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arXiv:2104.02288 · Physical review. B./Physical review. B

Superconductivity with and without glue and the role of the double-occupancy forbidding constraint in the t−J−V model

Luciano Zinni, Matías Bejas, A. Greco

Published Apr 5, 2021• 7 citations
arXivHTMLPDF

Abstract

The occurrence of retarded (with glue) and unretarded (without glue) pairing is thoroughly discussed in cuprates. We analyze some aspects of this problem in the context of the $t\text{\ensuremath{-}}J\text{\ensuremath{-}}V$ model in a large-$N$ approximation. When $1/N$ renormalizations are neglected the mean-field result is recovered, where the unretarded $d$-wave superconducting pairing triggered by the spin-exchange interaction $J$ is obtained. However, the presence of a nonnegligible nearest-neighbors Coulomb interaction $V(\mathbf{q})$ kills superconductivity. If the non-double-occupancy constraint and its fluctuations are considered, the situation changes drastically. In this case, $V(\mathbf{q})$ is screened making $d$-wave superconductivity very robust. In addition, we show that the early proposal for the presence of an unretarded pairing contribution triggered by the spin-exchange interaction $J$ can be discussed in this context.

DOI
10.1103/physrevb.103.134504

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The occurrence of retarded (with glue) and unretarded (without glue) pairing is thoroughly discussed in cuprates. We analyze some aspects of this problem in the context of the t\ensuremath-J\ensuremath-Vt\text{\ensuremath{-}}J\text{\ensuremath{-}}Vt\ensuremath-J\ensuremath-V model in a large-NNN approximation. When 1/N1/N1/N renormalizations are neglected the mean-field result is recovered, where the unretarded ddd-wave superconducting pairing triggered by the spin-exchange interaction JJJ is obtained. However, the presence of a nonnegligible nearest-neighbors Coulomb interaction V(q)V(\mathbf{q})V(q) kills superconductivity. If the non-double-occupancy constraint and its fluctuations are considered, the situation changes drastically. In this case, V(q)V(\mathbf{q})V(q) is screened making ddd-wave superconductivity very robust. In addition, we show that the early proposal for the presence of an unretarded pairing contribution triggered by the spin-exchange interaction JJJ can be discussed in this context.
Many theoretical approaches find ddd-wave superconductivity in the prototypical one-band Hubbard model for high-temperature superconductors. At strong coupling ($U\ensuremath{\ge}W$, where UUU is the on-site repulsion and W=8tW=8tW=8t the bandwidth) pairing is controlled by the exchange energy J=4t2/UJ=4{t}^{2}/UJ=4t2/U. One may then surmise, ignoring retardation effects, that near-neighbor Coulomb repulsion VVV will destroy superconductivity when it becomes larger than JJJ, 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 VVV always reduces the spin fluctuations and hence ddd-wave pairing, at strong coupling, in the underdoped regime, the increase of $J=4{t}^{2}/(U\ensuremath{-}V)$ caused by VVV increases binding at low frequency while the pair-breaking effect of VVV 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 ddd-wave superconductivity from VVV.
The question of whether one should speak of a "pairing glue" in the Hubbard and t-J models is basically a question about the dynamics of the pairing interaction. If the dynamics of the pairing interaction arises from virtual states, whose energies correspond to the Mott gap, and give rise to the exchange coupling J, the interaction is instantaneous on the relative time scales of interest. In this case, while one might speak of an "instantaneous glue," this interaction differs from the traditional picture of a retarded pairing interaction. However, as we will show, the dominant contribution to the pairing interaction for both of these models arises from energies reflecting the spectrum seen in the dynamic spin susceptibility. In this case, the basic interaction is retarded, and one speaks of a spin-fluctuation glue which mediates the d-wave pairing.
The question of whether one should speak of a "pairing glue" in the Hubbard and t-J models is basically a question about the dynamics of the pairing interaction. If the dynamics of the pairing interaction arises from virtual states, whose energies correspond to the Mott gap, and give rise to the exchange coupling J, the interaction is instantaneous on the relative time scales of interest. In this case, while one might speak of an "instantaneous glue", this interaction differs from the traditional picture of a retarded pairing interaction. However, if the energies correspond to the spectrum seen in the dynamic spin susceptibility, then the interaction is retarded and one speaks of a spin-fluctuation glue which mediates the d-wave pairing. Here we present results from numerical studies which provide insight into this question.
We study the effect of the correlated hopping term and the intersite Coulomb interaction term on principal features of the ddd-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 KKK. 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.
Dynamic cluster quantum Monte Carlo calculations for a doped two-dimensional extended Hubbard model are used to study the stability and dynamics of ddd-wave pairing when a nearest-neighbor Coulomb repulsion VVV is present in addition to the on-site Coulomb repulsion UUU. We find that ddd-wave pairing and the superconducting transition temperature Tc{T}_{c}Tc​ are only weakly suppressed as long as VVV does not exceed U/2U/2U/2. This stability is traced to the strongly retarded nature of pairing that allows the ddd-wave pairs to minimize the repulsive effect of VVV. When VVV approaches U/2U/2U/2, large momentum charge fluctuations are found to become important and to give rise to a more rapid suppression of ddd-wave pairing and Tc{T}_{c}Tc​ than for smaller VVV.
Our previous mean-field study concerning superconducting pairings in the extended Hubbard model with on-site repulsive and intersite attractive interaction and arbitrary electron density is extended to include the effects of nearest-neighbor exchange (JJJ) and correlated hopping (KKK) interaction. Detailed numerical analysis of sss-, ppp-, and ddd-wave pairing solutions is performed for the two-dimensional square lattice with nearest- (ttt) and next-nearest- (t2{t}_{2}t2​) 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 ddd-wave and the extended sss-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 t2t\frac{{t}_{2}}{t}tt2​​ ratio, giving in particular for t2=0{t}_{2}=0t2​=0 sss-wave (ddd-wave) pairing as most favorable in the low (high) density limit, but increasing t2{t}_{2}t2​ can even reverse this tendency. The correlated hopping term which breaks the electron-hole symmetry affects sss-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.