Crystal-symmetry-based selection rules of anharmonic phonon scattering from a group theory formalism*

Phonon-phonon scattering serves a significant role in heat conduction in solids. Researchers have
derived many selection rules of phonon-phonon scattering imposed by energy and momentum
conservation conditions, as well as crystal symmetries. However, a systematic formalism to
generate all crystal-symmetry-based selection rules of phonon-phonon scatterings in a given
material is still lacking. In this work, using group theory, we provide a general method to
enumerate these selection rules and illustrate our method using model systems graphene and 1D
systems with a screw axis. Our analysis provides new explanations to previous findings of
phonon-phonon scattering selection rules in these systems and gives clues to new selection rules.
Our study provides a new tool to understand the relationship among crystal symmetry, phonon
scattering, and lattice thermal conductivity.