Finite quasiparticle lifetime in disordered superconductors

Abstract

We investigate the complex conductivity of a highly disordered MoC superconducting film with ${k}_{F}l\ensuremath{\approx}1$, where ${k}_{F}$ is the Fermi wave number and $l$ is the mean free path, derived from experimental transmission characteristics of coplanar waveguide resonators in a wide temperature range below the superconducting transition temperature ${T}_{c}$. We find that the original Mattis-Bardeen model with a finite quasiparticle lifetime, $\ensuremath{\tau}$, offers a perfect description of the experimentally observed complex conductivity. We show that $\ensuremath{\tau}$ is appreciably reduced by scattering effects. Characteristics of the scattering centers are independently found by scanning tunneling spectroscopy and agree with those determined from the complex conductivity.