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

TL;DR

This paper analyzes how Coulomb repulsion influences hole pairing in cuprate superconductors, finding that only d-wave pairing is consistent with experimental data and is unaffected by intersite Coulomb interactions.

Contribution

It demonstrates analytically that Coulomb repulsion does not hinder d-wave pairing in cuprates and shows s-wave pairing solutions are not feasible.

Findings

Only d-wave pairing satisfies self-consistency equations across doping levels.

Intersite Coulomb interaction does not affect d-wave pairing.

No solution for s-wave pairing exists in the model.

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 CuO$_2$ 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 superconducting phases with d-wave and s-wave pairing 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.