Demystifying umklapp vs normal scattering in lattice thermal conductivity

摘要

We discuss the textbook presentation of the concept of umklapp vs normal phonon-phonon scattering processes in the context of lattice thermal conductivity. A simplistic picture, in which the “momentum conservation” in a normal process leads to the conservation of the heat flux, is only valid within the single-velocity Debye model of phonon dispersion. Outside this model, the simple “momentum conservation” argument is demonstrably inaccurate and leads to conceptual confusion. Whether or not an individual scattering event changes the direction of the energy flow is determined by the phonon group velocity, which, unlike the quasimomentum, is a uniquely defined quantity independent of the choice of the primitive cell in reciprocal space. Furthermore, the statement that normal processes do not lead to a finite thermal conductivity when umklapp processes are absent is a statistical statement that applies to a phonon distribution rather than to individual scattering events. It is also important to understand that once umklapp processes are present, both normal and umklapp processes contribute to thermal resistance. A nuanced explanation of the subject would help avoid confusion of the student and establish a connection with cutting edge research.