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 two-dimensional (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 $(q>~k_F).\mathrm{}$ 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.