Kohn-Luttinger pseudo-pairing in a two-dimensional Fermi-liquid

TL;DR

This paper explores how repulsive interactions in a two-dimensional Fermi liquid can lead to unconventional superconductivity via the Kohn-Luttinger mechanism, resulting in finite-energy pairing and a mixture of normal and paired states.

Contribution

It demonstrates that second-order perturbation theory reveals an attractive harmonic in the scattering amplitude, indicating possible superconducting pairing due to the Kohn-Luttinger mechanism in 2D systems.

Findings

Attractive harmonic in quasiparticle scattering amplitude

Finite-energy pairing of electron excitations

Presence of fluctuating d-wave Cooper pairs at low temperatures

Abstract

We consider possible superconducting instabilities in a two-dimensional Fermi system with short-ranged repulsive interactions between electrons. The possibility of an unusual superconducting paring due to the Kohn-Luttinger mechanism is examined. The quasiparticle scattering amplitude is shown to possess an attractive harmonic in second-order perturbation theory for finite values of the energy transfer. The corresponding singularity in the pairing vertex leads to a superconducting pairing of the electron excitations with finite energies. We identify the energy transfer in the Cooper channel as the binding energy of the excited pair. At low enough temperatures, the Fermi system is a mixture of normal electron excitations and fluctuating d-wave Cooper pairs possessing a finite gap.