Motivated by the recent discovery of the anomalously nearest-neighbor attraction arising from the electron-phonon coupling, we quantitatively investigate the enhancing effects of this additional attractive channel on the
d-wave superconductivity based on dynamic cluster quantum Monte Carlo calculations of a doped two-dimensional extended Hubbard model with nearest-neighbor attraction $\ensuremath{-}V$. Focusing on the range of $0<\ensuremath{-}V/t\ensuremath{\le}2$, our simulations indicate that the dynamics of
d-wave projected pairing interaction is attractive at all frequencies and increases with
∣V∣. Moreover, turning on $\ensuremath{-}V$ attraction enhances the $(\ensuremath{\pi},\ensuremath{\pi})$ spin fluctuations but only enhances (suppresses) the charge fluctuations for small (large) momentum transfer. Thus, at $V/t=\ensuremath{-}1$ relevant to the ``holon folding branch'', the charge fluctuations are insufficient to compete with the
d-wave pairing interaction strengthened by enhanced spin fluctuations. Our work suggests the underlying rich interplay between the spin and charge fluctuations in giving rise to the superconducting properties.
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.
The nearest-neighbor superexchange-mediated mechanism for ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductivity in the one-band Hubbard model faces the challenge that nearest-neighbor Coulomb repulsion can be larger than superexchange. To answer this question, we use cellular dynamical mean-field theory (CDMFT) with a continuous-time quantum Monte Carlo solver to determine the superconducting phase diagram as a function of temperature and doping for on-site repulsion
U=9t and nearest-neighbor repulsion
V=0,2t,4t. In the underdoped regime,
V increases the CDMFT superconducting transition temperature
Tcd even though it decreases the superconducting order parameter at low temperature for all dopings. However, in the overdoped regime
V decreases
Tcd. We gain insight into these paradoxical results through a detailed study of the frequency dependence of the anomalous spectral function, extracted at finite temperature via the MaxEntAux method for analytic continuation. A systematic study of dynamical positive and negative contributions to pairing reveals that even though
V has a high-frequency depairing contribution, it also has a low frequency pairing contribution since it can reinforce superexchange through $J=4{t}^{2}/(U\ensuremath{-}V)$. Retardation is thus crucial to understanding pairing in doped Mott insulators, as suggested by previous zero-temperature studies. We also comment on the tendency to charge order for large
V and on the persistence of
d-wave superconductivity over extended-
s or
s+d wave.
Using a dynamical cluster quantum Monte Carlo approximation, we investigate the
d-wave superconducting transition temperature
Tc in the doped two-dimensional repulsive Hubbard model with a weak inhomogeneity. The inhomogeneity is introduced in the hoppings ${t}^{\ensuremath{'}}$ and
t in the form of a checkerboard pattern where
t is the hopping within a $2\ifmmode\times\else\texttimes\fi{}2$ plaquette, and ${t}^{\ensuremath{'}}$ is the hopping between the plaquettes. We find inhomogeneity suppresses
Tc. The characteristic spin excitation energy and the strength of
d-wave pairing interaction decrease with decreasing
Tc, suggesting a strong correlation between these quantities.
We study, through the variational Monte Carlo technique, an extended Hubbard model away from half filled band density which contains two competing nearest-neighbor interactions: a superexchange J favoring d-wave superconductivity and a repulsion V opposing it. We find that the on-site repulsion U effectively enhances the strength of J while suppressing that of V, thus favoring superconductivity. This result shows that attractions which do not involve charge fluctuations are very well equipped against strong electron-electron repulsion so much to get advantage from it.
We compute the two-particle quantities relevant for superconducting correlations in the two-dimensional Hubbard model within the dynamical cluster approximation. In the normal state we identify the parameter regime in density, interaction, and second-nearest-neighbor hopping strength that maximizes the d_{x^{2}-y^{2}} superconducting transition temperature. We find in all cases that the optimal transition temperature occurs at intermediate coupling strength, and is suppressed at strong and weak interaction strengths. Similarly, superconducting fluctuations are strongest at intermediate doping and suppressed towards large doping and half filling. We find a change in sign of the vertex contributions to d_{xy} superconductivity from repulsive near half filling to attractive at large doping. p-wave superconductivity is not found at the parameters we study, and s-wave contributions are always repulsive. For negative second-nearest-neighbor hopping the optimal transition temperature shifts towards the electron-doped side in opposition to the van Hove singularity, which moves towards hole doping. We surmise that an increase of the local interaction of the electron-doped compounds would increase T_{c}.