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 rivisit 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 - does not exist: it is simply an artifact 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 may account for the surprisingly good agreement between semiclassical and rigorous quantum-transport calculations.