Raman scattering in a two-dimensional electron gas: Boltzmann equation approach

The inelastic light scattering in a two-dimensional electron gas is studied theoretically using the Boltzmann equation techniques. Electron-hole excitations produce the Raman spectrum essentially different from the one predicted for the 3D case. In the clean limit it has the form of a strong nonsymmetric resonance due to the square-root singularity at the electron-hole frequency ω=vk, while in the opposite dirty limit the usual Lorentzian shape of the cross section is reestablished. The effects of electromagnetic field are considered self-consistently, and the contribution from collective plasmon modes is found. It is shown that unlike 3D metals where plasmon excitations are unobservable (because of very large required transferred frequencies), the two-dimensional electron system gives rise to a low-frequency (ω~k^1/2) plasmon peak. A measurement of the width of this peak can provide data on the magnitude of the electron-scattering rate.