Contribution of drifting carriers to the Casimir-Lifshitz and Casimir-Polder interactions with semiconductor materials

We develop a new theory for Casimir-Lifshitz and Casimir-Polder interactions with semiconductor surfaces that takes into account charge drift in the bulk material. The corresponding frequency-dependent dispersion relations describe a crossover between Lifshitz results for dielectrics and for good conductors. In the quasi-static limit, our calculated reflection amplitudes coincide with those recently computed to account for Debye screening in the thermal Lifshitz force with conducting surfaces with small density of carriers.