Hubbard U Enhanced Superconductivity

We present a. study of the superconducting properties of models containing the Hubbard rnpulsion term. This strnng on-site repulsion is considered as a key ingTedient of the high tempera.turn superconductivity. Though the fact that for the normal, lovv temperature superconductors, rnpulsion destroys superconducting order, it is argued in the present thesis, that for the pairing of the d-·wave symmetry in the strongly correlated electronic systems its effect is to enhance and may be to cause superconductivity. Various methods such as Variational Monte Carlo, Gutzwiller Approximation, Time Dependent Hartree-Fock and Fixed Node Approximation have been used to investigate t - U - W model, t - U - J - V and pure Hubbard models. In this thesis, by considering correlations contribution to the BCS condensation energy due to the Hubbard U it is shown that the latter lowers the total energy of a d-wave superconductor in the weak coupling limit, thus enforcing the stability of such superconductor. This effect appears to be mainly due to the enhancement of the spin fluctuations near the nesting vector Q = ( π, π). It is then studied the crossover from weak to strong coupling regimes in t - U - J - V model by increasing U. Remarkably in this model an order of magnitude growth of the superconducting order parameter is found and explained as being due to the Hubbard repulsion. vVe fi.nd also, that the pairings, originally induced by spin or charge fluctuations upon increase of U are differently renormalized, being the former enhanced, while the latter suppressed. In the fi.nal part of the thesis the superconductivity in the pure Hubbard model is carefully studied by means of Variational Monte Carlo and related numerical methods aimed to improve variational results. VVe observe the onset of strong coupling superconductivity at U/t ~ 7 within the Fixed Node Approximation in the systems of large size and compare our results for small clusters with those of Lanczos diagonalization. We show that Variational Monte Carlo, though overestimating the quasiparticle weight (ZvMc > Zexact) succeeds in reproducing the correct pairing between quasiparticles.