Coulomb repulsion of holes and competition between \({d_{{x^2} - {y^2}}}\) -wave and s-wave parings in cuprate superconductors

Abstract

The effect of the Coulomb repulsion of holes on the Cooper instability in an ensemble of spin–polaron quasiparticles has been analyzed, taking into account the peculiarities of the crystallographic structure of the CuO₂ plane, which are associated with the presence of two oxygen ions and one copper ion in the unit cell, as well as the strong spin–fermion coupling. The investigation of the possibility of implementation of superconducting phases with d-wave and s-wave of the order parameter symmetry has shown that in the entire doping region only the d-wave pairing satisfies the self-consistency equations, while there is no solution for the s-wave pairing. This result completely corresponds to the experimental data on cuprate HTSC. It has been demonstrated analytically that the intersite Coulomb interaction does not affect the superconducting d-wave pairing, because its Fourier transform V_q does not appear in the kernel of the corresponding integral equation.