The “pair” Fermi contour and high-temperature superconductivity

Superconducting pairing of holes with a large (on the order of doubled Fermi) total pair momentum and small relative motion momenta is considered taking into account the quasi-two-dimensional electronic structure of high-T _c cuprates with clearly defined nesting of the Fermi contour situated in an extended neighborhood of the saddle point of the electronic dispersion law (the momentum space region with a hyperbolic metric) and the arising of a spatially inhomogeneous (stripe) structure as a result of the redistribution of current carriers (holes) that restores regions with antiferromagnetic ordering. The superconducting energy gap and condensation energy were determined, and their dependences on the doping level were qualitatively studied. The energy gap was shown to exist in some hole concentration region limited on both sides. The superconducting state with a positive condensation energy appears in a narrower range of doping within this region. The reason for the arising of the superconducting state at a repulsive screened Coulomb interaction between holes is largely the redistribution of hole pairs in the momentum space related to the special features of the hyperbolic metric, which is responsible for the formation of the “pair” Fermi contour, and the renormalization of the kinetic energy of holes when the chemical potential changes because of the condensation of pairs. Hole pairs of the type under consideration exist not only in the condensate but also in the form of quasi-stationary states with very weak decay at temperatures substantially exceeding the superconducting transition temperature. The pseudogap region of the phase diagram of high-T _c cuprates is related to such states. The pairing mechanism under consideration allows not only the principal characteristics of the phase diagram but also key experimental data on high-T _c cuprate materials to be qualitatively explained.