Observation of Poiseuille flow of phonons in black phosphorus

Machida, Yo; Subedi, Alaska; Akiba, Kazuto; Miyake, Atsushi; Tokunaga, Masashi; Akahama, Yuichi; Izawa, Keisuke; Behnia, Kamran

doi:10.1126/sciadv.aat3374

Cited by 74 publications

(82 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Both conclusions are difficult to understand if one takes them at face value, but the new framework offers a way to understand them as a consequence of adhering to an effective Fourier framework to interpret hydrodynamic effects. Despite the presence of hydrodynamic effects being widely accepted in two-dimensional materials such as graphene [4,11] or black phosphorus [12], their presence in three-dimensional materials such as silicon is still debated, despite recent experimental observations attributed to Poiseuille flow in SrTiO 3 at low temperature [13]. Unfortunately, the lack of access to the microscopic information in the experimental setups does not always allow one to discriminate between the two alternative interpretations.…”

Section: Introductionmentioning

confidence: 99%

Indications of Phonon Hydrodynamics in Telescopic Silicon Nanowires

et al. 2019

View full text Add to dashboard Cite

The validity of Fourier's law in telescopic nanowires is tested by means of molecular dynamics simulations. We observe that the radial dependence of the heat-flux profile, the temperature jump, and the appearance of vorticity obtained in molecular dynamics telescopic wires near the contact point acquire a hydrodynamic character, and we show that they are incompatible with Fourier's law. We propose the Guyer-Krumhansl equation as a generalization capable of capturing these hydrodynamic effects. Latticedynamics results show that the thermal average of the confined modes shows no radial dependence of the vibrating energy inside the wire. This means that hydrodynamic effects could not be related to the confinement effects in these small systems.

show abstract

Section: Introductionmentioning

confidence: 99%

Indications of Phonon Hydrodynamics in Telescopic Silicon Nanowires

et al. 2019

View full text Add to dashboard Cite

show abstract

“…In the hydrodynamic regime, where Poiseuille flow or second sound occur, Fourier's law fails [43][44][45][46], depriving us of the most common tool used to predict the temperature profile in a material. In addition, experiments have shown examples of Fourier's law failure not only in the hydrodynamic regime but also in the ballistic regime, i.e.…”

Section: Introductionmentioning

confidence: 99%

Generalization of Fourier’s Law into Viscous Heat Equations

2020

View full text Add to dashboard Cite

Heat conduction in dielectric crystals originates from the propagation of atomic vibrational waves, whose microscopic dynamics is well described by linearized or generalized phonon Boltzmann transport. Recently, it was shown that the thermal conductivity can be resolved exactly and in a closed form as a sum over relaxons, i.e. the collective phonon excitations that are eigenvectors of Boltzmann equation's scattering matrix [Cepellotti and Marzari, Phys. Rev. X 6, 041013 (2016)]. Relaxons have a well-defined parity and only odd relaxons contribute to the thermal conductivity. Here, we show that the complementary set of even relaxons determines another quantity -the thermal viscosity -that enters into the description of heat transport in the hydrodynamic regime, where dissipation of crystal momentum by Umklapp scattering phases out. We also show how the thermal viscosity and conductivity parametrize two novel viscous heat equations -two coupled equations for the local temperature and drift velocity fields -which represent the thermal counterpart of the Navier-Stokes equations of hydrodynamics in the linear, laminar regime. These viscous heat equations are derived from a coarse-graining of the linearized Boltzmann transport equation for phonons, and encompass both limits of Fourier's law or second sound for strong or weak Umklapp dissipation, respectively. Last, we introduce the Fourier deviation number, a dimensionless parameter that quantifies the steady-state deviations from Fourier's law due to hydrodynamic effects. We showcase these findings in a test case of a complex-shaped device made of silicon or diamond. This formulation generalizes rigorously Fourier's heat equation, and extends the reach of microscopic computational techniques to characterize the fundamental parameters governing heat conduction. * michele.simoncelli@epfl.ch ics. Sussmann and Thellung [12], starting from the linearized BTE (LBTE) in absence of momentumdissipating (Umklapp) phonon-phonon scattering events, derived mesoscopic equations in terms of temperature and phonon drift velocity, the thermal counterpart of pressure and fluid velocity in liquids. Further advances came from Gurzhi [13,14] and Guyer & Krumhansl [15,16] who, including the effect of weak crystal momentum dissipation, obtained equations for damped second sound and Poiseuille heat flow. Among early works, we also mention the discussions on phonon hydrodynamics using approaches different from the LBTE of Refs. [17,18]. While correctly capturing the qualitative features of phonon hydrodynamics, all the theoretical investigations mentioned above are heuristic, e.g. they assume simplified phonon dispersion relations (either power-law [13,14] or linear isotropic [12,15,16]), or neglect momentum dissipation. A more rigorous and general formulation -albeit valid only in the hydrodynamic regime of weak Umklapp scattering -was introduced by Hardy, who extended the discussion of second sound [19] and, together with Albers, of Poiseuille flow in terms of mesoscopic transport equations...

show abstract

“…In the past decades, three phonon hydrodynamic phenomena have been predicted both theoretically [23,24,33,34,39,40] and experimentally [18-21, 25, 35, 41-43], such as the second sound [4,18,19,25,33,41,44], phonon poiseuille flow [21] and Knudsen minimum [34,40]. The second sound is that the transient heat propagates like sound wave because the N scattering recovers the temperature wave equation [22,23,25,44,45].…”

Section: Introductionmentioning

confidence: 99%

“…Different from the second sound, the phonon poiseuille flow is a steady problem. Namely, under a small temperature gradient, the heat flux flows in an infinite long and finite width ribbon like the fluid flows in a long tube with parabolic distributions [21,34]. In addition, as the ribbon width decreases, there is a minimum value of the non-dimensional thermal conductivity, which is the phonon Knudsen minimum [34,40].…”

Section: Introductionmentioning

confidence: 99%

Heat vortex in hydrodynamic phonon transport of two-dimensional materials

Shang

Zhang

Guo

et al. 2020

Sci Rep

View full text Add to dashboard Cite

In this work, the heat vortexes in two-dimensional porous or ribbon structures are investigated based on the phonon Boltzmann transport equation (BTE) under the Callaway model. First, the separate thermal effects of normal (N) scattering and resistive (R) scattering are investigated with frequency-independent assumptions. And then the heat vortexes in graphene are studied as a specific example. It is found that the heat vortexes can appear in both ballistic (rare R/N scattering) and hydrodynamic (N scattering dominates) regimes but disappear in the diffusive (R scattering dominates) regime. As long as there is not sufficient R scattering, the heat vortexes can appear in present simulations.

show abstract

Observation of Poiseuille flow of phonons in black phosphorus

Abstract: Hydrodynamic flow of phonons, previously detected only in a handful of solids, is observed in black phosphorus.

Cited by 74 publications

References 50 publications

Indications of Phonon Hydrodynamics in Telescopic Silicon Nanowires

Indications of Phonon Hydrodynamics in Telescopic Silicon Nanowires

Generalization of Fourier’s Law into Viscous Heat Equations

Heat vortex in hydrodynamic phonon transport of two-dimensional materials

Contact Info

Product

Resources

About