Collective modes and ultrasonic attenuation in a pseudogapped superconductor
We develop a theory of collective modes in a model of strongly disordered s-wave superconductor with a localization-induced pseudogap ΔP, that is much larger than superconducting gap Δ. Then we applied the obtained results to the calculation of the ultrasound decay rate α(ω) at low-frequencies ω≪kBT/ℏ. We show that at low temperatures T≪Tc the magnitude of the decay rate α(ω) is controlled by the ratio of T/Δ, while single-particle gap ΔP does enter the result for α(ω). Thus, we propose a new method to measure the collective gap Δ in a situation when strong pseudogap is present.