In this paper, we analyze a simple extended Hubbard model with an intermediate on-site interaction (both repulsive and attractive) and a weak intersite attractive interaction. Following Hubbard decoupling approximations and introducing Hubbard subband operators, we obtain a generalized gap function for singlet s-wave pairing that explicitly depends on the Hubbard subband energies. For the on-site repulsive-interaction case, we find that the superconductivity is not destroyed in the intermediate-interaction regime, contrary to the prediction of a Hartree-Fock mean-field treatment. The essential consequence of the on-site repulsion is the formation of the Hubbard subbands separated by the Mott-Hubbard gap, and it is within these subbands that pairing induced by the intersite interaction occurs. For the attractive on-site interaction case, the on-site pairing amplitude is found to be proportional to the bandwidth, and the gap function has contributions from both on-site and intersite pairing. The relevance of the model to high-temperature superconductivity is discussed.
Phase diagram of the extended Hubbard model with on-site repulsion and nearest-neighbor attraction is obtained for various band fillings, covering the strong-correlation regime, in one dimension by mapping the system to the Tomonaga-Luttinger model with use of exact diagonalization of finite systems. We find that the strong electron correlation makes the superconducting region, which is sandwiched between spin-density wave and phase-separation regions, significantly wider than expected from the weak-coupling g-ology.
The superfluid characteristics of the attractive Hubbard model are analyzed for any coupling |U| and arbitrary electron concentration (0n2) by means of the slave-boson mean-field method and also by the perturbative treatment of the strong-coupling limit. The slave boson method takes into account correlations of electrons and yields a reliable description of the crossover from BCS-type superconductivity to local pair (composite bosons) superconductivity with increasing |U|. The results for the ground state (the free energy, the gap in the excitation spectrum) and the electromagnetic characteristics (the critical magnetic field, the London penetration depth, the coherence length) are compared with those obtained by the Hartree-Fock approximation and by the self-consistent second-order perturbation theory in the weak-coupling limit as well as with those obtained using perturbational approaches in the strong-coupling limit. We show that the slave-boson method, in contrast to the Hartree-Fock approximation, gives credible results for all investigated quantities in the whole interaction range, interpolating smoothly between the BCS and local pair regimes. A comparison of theoretical predictions for our simple model with experimental data for various families of short-coherence-length superconductors suggests that the best agreement can be obtained for intermediate values of the local attraction. \textcopyright{} 1996 The American Physical Society.
Many theoretical approaches find
d-wave superconductivity in the prototypical one-band Hubbard model for high-temperature superconductors. At strong coupling ($U\ensuremath{\ge}W$, where
U is the on-site repulsion and
W=8t the bandwidth) pairing is controlled by the exchange energy
J=4t2/U. One may then surmise, ignoring retardation effects, that near-neighbor Coulomb repulsion
V will destroy superconductivity when it becomes larger than
J, a condition that is easily satisfied in cuprates, for example. Using cellular dynamical mean-field theory with an exact diagonalization solver for the extended Hubbard model, we show that pairing at strong coupling is preserved, even when $V\ensuremath{\gg}J$, as long as $V\ensuremath{\lesssim}U/2$. While at weak coupling
V always reduces the spin fluctuations and hence
d-wave pairing, at strong coupling, in the underdoped regime, the increase of $J=4{t}^{2}/(U\ensuremath{-}V)$ caused by
V increases binding at low frequency while the pair-breaking effect of
V is pushed to high frequency. These two effects compensate in the underdoped regime, in the presence of a pseudogap. While the pseudogap competes with superconductivity, the proximity to the Mott transition that leads to the pseudogap, and retardation effects, protect
d-wave superconductivity from
V.
Slave boson mean-field studies of the ground state of the Hubbard model with correlated hopping were performed. The approach qualitatively recovers the exact results for the case when the hopping integral
t equals the correlated hopping integral
X. The phase diagram for the strongly correlated state with only singly occupied sites, the weakly correlated state, where single and double occupation is allowed, and for the superconducting state, was determined for any value of
X and any electron concentration
n. At the half-filled band
(n=1) a direct transition from the superconductor to the Mott insulator was found. In the region of strong correlations the superconducting solution is stable for
n close to 1, in contrast to the case of weak correlations, in which superconductivity occurs at $n\ensuremath{\approx}0$ and $n\ensuremath{\approx}2.$ We have also found that strong correlations change the characteristics of the superconducting phase, e.g., the gap in the excitation spectrum exhibits a nonexponential dependence on the on-site Coulomb integral
U close to the phase-transition point.
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.