arXiv:2608.24337

Influence of the inter-orbital interaction and kinetic terms on superconductivity: a simple two-orbital Hubbard model

Vito Marino, Diego Florez-Ablan, Luca F. Tocchio, Massimo Capone, Federico Becca

Published Aug 25, 2026• 0 citations

Abstract

We investigate a minimal two-orbital Hubbard model with intra- and inter-orbital nearest-neighbor hopping $t$ and $\tilde{t}$, 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 $\tilde{t}$. For $\tilde{t}=0$, 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 $\tilde{t}$ provides an additional boost to superconducting correlations, an effect driven by the simultaneous presence of flat and broad bands in the electronic structure.

DOI: 10.48550/arxiv.2608.24337

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arXiv:2608.24337

Influence of the inter-orbital interaction and kinetic terms on superconductivity: a simple two-orbital Hubbard model

Vito Marino, Diego Florez-Ablan, Luca F. Tocchio, Massimo Capone, Federico Becca

Published Aug 25, 2026• 0 citations

arXiv HTML PDF

Abstract

We investigate a minimal two-orbital Hubbard model with intra- and inter-orbital nearest-neighbor hopping

t

and

\tilde{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

\tilde{t}

. For

\tilde{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

\tilde{t}

provides an additional boost to superconducting correlations, an effect driven by the simultaneous presence of flat and broad bands in the electronic structure.

DOI: 10.48550/arxiv.2608.24337

Related papers

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We investigate a minimal two-orbital Hubbard model with intra- and inter-orbital nearest-neighbor hopping

t

and

\tilde{t}

, as well as intra- and inter-orbital density-density interactions

U

and

U'

U/t=10

, superconducting correlations are highly enhanced by the presence of inter-orbital terms,

U'

and

\tilde{t}

. For

\tilde{t}=0

, a finite value of

U'

effectively screens the intra-orbital repulsion

U

\tilde{t}

provides an additional boost to superconducting correlations, an effect driven by the simultaneous presence of flat and broad bands in the electronic structure.

J

) and correlated hopping (

K

) interaction. Detailed numerical analysis of

s

p

-, and

d

-wave pairing solutions is performed for the two-dimensional square lattice with nearest- (

t

) and next-nearest- (

{t}_{2}

) neighbor hopping, and the resulting mutual stability phase diagrams are given as a function of band filling and the interaction parameters. Antiferromagnetic exchange can enhance both the

d

-wave and the extended

s

-wave pairing. If it prevails over the repulsive intersite density-density interaction, such a term can be a leading mechanism for superconductivity. However, its effects strongly depend on the band filling and the

\frac{{t}_{2}}{t}

ratio, giving in particular for

{t}_{2}=0

s

-wave (

d

-wave) pairing as most favorable in the low (high) density limit, but increasing

{t}_{2}

can even reverse this tendency. The correlated hopping term which breaks the electron-hole symmetry affects

s

-wave pairing mostly. A condensation transition (phase separation), possible in the presence of the attractive density-density interaction, is also analyzed within the random-phase approximation, and stability conditions of such an electron droplet phase with respect to other types of ordering are determined as a function of the band filling for the two-dimensional square lattice.

s^{\pm}

-wave superconducting state appears in the small-correlation regime, and the

d_{x^2 - y^2}

-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.

We study the effect of the correlated hopping term and the intersite Coulomb interaction term on principal features of the

d

-wave superconducting (SC) state, in both the electron- and hole-doped regimes within the $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ model. In our analysis, we use the approach based on the diagrammatic expansion of the Gutzwiller wave function (DE-GWF), which allows us to go beyond the renormalized mean-field theory (RMFT). We show that the correlated hopping term enhances the pairing at the electron-doped side of the phase diagram. Moreover, the so-called non-BCS regime (which manifests itself by the negative kinetic energy gain at the transition to the SC phase) is narrowed down with the increasing magnitude of the correlated hopping $\ensuremath{\sim}K$. Also, the doping dependencies of the nodal Fermi velocity and Fermi momentum, as well as the average number of double occupancies, are analyzed with reference to the experimental data for selected values of the parameter

K

. For the sake of completeness, the influence of the intersite Coulomb repulsion on the obtained results is provided. Additionally, selected results concerning the Hubbard-model case are also presented. A complete model with all two-site interactions is briefly discussed in Appendix for reference.

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

\vert U\vert

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.