The description of the superconductivity in atomic representation for [formula omitted] model

Abstract

The diagram technique method for Hubbard operators has been used to describe the superconducting (SC) phase of the t – t ′ – t ″ – J * model. The new exact representation for the matrix one-particle Green's function has been derived. The main peculiarity of the obtained representation lies in the fact that not only anomalous components of the mass operator Σ 0 σ , σ ¯ 0 ( k , i ω m ) but also an anomalous components P 0 σ , σ ¯ 0 ( k , i ω m ) of the matrix strength operators P ^ ( k , i ω m ) are taken into account. In the one-loop approximation all analytical contributions of the normal Σ 0 σ , 0 σ ( k , i ω m ) , P 0 σ , 0 σ ( k , i ω m ) and of the anomalous Σ 0 σ , σ ¯ 0 ( k , i ω m ) , P 0 σ , σ ¯ 0 ( k , i ω m ) components mass and strength operators have been calculated. The Matsubara's frequencies dependence of the anomalous strength operator gave rise to description of the SC-phase by an infinite system of integral equations. Taking into account hoppings of electrons between sites situated within the limits of three coordination spheres this system was solved exactly. The influence of three-site interactions and intensity of hoppings on the existence of SC-phase with d x 2 - y 2 -type of the order parameter symmetry have been analyzed. It has been analyzed also the influence of the normal component P 0 σ , 0 σ ( k , i ω m ) on the function distribution of the Fermi-quasiparticles in the normal phase. It is shown that strong electron correlations give rise to degradation of the Fermi function even if the temperature much less than Fermi energy.