also direct Coulomb repu lsion nontrivial symmetries such as d wave become more stable than the s-wave order parameter below a critical value for the doping even for the considered phonon-mediated superconductivity. Most dramatic, howe ver, is the quenching of the resistivity due to electron-phonon scatte ring both in the t and the tt' models at intermediate and small doping s. This result may explain the absence of phonon features in the exper imental transport coefficients of high-T-c compounds.