We study a two-orbital attractive Hubbard model with a repulsive Hund's exchange coupling
J as an idealized model for a two-band superconductor. This framework is motivated by a system where a large isotropic electron-phonon coupling drives the on-site Hubbard repulsion
U negative, while leaving the exchange term unaffected. We focus on the intra-orbital (intra-band) singlet superconducting phase and we solve the model at zero temperature and half-filling using Dynamical Mean-Field Theory. Already at
J=0, the two-orbital model features a superconductor-insulator transition as
∣U∣ grows, as opposed to the single-orbital case which remains superconducting for any
U<0. We find that a finite
J strengthens the effect of the attractive
U, both in the normal state and, more significantly, in the superconducting state. However, this pushes the system towards an effectively stronger coupling, hence to a faster transition to the insulating state. Remarkably, the transition from a superconductor to an insulator occurs with a vanishing quasi-particle weight
Z and in a scenario that recalls strongly correlated superconductivity close to a Mott transition, even though the present model is dominated by attractive interactions.
We investigate the attractive Hubbard model in infinite spatial dimensions by combining dynamical mean-field theory with a strong-coupling continuous-time quantum Monte Carlo method. By calculating the superfluid order parameter and the density of states, we discuss the stability of the superfluid state. In the intermediate-coupling region above the critical temperature, the density of states exhibits a heavy fermion behavior with a quasiparticle peak in the dense system, while a dip structure appears in the dilute system. The formation of the superfluid gap is also addressed.
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 ``dynamic'' Hubbard Hamiltonian describes interacting fermions on a lattice whose on-site repulsion is modulated by a coupling to a fluctuating bosonic field. We investigate one such model, introduced by Hirsch, using the determinant quantum Monte Carlo method. Our key result is that the extended
s-wave pairing vertex, repulsive in the usual static Hubbard model, becomes attractive as the coupling to the fluctuating Bose field increases. The sign problem prevents us from exploring a low enough temperature to see if a superconducting transition occurs. We also observe a stabilization of antiferromagnetic correlations and the Mott gap near half-filling, and a near linear behavior of the energy as a function of particle density which indicates a tendency toward phase separation.
An intricate interplay between superconductivity, pseudogap, and Mott transition, either bandwidth driven or doping driven, occurs in materials. Layered organic conductors and cuprates offer two prime examples. We provide a unified perspective of this interplay in the two-dimensional Hubbard model within cellular dynamical mean-field theory on a 2×2 plaquette and using the continuous-time quantum Monte Carlo method as impurity solver. Both at half filling and at finite doping, the metallic normal state close to the Mott insulator is unstable to d-wave superconductivity. Superconductivity can destroy the first-order transition that separates the pseudogap phase from the overdoped metal, yet that normal state transition leaves its marks on the dynamic properties of the superconducting phase. For example, as a function of doping one finds a rapid change in the particle-hole asymmetry of the superconducting density of states. In the doped Mott insulator, the dynamical mean-field superconducting transition temperature T(c)(d) does not scale with the order parameter when there is a normal-state pseudogap. T(c)(d) corresponds to the local pair formation temperature observed in tunneling experiments and is distinct from the pseudogap temperature.
The quantum Monte Carlo method is used to reexamine superconductivity in the single-band Hubbard model in two dimensions. Instead of the conventional pairing, we consider a ``correlated pairing,'' 〈c-${\mathrm{tilde}}_{\mathrm{i}\mathrm{\ensuremath{\uparrow}}}$c-${\mathrm{tilde}}_{{\mathrm{i}}^{|\mathrm{I}\mathrm{H}}\mathrm{\ensuremath{\downarrow}}}$〉 with c-${\mathrm{tilde}}_{\mathrm{i}\mathrm{\ensuremath{\sigma}}}$\ensuremath{\equiv}${\mathrm{c}}_{\mathrm{i}\mathrm{\ensuremath{\sigma}}}$(1-${\mathrm{n}}_{\mathrm{i}\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\sigma}}}$), which is inferred from the t-J model, the strong-coupling limit of the Hubbard model. The pairing in the d-wave channel is found to possess both a divergence like 1/T in the pairing susceptibility and a growth of the ground-state pairing correlation with sample size, indicating an off-diagonal long-range order near (but not exactly at) half-filling.