We develop a theory of the longitudinal excitations of the two-dimensional electron gas in the random-phase approximation. The random-phase approximation describes quantitatively the plasmonic modes in the range of q vectors realized in experiments. We show that the first effects that arise when going to higher q vectors: At large magnetic fields we find discontinuities in the plasmon dispersion at integer filling factors related to the incompressible state at these magnetic fields. Second, in the low-magnetic-field regime, modes arise with 1/B-periodic frequency oscillations, which are governed by the geometrical relation of the wavelength and the radius of the cyclotron orbit at the Fermi energy.

• Received 1 August 1994

DOI:https://doi.org/10.1103/PhysRevB.50.17670