Interaction induced electron self-interference in a semiconductor: The phonon staircase effect

The exact quantum mechanics of a model semiconductor system of an electron with a discrete and equidistant energy spectrum interacting with a single phonon mode is presented. An electron initially excited into a coherent superposition of states interacts with phonons thereby creating a self-interference in time which reduces the emission of phonons to isolated bursts. This self-interference effect gives rise to steplike behavior in the relaxation kinetics of the electron and phonons. We show that this ''phonon staircase'' effect is a consequence of a correlated initial electron distribution and the violation of energy conservation in the electron-phonon interaction on short time scales.