Superconductivity in the Uniform Electron Gas: Irrelevance of Kohn-Luttinger Mechanism

TL;DR

This study investigates the origin of superconductivity in the uniform electron gas, demonstrating that dynamic screening, not the Kohn-Luttinger mechanism, is the primary driver of Cooper instability at small to intermediate Coulomb parameters.

Contribution

The paper shows that in the jellium model, superconductivity arises mainly from dynamic screening effects, with the Kohn-Luttinger mechanism being negligible, challenging previous assumptions.

Findings

Superconductivity emerges from repulsive interactions via dynamic screening.

Kohn-Luttinger contribution to Cooper instability is negligible.

Random phase approximation accurately captures the dominant mechanism.

Abstract

We study the Cooper instability in jellium model in the controlled regime of small to intermediate values of the Coulomb parameter $r_s \leq 2$. We confirm that superconductivity naturally emerges from purely repulsive interactions described by the Kukkonen-Overhauser vertex function. By employing the implicit renormalization approach we reveal that even in the small-$r_s$ limit, the dominant mechanism behind Cooper instability is based on dynamic screening of the Coulomb interaction--accurately captured by the random phase approximation, whereas the Kohn-Luttinger contribution is negligibly small and, thus, not relevant.