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.
As a model for high-
Tc superconductors, a two-band Hubbard model is proposed. When the Coulomb interactions are introduced between the \ensuremath{\alpha} and \ensuremath{\beta} orbitals, an effective attraction of carriers in the \ensuremath{\beta} (doped) band is shown to arise in an appropriate condition. The quantum Monte Carlo method is used to confirm the occurrence of Cooper pairing in finite two-band Hubbard systems. The attraction, which also appears in the density-density correlation, enhances the on-site singlet Cooper pair-pair correlation in the \ensuremath{\beta} band and suppresses the antiferromagnetic spin-spin correlation in the \ensuremath{\alpha} band. The criterion for the pairing and the nature of the pairing are discussed. Thus we provide a mechanism of superconductivity specific to strongly correlated two-band systems.
We investigate a minimal two-orbital Hubbard model with intra- and inter-orbital nearest-neighbor hopping
t and
t~, as well as intra- and inter-orbital density-density interactions
U and
U′ by means of variational ansätze based on Jastrow-Slater wave functions within quantum Monte Carlo techniques. To focus on the electronic mechanisms of superconductivity, we restrict the variational ansätze to uniform nonmagnetic states with an explicit pairing amplitude and compute the pairing correlations as a function of filling and model parameters. At
U/t=10, superconducting correlations are highly enhanced by the presence of inter-orbital terms,
U′ and
t~. For
t~=0, a finite value of
U′ effectively screens the intra-orbital repulsion
U, producing a shift in the superconducting dome. Consequently, inter-orbital repulsion yields a sizable increase in electron pairing compared to the single-orbital baseline. Furthermore, introducing a finite
t~ provides an additional boost to superconducting correlations, an effect driven by the simultaneous presence of flat and broad bands in the electronic structure.
We study the effect of random dilution of attraction centers on electron pairing in a generalization of the negative
U Hubbard model where the interaction
Ui, defined on the two dimensional lattice, can be
−∣U∣ and 0 with probability
c and
1−c depending on the lattice site
i. Using the determinant quantum Monte Carlo approach, we find the critical concentration
c0 of negative centers which leads to superconductivity, and show how the evolution of the local density on the two types of sites lends insight into the formation of global phase coherence.
Using the variational cluster approach based on the self-energy functional theory, we study the possible occurrence of excitonic order and superconductivity in the two-orbital Hubbard model with intra- and inter-orbital Coulomb interactions. It is known that an antiferromagnetic Mott insulator state appears in the regime of strong intra-orbital interaction, a band insulator state appears in the regime of strong inter-orbital interaction, and an excitonic insulator state appears between them. In addition to these states, we find that the
s±-wave superconducting state appears in the small-correlation regime, and the
dx2−y2-wave superconducting state appears on the boundary of the antiferromagnetic Mott insulator state. We calculate the single-particle spectral function of the model and compare the band gap formation due to the superconducting and excitonic orders.