The two-dimensional boson-fermion model of high-temperature superconductors, numerically studied by Domanski (Phys. Rev. B v.66, 134512 (2002)) is not a superconductor. The critical temperature of the model is zero for any symmetry of the order parameter. The opposite conclusion advocated by Domanski and some other authors stems from an erroneous mean-field approximation neglecting the boson self-energy. The approximation is qualitatively incorrect even in three dimensions. Taking into account the boson self-energy changes the phase transition in 3D BFM, which is not a mean-field second-order phase transition. There are real bosons in the model at and below Tc of 3D BFM, but not only fermions and their Cooper pairs.
A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting Tc by taking into account the pairing mediated by charge and spin fluctuations and phonons. We found the d-wave pairing with high-Tc mediated by spin fluctuations induced by the strong kinematic interaction for the Hubbard operators. Contributions to the d-wave pairing coming from the intersite Coulomb repulsion and phonons turned out to be small.
The understanding of the mechanisms responsible for superconductivity in strongly correlated systems is an interesting and important subject in condensed matter physics. Several theoretical proposals were considered for these systems. The Coulomb interaction between electrons allow a new approach to study this problem. In this paper, we use a usual Hubbard model with a local repulsive interaction to describe a 2D system. The system of equations are solved using the Green's functions method, within a Hubbard-I mean field approximation, which allows to treat the strong interaction limit. We consider both cases of attractive and repulsive interactions and obtain the zero temperature phase diagram of the model. Our results show, in the repulsive case, the existence of a superconducting ground state mediated by the kinetic electronic energy and described by a non-local order parameter. A minimum value of the repulsive interaction
Umin is required to create a pairing state. At finite temperatures, for strong interactions, the critical temperature
Tc shows a saturation similar to the Bose-Einstein condensation observed for strong attractive interactions.
The feasibility of a perturbation expansion for Green's functions of the t-J model directly in terms of X-operators is demonstrated using the Baym-Kadanoff functional method. As an application we derive explicit expressions for the kernel of the linearized equation for the superconducting order parameter in leading order of a 1/N expansion. The linearized equation is solved numerically on a square lattice taking instantaneous and retarded contributions into account. Classifying the order parameter according to irreducible representations of the point group C4v of the square lattice and according to even or odd parity in frequency we find that a reasonably strong instability occurs only for even frequency pairing with d-wavelike symmetry. The corresponding transition temperature Tc is where t is the nearest-neighbor hopping integral. The underlying effective interaction consists of an attractive, instantaneous term and a retarded term due to charge and spin fluctuations. The latter is weakly attractive at low frequencies below ,strongly repulsive up to and attractive towards even higher energies. Tc increases with decreasing doping until a d-wavelike bond-order wave instability is encountered near optimal doping at for J=0.3. Tc is essentially linear in J and rather insensitive to an additional second-nearest neighbor hopping integral t'. A rather striking property of Tc is that it is hardly affected by the soft mode associated with the bond-order wave instability or by the Van Hove singularity in the case with second-nearest neighbor hopping. This unique feature reflects the fact that the solution of the gap equation involves momenta far away from the Fermi surface (due to the instantaneous term) and many frequencies (due to the retarded term) so that singular properties in momentum or frequency are averaged out very effectively.
The principal purpose of this topical review is to single out some of the universal features of high-temperature (high-Tc) and related strongly-correlated systems, which can be compared with experiment in a quantitative manner. The description starts with the concept of exchange-interaction-mediated (real-space) pairing, combined with strong correlations among narrow band electrons, for which the reference state is that of the Mott–Hubbard insulator. The physical discussion of concrete properties relies on variational approach, starting from generalized renormalized mean-field theory (RMFT) in the form of statistically-consistent Gutzwiller approximation (SGA), and its subsequent generalization, i.e., a systematic Diagrammatic Expansion of the Variational (Gutzwiller-type) Wave Function (DE-GWF). The solution leads to the two energy scales, one involving unconventional quasiparticles close to the Fermi energy, and the other reflecting the fully correlated state, involving electrons deeper below the Fermi surface. Those two regimes are separated by a kink in the dispersion relation, which is observed in photoemission. As a result, one obtains both the doping dependent properties in the correlated state, and effective renormalized quasiparticles. The reviewed ground-state characteristics for high-Tc systems encompass high-Tc superconductivity, nematicity, charge- (and pair-) density-wave effects, as well as non-BCS kinetic energy gain in the paired state. The calculated dynamic properties are: the universal Fermi velocity, the Fermi wave-vector, the effective mass enhancement, the pseudogap; and the d-wave gap magnitude. We discuss that, within the variational approach, the minimal realistic model is represented by the so-called t-J-U Hamiltonian. Inadequacy of the t-J and Hubbard models, particularly of their RMFT versions, is discussed explicitly. For heavy fermion systems, modeled by the Anderson lattice model and with the DE-GWF approach, we discuss the phase diagram, encompassing superconducting, Kondo insulating, ferro- and anti-ferromagnetic states. The superconducting state is then a two-d-wave gap system. If the orbital degeneracy of f-electrons is included, the coexistent ferromagnetic- (spin–triplet) superconducting phases appear and match those observed for UGe2 in a semiquantitative manner. Finally, in the second part, we generalize our approach to the collective spin and charge fluctuations in high-Tc systems, starting from variational approach, defining the saddle-point state, and combining it with 1/N expansion. The present scheme differs essentially from that starting from the saddle-point Hartree–Fock approximation, and incorporating the fluctuations in the random phase approximation (RPA). The spectrum of collective spin and charge excitations is determined for the Hubbard and t-J-U models, and subsequently compared quantitatively with recent experiments. The Appendices provide formal details to make this review self-contained.
Many theoretical approaches find
d-wave superconductivity in the prototypical one-band Hubbard model for high-temperature superconductors. At strong coupling ($U\ensuremath{\ge}W$, where
U is the on-site repulsion and
W=8t the bandwidth) pairing is controlled by the exchange energy
J=4t2/U. One may then surmise, ignoring retardation effects, that near-neighbor Coulomb repulsion
V will destroy superconductivity when it becomes larger than
J, 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
V always reduces the spin fluctuations and hence
d-wave pairing, at strong coupling, in the underdoped regime, the increase of $J=4{t}^{2}/(U\ensuremath{-}V)$ caused by
V increases binding at low frequency while the pair-breaking effect of
V 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
d-wave superconductivity from
V.