Hole dynamics in doped cuprates: High-Tcsuperconductivity originated from antiferromagnetic exchange as a direct attractive interaction

A strong-coupling-limit theory of hole dynamics in copper oxide superconductors is developed. The theory is based on the t-${\mathit{t}}^{\prime }$-J model and the diagrammatic technique for projection operators. For the normal state two different phases at finite temperature are found. For the first (which is realized at low doping), a Fermi surface (FS) is formed by doped holes only and so has a volume proportional to δ, while d electrons are responsible for a localized magnetism. For the second (which is realized at intermediate doping), the d electrons become a part of the FS the volume of which is proportional to 1+δ, while the system loses the magnetic moments associated with d electrons. A transition between the two phases is of first order and the FS changes abruptly from a small to a large one. The phase with the small FS is unstable when lowering the temperature in as much as a spin susceptibility diverges at k=${\mathit{Q}}_{\mathrm{AF}}$. Therefore, at low temperature within the doping range corresponding to this phase, a long-range antiferromagnetic (AF) ground state or quantum-disordered ground state is realized depending on doping. Most attention in the paper is paid to the second state characterized by a saddle- point (SP) singularity and a large Fermi surface. Self-consistent calculations for the chemical potential show that at some critical doping which depends on the ratio of hopping parameters ${\mathit{t}}^{\prime }$/t, the Fermi level crosses the SP. For this phase, a short-distance superconducting (SC) pairing of d-wave symmetry with a large amplitude of the SC gap is found at low temperature. The critical temperature is very high. The superconducting pairing has a magnetic origin but the mechanism is different from an exchange by spin waves. The mechanism is related to the AF exchange between localized spins, turning out to be a direct attractive interaction between carriers. The latter point is a consequence of the specific nature of carriers appearing as a result of strong on-site Coulomb repulsion. On the other hand, the specific kinematic properties of the carriers create a strong constraint on symmetry of the superconducting order parameter which eliminates all symmetries without nodes and favors strongly d-wave symmetry. In such a situation the existence of a saddle point close to the Fermi level is a factor providing a maximum value of the effective interaction. An interrelation between an extension of the SP singularity and a value of the amplitude of the SC gap is analyzed; a saturation effect is found. © 1996 The American Physical Society.