Umklapp scattering is not necessarily resistive

Since Peierls's 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 distances than previously expected.