Observation of Second Sound in Bismuth

Abstract

We have observed the transition from ballistic to second sound to diffusive propagation of heat (phonon) pulses in the semimetal bismuth in the temperature range of 1.2 to 4.0 K. The saturated second-sound velocity is found to be independent of orientation and has a a value of (0.78\ifmmode\pm\else\textpm\fi{}0.05)\ifmmode\times\else\texttimes\fi{}${10}^{5}$ cm/sec ($\frac{1}{3}\sqrt{3}$ times the Debye velocity). The inverse of the normal process phonon lifetime has a value ${{T}_{N}}^{\ensuremath{-}1}=4.49\ifmmode\times\else\texttimes\fi{}{10}^{4}{T}^{4}$ ${\mathrm{sec}}^{\ensuremath{-}1}$. Scattering due to the hole-phonon interaction is observed for ballistic $L$ modes propagating along the ${C}_{3}$ axis.