Umklapp scattering is not necessarily resistive

Abstract

Since Peierls' pioneering work, it is generally accepted that phonon-phonon scattering processes consist of momentum-conserving normal scatterings and momentum-destroying Umklapp scatterings, and that the latter always induce thermal resistance. We show in this work that Umklapp scatterings are not necessarily resistive -no thermal resistance is induced if the projected momentum is conserved in the direction of heat flow. This distinction is especially important in anisotropic materials such as graphite and black phosphorous. By introducing a direction-dependent definition of normal and Umklapp scattering, we can model thermal transport in anisotropic materials using the Callaway model accurately. This accuracy is physically rooted in the improved description of mode-specific phonon dynamics. With the new definition, we predict that second sound might persist over much longer distance than previously expected.

Size effect on phonon hydrodynamics in graphite microstructures and nanostructures

“…16(a). Also, the present iterative solution is quite consistent with the reference one [35] with the same pseudopotential and vdW functional, inferring that the first-principles calculation in Sec. II B 1 is reliable.…”

“…However, it contradicts the results of phonon drift in graphite as detailed in Appendix A. The recent studies [26,35] proposed that the classification of normal and Umklapp scatterings in anisotropic materials should be based on the projected momentum along 075450-3 FIG. 2.…”

“…The modified definition is similar for heat transport along the c-axis direction. The present definition has one advantage over the previous one [26,35]: the normal and Umklapp scattering rates would be unique when the heat flow direction varies in real space along the basal plane of a graphite ribbon with irregular geometrical shapes. With the modified definition in Eq.…”

“…In this paper, a pertinent computational framework is developed based on a deterministic numerical solution of Callaway's model. The normal and Umklapp phonon scattering rates in graphite are calculated through careful consideration of both the van der Waals (vdW) interaction [34] and the special definition of the Umklapp process in strongly anisotropic systems [26,35]. We also introduce an efficient approximate scheme to treat the anisotropic phonon properties of graphite, which is essentially different from the 2D graphene system [30,31].…”

Tailored elastic surface to body wave Umklapp conversion

“…We stress that these mechanisms do not violate momentum conservation 1 ; unlike in conventional graded structures we are not considering only the true momenta of interfering waves (phonons) within a crystal, but taking advantage of the momentum of the system as a whole. Nuances of this simplistic definition arise due to the apparent interchangeability of N-process and U-process through altering the primitive cell, and the associated (quasi)momentum conservation [19][20][21] . The distinction is achieved throughout by analysing the dispersion curves of the locally periodic elements, along with simplified isofrequency contours ( Supplementary Figs.…”