We investigate the anharmonic phonon scattering across a weakly interacting interface by developing a quantum mechanics-based theory. We find that the contribution from anharmonic three-phonon scatterings to interfacial thermal conductance can be cast into Landauer formula with transmission function being temperature-dependent. Surprisingly, in the weak coupling limit, the transmission due to anharmonic phonon scattering is unbounded with increasing temperature, which is physically impossible for two-phonon processes. We further reveal that the anharmonic contribution in a real heterogeneous interface (e.g., between graphene and monolayer molybdenum disulfide) can dominate over the harmonic process even at room temperature, highlighting the important role of anharmonicity in weakly interacting heterogeneous systems.
