Thermal Transport in Crystals as a Kinetic Theory of Relaxons

Abstract

Thermal conductivity in dielectric crystals is the result of the relaxation of lattice vibrations described by the phonon Boltzmann transport equation. Remarkably, an exact microscopic definition of the heat carriers and their relaxation times is still missing: phonons, typically regarded as the relevant excitations for thermal transport, cannot be identified as the heat carriers when most scattering events conserve momentum and do not dissipate heat flux. This is the case for twodimensional or layered materials at room temperature, or three-dimensional crystals at cryogenic temperatures. In this work we show that the eigenvectors of the scattering matrix in the Boltzmann equation define collective phonon excitations, termed here relaxons. These excitations have well defined relaxation times, directly related to heat flux dissipation, and provide an exact description of thermal transport as a kinetic theory of the relaxon gas. We show why Matthiessen's rule is violated, and construct a procedure for obtaining the mean free paths and relaxation times of the relaxons. These considerations are general, and would apply also to other semiclassical transport models, such as the electronic Boltzmann equation. For heat transport, they remain relevant even in conventional crystals like silicon, but are of the utmost importance in the case of two-dimensional materials, where they can revise by several orders of magnitude the relevant time-and length-scales for thermal transport in the hydrodynamic regime. arXiv:1603.02608v3 [cond-mat.mtrl-sci]

Thermal conductivity decomposition in two-dimensional materials: Application to graphene

“…However, the general trend is clear: Applying a tensile strain reduces v in and enhances v out , which means that tensile strain softens the in-plane phonons but hardens the out-of-plane phonons. The fact that we need to treat the group velocities as fitting parameters may be justified in terms of the concept of relaxons proposed by Cepellotti and Marzari [5]. The large relaxation times of the flexural modes observed in our MD results should be related to the relaxation times of relaxons whose velocities are not the same as the phonon velocities.…”

“…The high lattice thermal conductivity [1,2] of twodimensional (2D) graphene and other carbon nanostructures has stimulated intensive studies to understand phonon transport in them [3][4][5]. Apart from holding great prospects for thermal management applications in nanoelectronic devices, graphene also serves as a benchmark for investigating fundamental questions regarding thermal transport in lowdimensional systems.…”

“…One exception is the method by Gill-Comeau and Lewis [34], where the total thermal conductivity is decomposed into a single-particle component and a collective one, the latter being crucial to materials in which the nonresistive normal (non-umklapp) scattering is important, which is the case for graphene [10,14,15]. Another recent development proposes that heat conduction in 2D materials is due to relaxons, which are wave packets of phonons that arise in the context of the linearized Boltzmann equation [5].…”

Transport waves as crystal excitations

“…Therefore, to find an equation for a temperature wave, one must look for waves in the phonon excitation numbers ∆n µ . One can use the LBTE to describe the dynamics of ∆n µ [23]:…”

“…We stress that these waves do not represent single particle excitations, but are collective excitations of the equilibrium distribution functions. For the case of thermal transport, these excitations represent energy (heat) or temperature waves, that in the long wavelength limit reduce to relaxons [23], i.e. the heat carriers of bulk steady arXiv:1612.04317v2 [cond-mat.mtrl-sci] 1 Sep 2017 state transport.…”