Superconductivity in the three-band model of cuprates: Variational wave function study and relation to the single-band case

Abstract

The d-wave superconductivity is analyzed within the three-band d-p model with the use of the diagrammatic expansion of the Guztwiller wave function method (DE-GWF). The determined stability regime of the superconducting state appears in the range of hole doping δ 0.35, with the optimal doping close to δ ≈ 0.19. The pairing amplitudes between the d-orbitals due to copper and px/py orbitals due to oxygen are analyzed together with the hybrid d-p pairing. The d-d pairing between the nearest neighboring atomic sites leads to the dominant contribution to the SC phase. Moreover, it is shown that the decrease of both the Coulomb repulsion on the copper atomic sites (U d ) and the charge transfer energy between the oxygen and copper atomic sites ( dp ) increases the pairing strength as it moves the system from the strong to the intermediate-correlation regime, where the pairing is maximized. Such a result is consistent with our analysis of the ratio of changes in the hole content at the d and p orbitals due to doping, which, according to experimental study, increases with the increasing maximal critical temperature [cf. Nat. Commun. 7, 11413 (2016)]. Furthermore, the results for the three-band model are compared to those for the effective single-band picture and similarities between the two approaches are discussed. For the sake of completeness, the normal-state characteristics determined from the DE-GWF approach are compared with those resulting from the Variational Quantum Monte Carlo method with inter-site correlations included through the appropriate Jastrow factors. arXiv:1812.03677v1 [cond-mat.supr-con]

Superconductivity and intra-unit-cell electronic nematic phase in the three-band model of cuprates

“…Within our approach the nematicity appears as a result of strong inter-electronic correlations, which are taken into account by the higher order terms of the diagrammatic expansion of the Gutzwiller wave function (DE-GWF method). The method has been recently applied to both the single-and three-band descriptions of the paired phase of the cuprates and leads to good agreement with the principal experimental observations [21][22][23]. In contrast to the previous results obtained for the Emery model [17][18][19][20], we show that the nematic behavior of the electronic wave function can be induced by inter-electronic correlations, with the dominant role of the onsite Coulomb repulsion at the copper d-orbitals, even without the corresponding intersite oxygen-oxygen term.…”

“…To take into account the inter-electronic correlations resulting from the significant onsite Coulomb repulsion at the copper atomic sites, we use the approach based on the so-called diagrammatic expansion of the Gutzwiller wave function (DE-GWF method). The method has been discussed by us extensively and applied to both single-and multi-band models [21,22,[27][28][29][30] as well as recently to the description of the superconducting phase of the cuprates within the three band Emery model [23], which is also considered here.…”

“…By minimizing the energy of the system over the variational parameters one reduces the number of configurations which correspond to increased interaction energies. The details of the DE-GWF calculation scheme as applied to the d-wave superconducting phase in the three-band Emery model are provided in reference [23]. It should be noted, that the C 4 symmetry breaking leads to much more involved calculations, since the number of the so-called hopping and pairing lines which determine the |Ψ 0 wave function (cf.…”

“…Refs. [21,23] for the definition of the lines) is twice as large as that corresponding to the situation in which the C 4 symmetry is preserved. In the considered model, the nematicity is realized by the p-orbital polarization which means that n px = n py within each unit cell.…”

“…Thus, the i site index in the variational parameters λ Γ|il can be dropped and we end up with three sets of variational parameters λ Γ|d , λ Γ|px , and λ Γ|py , which correspond to different electronic configurations at the three orbitals appearing in the model. As we have shown in reference [23], due to the fact that the Coulomb repulsion at the copper orbitals is the dominant energy in the system, the projection at the oxygen orbitals can be omitted by taking λ Γ|px = λ Γ|py ≡ 1. This assumption is also applied here.…”