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

Abstract

We study the effect of characteristic size variation on the phonon thermal transport in crystalline GeTe for a wide range of temperatures using the first-principles density-functional method coupled with the kinetic collective model approach. The characteristic size dependence of phonon thermal transport reveals an intriguing collective phonon transport regime, located in between the ballistic and the diffusive transport regimes. Therefore, systematic investigations have been carried out to describe the signatures of phonon hydrodynamics via the competitive effects between grain size and temperature. A characteristic nonlocal length associated with phonon hydrodynamics and a heat wave propagation length has been extracted. The connections between phonon hydrodynamics and these length scales are discussed in terms of the Knudsen number. Further, the scaling relation of thermal conductivity as a function of characteristic size in the intermediate size range emerges as a crucial indicator of the strength of the hydrodynamic behavior. A ratio concerning normal and resistive scattering rates has been employed to understand these different scaling relations, which seems to control the strength and prominent visibility of the collective phonon transport in GeTe. This systematic investigation emphasizes the importance of the competitive effects between temperature and characteristic size on phonon hydrodynamics in GeTe, which can lead to a better understanding of the generic behavior and consequences of the phonon hydrodynamics and its controlling parameters in low-thermal conductivity materials.

Phonon hydrodynamics in crystalline materials

“…Between ballistic (linear scaling of κ with L) and diffusive (L independent κ) thermal transport regime, a superlinear scaling in the intermediate L regime was found assisting a Knudsen minimumlike hydrodynamic feature at a particular temperature [145]. On the contrary, sublinear scaling leads to weak phonon hydrodynamics.…”

“…By decomposing κ into ballistic and scattered contributions, Knudsen minimum was observed to be present at 100 K at width ≈ 0.7 µm for suspended graphene [176]. In a recent ab initio study [145], three dimensional crystalline GeTe was found to exhibit a shallow Knudsen minimum like feature at low temperature marking the onset of the phonon hydrodynamics.…”

“…Here we note that in a situation of negligible presence of Umklapp scattering and zero drift velocity at the boundary, thermal conductivity actually scales as W 2 . However, the unavoidable presence of Umklapp scattering in the real samples forces the exponent to take the value α, where 1 < α < 2 [49,145,169]. This superlinear width dependency of κ is strikingly distinct from the ballistic and the diffusive thermal transport regimes where κ varies linearly and stays constant with the width of the sample, respectively [15,49,145].…”

“…temperature and grain size. Systematic investigation of thermal transport as a function of characteristic size [145] revealed the complete hydrodynamic window in temperature-grainsize plane via Knudsen number and average scattering rate analysis using GK conditions.…”

“…Moreover, the scaling of thermal conductivity (κ) with characteristic length (L) was found to dictate the existence of the Knudsen minimumlike prominent hydrodynamic feature [145].…”