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We study the effect of characteristic size variation on the phonon thermaltransport in crystalline GeTe for a wide range of temperatures using thefirst-principles density-functional method coupled with the kinetic collectivemodel approach. The characteristic size dependence of phonon thermal transportreveals an intriguing collective phonon transport regime, located in betweenthe ballistic and the diffusive transport regimes. Therefore, systematicinvestigations have been carried out to describe the signatures of phononhydrodynamics via the competitive effects between grain size and temperature. Acharacteristic nonlocal length associated with phonon hydrodynamics and a heatwave propagation length has been extracted. The connections between phononhydrodynamics and these length scales are discussed in terms of the Knudsennumber. Further, the scaling relation of thermal conductivity as a function ofcharacteristic size in the intermediate size range emerges as a crucialindicator of the strength of the hydrodynamic behavior. A ratio concerningnormal and resistive scattering rates has been employed to understand thesedifferent scaling relations, which seems to control the strength and prominentvisibility of the collective phonon transport in GeTe. This systematicinvestigation emphasizes the importance of the competitive effects betweentemperature and characteristic size on phonon hydrodynamics in GeTe, which canlead to a better understanding of the generic behavior and consequences of thephonon hydrodynamics and its controlling parameters in low-thermal conductivitymaterials.

Effect of characteristic size on the collective phonon transport in crystalline GeTe