Fig. 2: Measured relaxation time and variance compared with quasiparticle fluctuation theory.

The gray circles and red squares are determined from a fit to the measured fluctuation spectra (see “Methods”), which gives the relaxation time (a) and variance (b) of the quasiparticle fluctuation. The red squares are for the inductor on a SiN membrane (see Fig. 1b) and the gray circles on a SiN/Si solid substrate, as indicated by the legend. Error bars from statistical fit errors are smaller than the data points. The dashed lines in (a) are calculations for electron-phonon scattering time, Equation (3), which is 2D for T < 165 mK³⁵ and 3D for higher temperatures²⁷. The dashed lines in (b) are the variance of quasiparticle fluctuations for scattering events. The solid lines are for recombination. The red solid line in (a) includes the expected increase in relaxation time due to phonon trapping by the membrane (Fig. 1b). These curves are calculated without fit parameters, see “Methods”. The right axis in (b) gives the quasiparticle density corresponding to the variance of recombination events (the solid line).