Effect of long-range interactions on the Kohn-Luttinger mechanism of the Cooper instability in the Shubin-Vonsowsky model

TL;DR

This paper investigates how long-range intersite Coulomb interactions influence the Kohn-Luttinger mechanism of superconductivity within the Shubin-Vonsowsky model, revealing their impact on various pairing symmetries.

Contribution

It extends the Kohn-Luttinger theory by incorporating long-range Coulomb interactions and intersite hoppings, analyzing their effects on superconducting pairing symmetries.

Findings

Long-range interactions significantly alter the effective pairing interaction.

Inclusion of intersite hoppings affects the stability of different superconducting phases.

Multiple pairing symmetries are influenced by the extended Coulomb interactions.

Abstract

The problem of Cooper instability is studied by implementing the Kohn-Luttinger mechanism in the framework of the Shubin-Vonsowsky model taking into account the intersite Coulomb interactions within the first and second coordination spheres. It is shown that the Kohn-Luttinger renormalization for the effective interaction in the second-order terms of perturbation theory, as well as the inclusion of intersite hoppings in the second and third coordination spheres, significantly affects the interplay between the superconducting phases with $d_{xy}$-, $p$-, $s$-, and $d_{x^2-y^2}$-wave symmetries of the order parameter.