Observation of Poiseuille Flow of Phonons in Black Phosphorus

TL;DR

This study demonstrates Poiseuille flow of phonons in black phosphorus at low temperatures, revealing hydrodynamic heat transport characterized by size-dependent effects and enhanced normal scattering compared to silicon.

Contribution

It provides experimental evidence of phonon hydrodynamics in black phosphorus and identifies the key role of phonon scattering phase space and momentum exchange in enabling Poiseuille flow.

Findings

Thermal conductivity shows supercubic temperature dependence between 5 and 12 K.

Nonmonotonic phonon mean free path with a Knudsen minimum observed.

Enhanced normal scattering phase space compared to silicon.

Abstract

The travel of heat in insulators is commonly pictured as a flow of phonons scattered along their individual trajectory. In rare circumstances, momentum-conserving collision events dominate, and thermal transport becomes hydrodynamic. One of these cases, dubbed the Poiseuille flow of phonons, can occur in a temperature window just below the peak temperature of thermal conductivity. We report on a study of heat flow in bulk black phosphorus between 0.1 and 80 K. We find a thermal conductivity showing a faster than cubic temperature dependence between 5 and 12 K. Consequently, the effective phonon mean free path shows a nonmonotonic temperature dependence at the onset of the ballistic regime, with a size-dependent Knudsen minimum. These are hallmarks of Poiseuille flow previously observed in a handful of solids. Comparing the phonon dispersion in black phosphorus and silicon, we showthat the phase space for normal scattering events in black phosphorus is much larger. Our results imply that the most important requirement for the emergence of Poiseuille flowis the facility ofmomentum exchange between acoustic phonon branches. Proximity to a structural transition can be beneficial for the emergence of this behavior in clean systems, even when they do not exceed silicon in purity.