Calculation of Anharmonic Coupling Constants between Phonon Modes in GaAs

Abstract

Anharmonic coupling between phonon modes of a crystal determine many of its properties, thermal conductivity being a standard example. Although anharmonicity-related effects observed in bulk crystals (decay of the zone-center longitudinal optical (LO) phonon or acoustic wave attenuation) rely only on a small subset of anharmonic couplings, the full set of such constants is needed for a complete description of phonon-induced dephasing and relaxation of electrons and excitons in quantum dots [1–4]. The reason for this is that breaking of the translational symmetry and appearance of a quantized spectrum completely changes the energy-momentum conservation conditions and opens decoherence (relaxation and dephasing) paths which are not allowed in a bulk crystal. So far, only the anharmonic couplings between acoustic branches have been completely described [5], while the only known coupling involving optical phonons is that between the LO phonon and two longitudinal acoustic (LA) phonons, which seems to be responsible for the decay of the zone-center LO phonon in a bulk crystal [6] and is therefore accessible experimentally [7]. In this paper, we derive third-order anharmonic coupling constants between various phonon modes in a zinc-blende crystal. We use a model combining the