"Pair" Fermi contour and repulsion-induced superconductivity in cuprates
  The pairing of charge carriers with large pair momentum is considered in connection with high-temperature superconductivity of cuprate compounds. The possibility of pairing arises due to some essential features of quasi-two-dimensional electronic structure of cuprates: (i) The Fermi contour with strong nesting features; (ii) The presence of extended saddle point near the Fermi level; (iii) The existence of some ordered state (for example, antiferromagnetic) close to the superconducting one as a reason for an appearing of "pair" Fermi contour resulting from carrier redistribution in momentum space. In an extended vicinity of the saddle point, momentum space has hyperbolic (pseudoeuclidean) metrics, therefore, the principal values of two-dimensional reciprocal reduced effective mass tensor have unlike signs. Rearrangement of holes in momentum space results in a rise of "pair" Fermi contour which may be defined as zero-energy line for relative motion of the pair. The superconducting gap arises just on this line. Pair Fermi contour formation inside the region of momentum space with hyperbolic metrics results in not only superconducting pairing but in a rise of quasi-stationary state in the relative motion of the pair. Such a state has rather small decay and may be related to the pseudogap regime of underdoped cuprates. It is concluded that the pairing in cuprates may be due to screened Coulomb repulsion. In this case, the superconducting energy gap in hole-doped cuprates exists in the region of hole concentration which is bounded both above and below. The superconducting state with positive condensation energy exists in more narrow range of doping level inside this region. Such hole concentration dependence correlates with typical phase diagram of cuprates. 
V.I. Belyavsky, Yu.V. Kopaev