Plasmon dispersion in dilute two-dimensional electron systems: Quantum-classical and Wigner crystal-electron liquid crossover

We theoretically calculate the finite wave vector plasmon dispersion in a low density 2D electron layer taking into account finite temperature, finite layer width, and local field corrections. We compare our theoretical results with recent Raman scattering spectroscopic experimental 2D plasmon dispersion data in GaAs quantum wells at very low carrier densities ($r_s > 10$) and large wave vectors ($q \ge k_F$). We find good agreement with the experimental data, providing an explanation for why the experimentally measured dispersion seems to obey the simple classical long wavelength 2D plasmon dispersion formula. We also provide a critical discussion on the observable manifestations of the quantum-classical and the Wigner crystal - electron liquid crossover behavior in the 2D plasmon properties as a function of electron density and temperature in GaAs quantum well systems.