Excitations from a filled Landau level in the two-dimensional electron gas

We consider an interacting two-dimensional electron system, with a uniform positive background, in a strong perpendicular magnetic field at zero temperature, under conditions where an integral number of Landau levels are filled and the Coulomb energy e2εl0 is smaller than the cyclotron energy ℏωc. The elementary neutral excitations may be described alternatively as magnetoplasma modes, or as magnetic excitons—i.e., a bound state of a hole in a filled Landau level and one electron in an otherwise empty level—and they are characterized by a conserved wave vector k→. The dispersion relations may be calculated exactly, to first order in (e2εl0)ℏωc, for the lowest magnetoplasmon band, which comes in to the cyclotron frequency at k=0. We also calculate the spin-wave dispersion relations for the case where one spin state of a Landau level is completely occupied, and we discuss qualitatively the exciton spectrum for a partially filled Landau level, under the conditions of the fractional quantized Hall effect.