Crossover from phonon-mediated to repulsion-induced superconducting pairing with large momentum

There are asymmetric and symmetric solutions of the self-consistency equation which takes into account both phonon-mediated and Coulomb pairing interactions. The first of them leads to the order parameter with a nodal line and, in the case of pairing with large momentum, exists at any repulsive and attractive strengths. The second one arises if the attraction exceeds a level depending on the repulsion strength and dominates the pairing in the strong attraction limit. The competition of attraction and repulsion results in unusual isotope-effect exponent observed in the cuprates.