Collective modes in the two-dimensional electron liquid near the Wigner phase transition

We have investigated the properties of the collective modes of the two dimensional electron liquid in regions of phase space near the Wigner phase transition. We used a new method which we have recently developed for dealing with the strongly correlated electron liquid. We find that the dynamical correlations cause the dispersion curve of the 2D plasmon to pass through a maximum, leading to negative dispersion for larger q values and a much reduced value for the plasmon cut-off qc. It was of interest to discover, on comparing the plasmon dispersion curve with the corresponding curve for the phonon in the Wigner crystal, that the negative dispersion of the plasmon duplicated the turnover of the phonon dispersion curve at the edge of the Brillouin zone, q = 1/2G, and that the two curves were in close agreement for all q less than the plasmon cut–off. A new collective mode in the liquid phase on the high q side of the single-particle excitation spectrum was also found to match up with the phonon dispersion curve near q ~ G.