Mirror nesting and electron-hole asymmetry at repulsive superconducting pairing

The dependence of the superconducting order parameter Δ(k) on the momentum of the relative motion of a pair with a large total momentum K is numerically studied for the case of repulsive pairing with allowance for the kinematic and insulator constraints on the momentum transfer at scattering. The Fermi contour with nesting and mirror nesting, which is typical of cuprates and optimal for repulsion-induced superconductivity, lies in an extended vicinity of the saddle points of the dispersion law. A deviation from the mirror nesting cuts off the logarithmic singularity from below and bounds the pre-exponent in Δ(k). The effective coupling constant is determined by the degree of the electron-hole asymmetry. The suppression of the contribution of small momentum transfer processes by the impurity and electron-phonon scattering favors an increase in the order parameter amplitude. The nesting of the Fermi contour causes a Peierls singularity in the Coulomb interaction. The self-consistency equation allows the solutions that may be both antisymmetric and symmetric with respect to the momentum inversion. The maximum-amplitude antisymmetric solution in the case of a singlet pairing can be realized only for K ≠ 0.