Hydrodynamic heat transport regime in bismuth: a theoretical viewpoint

TL;DR

This paper provides a theoretical analysis of hydrodynamic heat transport in bismuth, predicting second sound phenomena and characterizing heat flow properties across temperatures, aligning with experimental data.

Contribution

It offers exact Boltzmann equation calculations of phonon flow in bismuth, predicting second sound and hydrodynamic regimes between 1.5 K and 3.5 K, and discusses a method to identify hydrodynamic behavior in bulk materials.

Findings

Prediction of second sound in bismuth between 1.5 K and 3.5 K.

Calculation of heat wave propagation length and drift velocity.

Proposal of a Gedanken-experiment to detect hydrodynamic regimes.

Abstract

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 $\approx$ 1.5 K and $\approx$ 3.5 K, in sample size of 3.86 mm and 9.06 mm, in consistency with the experimental observations. Hydrodynamic heat flow characteristics are given for any temperature: heat wave propagation length, drift velocity, Knudsen number. We discuss a Gedanken-experiment allowing to assess the presence of a hydrodynamic regime in any bulk material.