Origin of the Coulomb pseudopotential

We address the outstanding problem of electron pairing in the presence of strong Coulomb repulsion at small to moderate values of the Coulomb parameter, rs <= 2, and demonstrate that the pseudopotential framework is fundamentally biased and uncontrolled. Instead, one has to break the net result into two distinctively different effects: the Fermi liquid renormalization factor and the change in the effective low-energy coupling. The latter quantity is shown to behave nonmonotonically with an extremum at rs ti 0.75. Within the random-phase approx-imation, Coulomb interaction starts to enhance the effective pairing coupling at rs > 2, and the suppression of the critical temperature is entirely due to the renormalized Fermi liquid properties. Leading vertex corrections change this picture only quantitatively. Our results call for radical reconsideration of the widely accepted repulsive pseudopotential approach and show the need for precise microscopic treatment of Coulomb interactions in the problem of superconducting instability.

Automated summary

We address the issue of electron pairing in the presence of strong Coulomb repulsion at rs <= 2 and demonstrate the limitations of the pseudopotential framework. Instead, we propose separating the effects of Fermi liquid renormalization and the change in effective low-energy coupling. Our findings indicate a nonmonotonic behavior of the latter quantity with an extremum at rs ti 0.75. The Coulomb interaction enhances the pairing coupling at rs > 2, while the suppression of critical temperature is solely due to renormalized Fermi liquid properties. Leading vertex corrections have only a quantitative impact. Our results challenge the widely accepted repulsive pseudopotential approach and highlight the importance of precise microscopic treatment of Coulomb interactions in the study of superconducting instability.