We study the Cooper instability in jellium model in the controlled regime of small to intermediate values of the Coulomb parameter $r_s\le 2$. We confirm that superconductivity naturally emerges from purely repulsive interactions described by the Kukkonen-Overhauser vertex function. By employing the implicit renormalization approach and the discrete Lehmann representation 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.

Close

PrevNext

View figure in article

• Electron-phonon coupling
• Pairing mechanisms
• Superconducting gap
• Superconducting order parameter
• Superconducting phase transition
• BCS theory
• Luttinger–Kohn model