Phonon Hydrodynamic Transport: Observation of Thermal Wave-Like Flow and Second Sound Propagation in Graphene at 100 K

Several experimentaland theoretical investigations confirm thefailure of the classical Fourier's law in low-dimensional systemsand ultrafast thermal transport. Hydrodynamic heat transport has beenrecently considered as a promising avenue to thermal management andphonon engineering in graphitic materials. Non-Fourier features aretherefore required to describe and distinguish the hydrodynamic regimefrom other heat transport regimes. In this work, we provide an efficientframework for the identification of hydrodynamic heat transport andsecond sound propagation in graphene at 80 and 100 K. We solve boththe dual-phase-lag model and the Maxwell-Cattaneo-Vernotteequation based on the finite element method with ab initio data asinputs. We emphasize on the detection of thermal wave-like behaviorusing macroscopic quantities including the Knudsen number and secondsound velocity beyond Fourier's law. We present a clear observationof the crossover phenomena from the wave-like regime to diffusiveheat transport predicted in terms of mesoscopic equations. This presentformalism will contribute to a clear and deeper understanding of hydrodynamicheat transport in condensed systems for future experimental detectionof second sound propagation above 80 K.

Automated summary

This study provides an efficient framework for identifying hydrodynamic heat transport and second sound propagation in graphene. It solves the dual-phase-lag model and the Maxwell-Cattaneo-Vernotte equation using the finite element method with ab initio data. The study emphasizes the detection of thermal wave-like behavior using macroscopic quantities, going beyond Fourier's law. It also observes a crossover from the wave-like regime to diffusive heat transport, as predicted by mesoscopic equations. This research is of great importance for future experimental detection of second sound propagation above 80 K.