Observation of Poiseuille Flow of Phonons in Black Phosphorus

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. Here we report on a study of entropy flow in bulk black phosphorus between 0.1 K and 80 K. We find a thermal conductivity displaying a faster than cubic temperature dependence between 5 K and 12 K. Consequently, the effective phonon mean-free-path becomes non-monotonic 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 Si, we show that 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 flow is the facility of momentum exchange between acoustic phonon branches and indicate that the departure from the cubic symmetry can be beneficial for this behavior. Contrary to what was previously assumed, extreme purity is not a strict requirement for the observation of hydrodynamic phonon flow.