Hydrodynamic Heat Transport Regime in Bismuth: A Theoretical Viewpoint

Bismuth is one of the rare materials in which second sound has been experimentally observed. Our exact calculations of thermal transport with the Boltzmann equation predict the occurrence of this Poiseuille phonon flow between ≈1.5 and ≈3.5 K, in a sample size of 3.86 and 9.06 mm, consistent with the experimental observations. Hydrodynamic heat flow characteristics are given for any temperature: heat wave propagation length, drift velocity, and Knudsen number. We discuss a gedanken experiment allowing us to assess the presence of a hydrodynamic regime in any bulk material.