Magnetoplasma Modes of the Two Dimensional Electron Gas

A two-dimensional electron gas, such as is formed in the electron inversion layer of a GaAs/AlGaAs heterojunction or a silicon metal-oxide-semiconductor field-effect transistor (MOSFET), supports collective charge density wave oscillations at long wavelengths at the plasma frequency, (1.1)$$ {\omega_p}(q) = {(2\pi {n_e}{e^2}q/ \in {m^{*}})^{{\frac{1}{2}}}} $$ where ne is the electron density and ∈ is the dielectric constant of the surrounding medium. In a strong perpendicular magnetic field, because of the Landau quantization of the kinetic energy, the long wavelength density osciEations occur near multiples of the cyclotron frequency ωc = eB/m*c. These neutral excitations may be described as magnetoplasma modes or, equivalently, as “magnetic excitons,” since they involve the promotion of an electron from an occupied state in one Landau level to an unoccupied state in another level. In an ideal, non-interacting two-dimensional electron gas, the energy of these excitations is just equal to the kinetic energy difference of the two Landau levels, (n’ - n)ħωc and their lifetime is infinite. Both electron-electron interactions and disorder or impurity scattering will, in general, shift the energy of these modes and also give them a finite lifetime.