Momentum dependence of the spin susceptibility in two dimensions: nonanalytic corrections in the Cooper channel

TL;DR

This paper investigates how pair rescattering in the Cooper channel affects the spin susceptibility in 2D electron systems, revealing nonanalytic corrections and a negative slope at small momenta due to harmonic renormalization.

Contribution

It introduces a detailed diagrammatic method to calculate infinite-order corrections to spin susceptibility considering Cooper channel rescattering effects.

Findings

First derivative of spin susceptibility is negative at small momenta.

Harmonics in the scattering potential are renormalized independently.

Rescattering leads to nonanalytic corrections in 2D electron systems.

Abstract

We consider the effect of rescattering of pairs of quasiparticles in the Cooper channel resulting in the strong renormalization of second-order corrections to the spin susceptibility in a two-dimensional electron system. We use the Fourier expansion of the scattering potential in the vicinity of the Fermi surface to find that each harmonic becomes renormalized independently. Since some of those harmonics are negative, the first derivative of the spin susceptibility is bound to be negative at small momenta, in contrast to the lowest order perturbation theory result, which predicts a positive slope. We present in detail an effective method to calculate diagrammatically corrections to the spin susceptibility to infinite order.