Out-of-equilibrium relaxation dynamics of the superconducting order parameter in CsV$_3$Sb$_5$

Abstract: The application of a time-varying strain field drives a superconducting order parameter out of equilibrium. How the order parameter relaxes back to equilibrium depends both on the structure of the superconducting gap and on the nature of quasiparticle scattering. We report the discovery of an ultrasonic attenuation peak inside the superconducting state of the kagome superconductor CsV$<em>3$Sb$_5$. This peak is the natural consequence of the order parameter relaxation time matching the ultrasonic drive frequency near $T</em>{\rm c}$. From the measured frequency dependence of the peak, we extract a microscopic scattering time of $τ_N = 25$ ps. This timescale is two orders of magnitude longer than the elastic scattering time as determined by resistivity measurements, but is comparable to the inelastic scattering time determined by thermal transport. Within the conventional framework of order-parameter relaxation, this implies that elastic scattering is ineffective at relaxing the superconducting condensate, consistent with a sign-preserving $s$-wave state obeying Anderson's theorem.