Phonon scattering between zero-dimensional electronic states: Spatial versus Landau quantization

Acoustic phonon scattering of electrons and excitons in fully quantized systems based on GaAs/Gaₓ{Al}_{1{{-}}x}$As quantum wells is studied theoretically. We compare spatial quantization by lateral potentials (quantum dots) with Landau quantization by a magnetic field. In the Born approximation, the rate of electron scattering from the first excited state to the ground state of a parabolic quantum dot is one-half of the corresponding transition rate between Landau levels. When an increasing magnetic field is applied to a dot of sizable lateral confinement, the scattering rate first increases strongly, then exhibits pronounced oscillations, and finally decreases at high fields. Exciton relaxation by phonon emission is enhanced by a magnetic field in this system. The relaxation dynamics of quantum dot excitons strongly differs from that of magnetoexcitons in quantum wells.