Kohn-Luttinger effect in nested Fermion liquids

TL;DR

This paper investigates how the Kohn-Luttinger effect induces d-wave superconductivity in a 2D nested Fermion liquid with repulsive interactions, using renormalization group and bosonization methods, highlighting the competition with SDW order.

Contribution

It demonstrates that in a 2D nested Fermion liquid, the d_{x^2-y^2}-wave pairing emerges as the dominant instability due to the Kohn-Luttinger effect, extending understanding of unconventional superconductivity.

Findings

d_{x^2-y^2}-wave pairing is the most attractive channel.

Marginal Fermi liquid behavior observed without instability.

Superconducting instability occurs when SDW coupling is weak.

Abstract

We study the Kohn-Luttinger effect in a two-dimensional (2D) nested Fermion liquid with a repulsive interaction via the renormalization group method and identify the resulting order parameter symmetry. Using the band structure of the 2D Hubbard model close to half-filling as a prototype, we construct an effective low-energy theory. We use multidimensional bosonization to incorporate the zero-sound channel and find marginal Fermi liquid behavior in the absence of any instability. We show an analog of the Landau theorem in nested Fermion liquids, which serves as the criterion of the BCS instability. Including repulsive or antiferromagnetic exchange interactions in the low-energy theory, we show that the $d_{x^2-y^2}$-wave BCS channel is renormalized to be the most attractive. Below half-filling, when the nesting is not perfect, there is competition between the spin-density-wave (SDW) and the BCS channels; when the SDW coupling is small enough, there occurs a $d_{x^2-y^2}$-wave superconducting instability at sufficiently low temperatures.