Quasiparticle Lifetimes in Superconductors: Relationship with the Conductivity Scattering Rate

TL;DR

This paper investigates quasiparticle lifetimes in superconductors using BCS and Eliashberg theories, revealing significant suppression of inverse lifetime in the superconducting state and analyzing how conductivity measurements relate to scattering rates.

Contribution

It provides a non-perturbative calculation of quasiparticle inverse lifetimes in superconductors and compares these with perturbative results and conductivity-based estimates.

Findings

Inverse lifetime is significantly suppressed in the superconducting state.

Perturbative calculations agree well with non-perturbative results even with impurity scattering.

Quantitative discrepancies exist between inverse lifetime and scattering rates derived from conductivity measurements.

Abstract

We compute the single particle inverse lifetime, evaluated in the superconducting state. Within the BCS framework, the calculation can be done non-perturbatively, i.e. poles can be found well away from the real axis. We find that perturbative calculations are in good agreement with these results, even for non-zero impurity scattering. With electron-phonon scattering added to the problem, we use the Eliashberg equations, with impurity scattering, to calculate the quasiparticle inverse lifetime perturbatively. In all cases we find that the inverse lifetime is significantly suppressed in the superconducting state, particularly in the presence of impurity scattering. We also compute the far-infrared and microwave conductivity, and describe procedures for extracting scattering rates from conductivity measurements. While these procedures lead to scattering rates in qualitative agreement with the inverse lifetime, we find that quantitative agreement is lacking, in general.