Breakdown of Herring's processes in cubic semiconductors for subterahertz longitudinal acoustic phonons

In the present work we explain the anomalous behavior of the attenuation of the longitudinal acoustic phonon in GaAs as a function of the phonon energy ω in the subterahertz domain. These attenuations along the [100] direction show a plateau between 0.6 and 1 GHz at low temperatures. We found an excellent agreement between measurements performed by some of us, and new ab initio calculations of third-order anharmonic processes. The formation of the plateau is explained by the competition between different phonon-phonon scattering processes such as Herring's mechanism, which dominates at low frequencies, saturates, and disappears. The plateau is shown to be determined by the phononic final-state phase space available at a given temperature. We predict that a change of scattering mechanism should also show up in the attenuation of silicon around 1.2-1.7 THz, and argue that the attenuation plateau is a general feature of cubic semiconductors.