Quasiparticle Lifetimes and the Conductivity Scattering Rate

TL;DR

This paper compares quasiparticle lifetimes and conductivity scattering rates in superconductors, revealing qualitative agreement but quantitative discrepancies, and shows impurity scattering suppression near the Fermi surface within BCS theory.

Contribution

It provides a detailed comparison of quasiparticle lifetime and conductivity scattering rates in superconductors, including effects of impurities and electron-phonon interactions.

Findings

Qualitative agreement between scattering rates but quantitative differences

Impurity scattering is suppressed near the Fermi surface in the superconducting state

Derived explicit formulas for quasiparticle lifetime within BCS framework

Abstract

We compute the single-particle inverse lifetime, along with the conductivity-derived scattering rate, for a metallic system in an s-wave superconducting state. When both electron-phonon and electron-impurity scattering are included, we find that while these scattering rates are in qualitative agreement, in general quantitative agreement is lacking. We also derive results for the quasiparticle lifetime within the BCS framework with impurity scattering, which makes it clear that impurity scattering is suppressed for electrons near the Fermi surface in the superconducting state.