Measurement of phonon lifetimes in bulk superconducting tin

Phonon transport in β-Sn crystals was studied by heat-pulse techniques using superconducting tunnel junctions as detectors. At low temperature (0.6 K), pure ballistic propagation was observed up to the frequency cutoff ({~} 280 GHz) set by the pair-breaking processes; hence, we could determine the (anisotropic) superconducting gap associated with a given phonon mode. Then, the temperature-dependent attenuation by thermal quasiparticles was measured at fixed frequencies {} 150 GHz. For that particular experiment, the sensitivity of the Al detector was calibrated against a known optical flux. Extrapolation of the attenuation coefficients to the gap frequency leads to pair-breaking mean free paths in tin ranging from 1300 {} for the slow transverse mode with wave vector along [110], to 6700 {} for the longitudinal mode along [001]; this is much in excess of estimates from thin-film experiments quoted in the literature.