Comment on "Superconducting phases in the presence of Coulomb interaction: From weak to strong correlations''

TL;DR

This paper critiques a previous model of superconductivity under Coulomb interactions, corrects the gap equation, and shows that Coulomb repulsion generally suppresses superconductivity, aligning with earlier numerical findings.

Contribution

It provides a corrected mean-field gap equation considering Coulomb repulsion and demonstrates its detrimental effect on T_c, extending applicability to all U values with pairing fluctuations.

Findings

Coulomb repulsion U suppresses superconductivity.

Corrected gap equation aligns with previous numerical results.

Extension to all U values with pairing fluctuations possible.

Abstract

We examine the paper basic equations of T. Doma\'nski and K.I. Wysoki\'nski [Phys. Rev. B {\bf 59}, 173 (1999)], who calculated the critical superconducting temperature, T_c, in function of Coulomb correlations (U) for s- and d-wave order parameter symmetries. We give physical arguments, based on general theory of perturbation, that in their gap equation the Coulomb repulsion is counted twice. Because of that, we write down the right mean-field gap equation and solve it by using a normal state one-particle Green function which gives a Mott metal-insulator transition for $T > T_c$ and which is valid for any value of U. In consequence, we are not allowed to use mean-field theory for both U and pairing (V). Our numerical results for T_c vs U shows that U is detrimental to superconductivity which agrees with the numerical results of Doma\'nski and Wysoki\'nski. Our results can be extended to any value of the pairing interaction if superconducting pairing fluctuations are taken into account.