Finite quasiparticle lifetime in disordered superconductors

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We investigate the complex conductivity of a highly disordered MoC superconducting film with kFl≈ 1, where kF is the Fermi wavenumber 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 Tc. We find that the original Mattis-Bardeen model with a finite quasiparticle lifetime, τ, offers a perfect description of the experimentally observed complex conductivity. We show that τ is appreciably reduced by scattering effects. Characteristics of the scattering centers are independently found by the scanning tunneling spectroscopy and agree with those determined from the complex conductivity.