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.
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