A consistent microscopic theory of superconductivity for strongly correlated electronic systems is presented. The Dyson equation for the normal and anomalous Green functions for the projected (Hubbard) electronic operators is derived. To compare vari
ous mechanisms of pairing, the extended Hubbard model is considered where the intersite Coulomb repulsion and the electron-phonon interaction are taken into account. We obtain the $d$-wave pairing with high-$T_c$ induced by the strong kinematical interaction of electrons with spin fluctuations, while the Coulomb repulsion and the electron-phonon interaction are suppressed for the $d$-wave pairing. These results support the spin-fluctuation mechanism of high-temperature superconductivity in cuprates previously proposed in phenomenological models.
A microscopic theory of electronic spectrum and superconductivity within the $t$-$J$ model on the honeycomb lattice is formulated. The Dyson equation for the normal and anomalous Green functions for the two-band model in terms of the Hubbard operator
s is derived by applying the Mori-type projection technique. The self-energy is evaluated in the self-consistent Born approximation for electron scattering on spin and charge fluctuations induced by the kinematical interaction for the Hubbard operators. Superconducting pairing mediated by the antiferromagnetic exchange and spin fluctuations is discussed.
A microscopic theory for electronic spectrum of the CuO2 plane within an effective p-d Hubbard model is proposed. Dyson equation for the single-electron Green function in terms of the Hubbard operators is derived which is solved self-consistently for
the self-energy evaluated in the noncrossing approximation. Electron scattering on spin fluctuations induced by kinematic interaction is described by a dynamical spin susceptibility with a continuous spectrum. Doping and temperature dependence of electron dispersions, spectral functions, the Fermi surface and the coupling constant are studied in the hole doped case. At low doping, an arc-type Fermi surface and a pseudogap in the spectral function are observed.
A comparison of microscopic theories of superconductivity in the limit of strong electron correlations is presented. We consider results for the two-dimensional t-J model obtained within the projection technique for the Green functions in terms of th
e Hubbard operators and the slave-fermion representation for the RVB state. It is argued that the latter approach resulting in the odd-symmetry p-wave pairing for fermions is inadequate.
A microscopical theory of electronic spectrum and superconductivity is formulated within the two-dimensional anisotropic t-J model with t_{x} eq t_{y} and J_{x} eq J_{y}. Renormalization of electronic spectrum and superconductivity mediated by spin-f
luctuations are investigated within the Eliashberg equation in the weak coupling approximation. The gap function has d+s symmetry with the extended s-wave component being proportional to the asymmetry t_{y} - t_{x}. Some experimental consequences of the obtained results are discussed.
Dynamic spin susceptibility is calculated for the t-J model in the paramagnetic phase by applying the memory function method in terms of the Hubbard operators. A self-consistent system of equations for the memory function is obtained within the mode
coupling approximation. Both itinerant hole excitations and localized spin fluctuations give contributions to the memory function. Spin dynamics have a diffusive character in the hydrodynamic limit; spin-wave-like excitations are regained in the high-frequency region.
The pairing of quasiparticles in a CuO$_2$ plane is studied within a spin polaron formulation of the $t$-$t^{}$-$J$ model. Our numerical solution of the Eliashberg equations unambiguously shows d-wave pairing between spin polarons on different sublat
tices mediated by the exchange of spin-fluctuations, and a strong doping dependence of the quasiparticle bandwidth. The transition temperature $T_c$ is an increasing function of $J/t$ and crosses a maximum at an optimal doping concentration $delta_{opt}$. For the t-J model with $J/t=0.4$ we obtain $T_csimeq 0.013 t$ at $delta_{opt}simeq 0.2$.
