Magnetoplasmons and cyclotron resonance in disordered two-dimensional electronic systems

We discuss the interplay of disorder and interactions in determining the spectrum of inter-Landau-level excitations of a two-dimensional electron gas in a strong magnetic field. Our work is based in part on some new exact sum rules for the inter-Landau-level response functions of noninteracting electrons in a strong magnetic field and in part on perturbative approximations for interaction and disorder. We emphasize the importance of including vertex corrections in the response functions which are consistent with the approximation that has been used for the self-energy. In the absence of disorder or in the absence of interactions our perturbative approximations reduce to those used by earlier workers for those limits.