RKKY interaction in semiconductors: Effects of magnetic field and screening

We derive the Ruderman-Kittel-Kasuya-Yosida (RKKY) theory for semiconductors including band degeneracy, modulation of the band edges, and external fields. Explicit expressions are given for a three- and two-dimensional semiconductor in a magnetic field. Screening effects are included by calculating the density correlation function. We show that the RKKY theory with screening is equivalent to the mean-field Zener model.