Gauge-Invariant Formulation of Fermi's Golden Rule and Its Application to High-Field Transport in Semiconductors

A gauge-invariant formulation of Fermi's Golden rule is proposed. We shall revisit the conventional description of carrier-phonon scattering in the presence of high electric fields by means of a gauge-invariant density-matrix approach. We show that the so called intracollisional field effect, as usually accounted for, has been always overestimated due to the neglect of the time variation of the basis states, which in turn leads to a ill-defined Markov limit in the carrier-phonon interaction process. This is confirmed by our fully three-dimensional simulations of charge transport in state-of-the-art semiconductor superlattices.