Dynamical theory for strongly correlated two-dimensional electron systems

We describe a method for treating the time-dependent behavior of the electron cloud surrounding each electron in a two-dimensional electron gas. The method is based on a conserving solution of the quantum kinetic equation for the relaxation function of the system using the Mori formalism with two distinct memory functions, one for the collective degrees of freedom and one for the single-particle modes. At lower electron densities these dynamic effects are shown to become increasingly important and to play a part in the eventual solidification into a Wigner crystal. We find that the plasmon resonance energy ${\mathrm{\omega }}_{\mathit{p}}$(q) is strongly depressed compared with the random-phase approximation, leading to a negative dispersion for large q in the low-density region. We have determined the width of the plasmon peak and find that as the Wigner-crystal transition point is approached, the plasmon peak remains well defined even for q comparable to the Fermi momentum. For ${\mathit{r}}_{\mathit{s}}$≳20, we observe a low-energy peak in the excitation spectrum of the electron liquid for values of q matching the reciprocal vector of the Wigner lattice. The occurrence of this peak is matched by the appearance of a large peak in the static susceptibility at that q value.