Pair Fermi contour and repulsion-induced superconductivity in cuprates

The pairing of charge carriers with a 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 an 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 the appearance of a "pair" Fermi contour resulting from carrier redistribution in momentum space. In an extended vicinity of the saddle point, the momentum space has hyperbolic (pseudoeuclidean) metrics; therefore, the principal values of the two-dimensional reciprocal reduced effective mass tensor have unlike signs. At small momenta of the relative motion of a pair with a large pair momentum, the pairing is sensitive just to the sign and value of the effective mass and not to only the value of the Fermi velocity as in the case of Cooper pairing. The nesting of the Fermi contour results in an increase of the statistical weight of the pair with a large total momentum due to an extension of the momentum space domain which corresponds to permissible values of the relative motion momentum. The rearrangement of holes in momentum space results in the rise of a "pair" Fermi contour which may be defined as the zero-energy line for the relative motion of the pair. The superconducting gap arises just on this line. The pair Fermi contour formation inside the region of momentum space with hyperbolic metrics results in not only superconducting pairing but in a rise of a quasistationary 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 pairing in cuprates may be due to screened Coulomb repulsion. The pairing mechanism and the pair Fermi contour conception may provide a qualitative interpretation for the key experimental facts relating to cuprates.