Intrinsic scattering channels and selection rules in four-phonon interactions

We propose selection rules for four-phonon (4ph) scattering that clarify the predominance of the redistribution process. The cutoff frequencies for specific scattering channels are identified, with their feasibility determined by the magnitude of the a-o gap. We obtain substantive evidence to support the fact that the enhancement of 4ph scattering is due to the flat phonon dispersion. An extremely strong intraband scattering in the ZA branch is identified beyond expectation. The same enhancing effect can manifest between homothetic branches as an enhancement mechanism of interband scattering. The homothety is associated with the distribution trend of phonon group velocity, which can anticipate the intensity of 4ph scattering. Our work provides insights and perspectives into 4ph interaction.