Quasiparticle Interactions in Two and Three Dimensional Superconductors

TL;DR

This paper compares quasiparticle interactions in 2D and 3D s-wave superconductors, revealing that 2D systems exhibit stronger energy dependence in self-energies due to low-lying collective modes, emphasizing the need for low-dimensional treatment.

Contribution

It demonstrates the significant difference in quasiparticle self-energy energy dependence between 2D and 3D superconductors caused by collective modes.

Findings

Stronger energy dependence of self-energies in 2D superconductors.

Presence of low-lying collective modes in 2D enhances quasiparticle interactions.

Quasiparticle renormalizations differ markedly from normal state assumptions in low dimensions.

Abstract

I investigate the difference between the quasiparticle properties in two dimensional(2D)and three dimensional(3D) s-wave superconductors. Using the original BCS model for the pairing interaction and direct Coulomb interaction I show that quasiparticle interactions lead to a stronger energy dependence in the single-particle self-energies in 2D than in 3D superconductors. This difference arises from the presence of the low lying collective mode of the order parameter in the 2D case which ensures that oscillator strength in the response function is at low frequencies, $\sim \Delta$. This strong quantitative difference between 2D and 3D superconductors points to the importance of treating quasiparticle interactions in low dimensional superconductors rather than assuming that renormalizations remain unchanged from the normal state.