Hydrodynamic phonon transport: past, present and prospects

Abstract

The hydrodynamic phonon transport was studied several decades ago for verifying the quantum theory of lattice thermal transport. Recent prediction of significant hydrodynamic phonon transport in graphitic materials shows its practical importance for high thermal conductivity materials and brought a renewed attention. As the study on this topic has been inactive to some extent for several decades, we aim at providing a brief overview of the past studies as well as very recent studies. The topics we discuss in this chapter include the collective motion of phonons, several approaches to solve the Peierls-Boltzmann transport equation for hydrodynamic phonon transport, the role of normal scattering for thermal resistance, and the propagation of second sound. Then, we close this chapter with our perspectives for the future studies and the practical implication of hydrodynamic phonon transport.

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

“…Phonon hydrodynamics is a heat transport phenomena where the collective flow of phonons dominate the heat conduction in materials [1,[4][5][6][7][8]. This is enabled by significantly higher momentum conserving normal scattering (N) events compared to other dissipative scattering events * kanka.ghosh@u-bordeaux.fr [umklapp (U), isotope (I), and boundary scattering (B)], favoring damped wave propagation of temperature fluctuations [9,10].…”

A novel transient heat conduction phenomenon to distinguish the hydrodynamic and (quasi) ballistic phonon transport

“…In the absence of time-varying heat source or oscillatory boundaries, the temperature always exponentially decays with time due to involvement of first-order time-derivative in the diffusion equation. However, when the characteristic length/time of the thermal system is comparable to the phonon mean free path/relaxation time [1,2,3,4,5], or when the momentum-conserved normal (N) scattering dominates heat conduction [6,7,8,9], the Fourier's law may be broken [10,11,12,13] and the wave like propagation of heat [14,15,16,17,18,19] may appear.…”

“…In the past decades, many theoretical, numerical and experimental studies have been conducted on the wave like propagation of heat [14,20,11] in the non-Fourier regime. One of the underlying physical mechanisms of wave like propagation of heat is the hydrodynamic phonon transport [21,22,9,23,24,25], which emerges when the N scattering frequently happens and the momentum-destroying resistive (R) scattering rarely happens.…”

“…Note: There are some disputes about the term "hydrodynamic phonon transport" or "phonon hydrodynamic" in different references [11,3,43,32,33]. One of them [11,23] focus on the hydrodynamic phenomena of phonon transport due to strong N-scattering, while the other [43,44,3,45] uses the hydrodynamic equations to describe the quasiballistic or non-diffusive phonon transport, where the strong N scattering is not required.…”

“…Note: There are some disputes about the term "hydrodynamic phonon transport" or "phonon hydrodynamic" in different references [11,3,43,32,33]. One of them [11,23] focus on the hydrodynamic phenomena of phonon transport due to strong N-scattering, while the other [43,44,3,45] uses the hydrodynamic equations to describe the quasiballistic or non-diffusive phonon transport, where the strong N scattering is not required. In this study, the hydrodynamic phonon transport happens when the N scattering is much stronger than the boundary scattering and the boundary scattering is much stronger than the R scattering [8,7,32,33].…”