Selected universal experimental properties of high temperature superconducting (HTS) cuprates have been singled out in the last decade. One of the pivotal challenges in this field is the designation of a consistent interpretation framework within which we can describe quantitatively the universal features of those systems. Here we analyze in a detailed manner the principal experimental data and compare them quantitatively with the approach based on a single band of strongly correlated electrons supplemented with strong antiferromagnetic (super)exchange interaction (the so-called t-J-U model). The model rationale is provided by estimating its macroscopic parameters on the basis of the 3-band approach for the Cu-O plane. We use our original full Gutzwiller-wave-function solution by going beyond the renormalized mean field theory (RMFT) in a systematic manner. Our approach reproduces very well the observed hole doping (δ) dependence of the kinetic-energy gain in the superconducting phase, one of the principal non-Bardeen-Cooper-Schrieffer features of the cuprates. The calculated Fermi velocity in the nodal direction is practically δ-independent and its universal value agrees very well with that determined experimentally. Also, a weak doping dependence of the Fermi wave-vector leads to an almost constant value of the effective mass in a pure superconducting phase which is both observed in the experiment and reproduced within our approach. An assessment of the currently used models is carried out and the results of the canonical RMFT as a zeroth-order solution are provided for comparison to illustrate the necessity of introduced higher order contributions.

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]

We consider the superconducting and Mott-insulating states for the twisted bilayer graphene, modeled as two narrow-band system of electrons with appreciable intraatomic Coulomb interactions. The interaction induces kinetic exchange which leads to real-space, either triplet-or singlet-spin pairing, in direct analogy to heavy-fermions and high-temperature superconductors. By employing the statistically-consistent Gutzwiller method, we construct explicitly the phase diagram as a function of electron concentration for the spin-triplet d x 2 −y 2 + idxy paired case, as well as determine the topological edge states. The model reproduces principal features observed experimentally in a semi-quantitative manner. The essential role of electronic correlations in driving both the Mottinsulating and superconducting transitions is emphasized. The transformation of the spin-triplet state into its spin-singlet analogue is also analyzed, as well as the appearance of the phase separated superconducting+Mott-insulating state close to the half filling.

We demonstrate the stability of the spin-triplet paired s-wave (with an admixture of extended s-wave) state for the limit of purely repulsive interactions in a degenerate two-band Hubbard model of correlated fermions. The repulsive interactions limit represents an essential extension of our previous analysis (2013 New J. Phys. 15 073050), regarded here as I. We also show that near the halffilling the considered type of superconductivity can coexist with antiferromagnetism. The calculations have been carried out with the use of the socalled statistically consistent Gutzwiller approximation (SGA) for the case of a square lattice. We suggest that the electron correlations in conjunction with the Hundʼs rule exchange play the crucial role in stabilizing the real-space spintriplet superconducting state. A sizable hybridization of the bands suppresses the homogeneous paired state.

An orbitally degenerate two-band Hubbard model is analyzed with the inclusion of the Hund's rule-induced spin-triplet even-parity paired states and their coexistence with magnetic ordering. The so-called statistically consistent Gutzwiller approximation (SGA) has been applied to the case of a square lattice. The superconducting gaps, the magnetic moment and the free energy are analyzed as a function of the Hund's rule coupling strength and the band filling. Also, the influence of the intersite hybridization on the stability of paired phases is discussed. In order to examine the effect of correlations the results are compared with those calculated earlier within the Hartree-Fock (HF) approximation combined with the Bardeen-Cooper-Schrieffer (BCS) approach. Significant differences between the two methods used (HF + BCS versus SGA+real-space pairing) appear in the stability regions of the considered phases. Our results supplement the analysis of this canonical model used