Observation of the Poiseuille flow of phonons in black phosphorus

The travel of heat in an insulating solid is commonly pictured as a flow of phonon quasi-particles. In such a picture, phonons are decelerated by scattering with each other. However, in rare circumstances, momentum-conserving scattering between phonons dominate, and phonons can enter a hydrodynamic regime, where they flow like fluids inside a crystalline lattice and retard only by hitting the sample boundaries. This phenomenon dubbed “phonon Poiseuille flow”, which is a phononic counterpart of the Poiseuille flow in classical hydrodynamics, was thought to occur only in ultrapure solids.
In the presentation, we report on a study of heat flow in bulk black phosphorus, a material attracting renewed attention for a variety of fundamental and technological reasons. We show that the thermal conductivity of this material exhibits a faster than cubic temperature dependence just below the peak temperature of thermal conductivity. 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, the low-energy phonon density of states in black phosphorus is found to be much larger, favoring normal momentum-conserving scattering events. Contrary to the previous belief, our results imply that the most important requirement for the emergence of Poiseuille flow is the facility of momentum exchange between acoustic phonon branches [1].

[1] Y. Machida et al., Sci. Adv. 4, eaat3374 (2018).