Gauge-invariant formulation of Fermi's golden rule: 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 an ill-defined Markov limit in the carrier-phonon interaction process. This may account for the surprisingly good agreement between semiclassical and rigorous quantum-transport calculations previously reported, and is confirmed by our fully three-dimensional simulations of charge transport in state-of-the-art semiconductor superlattices, which show significant current overestimations.