Dynamic correlations in the highly dilute 2D electron liquid: loss function, critical wave vector and analytic plasmon dispersion

Correlations, highly important in low–dimensional systems, are known to decrease the plasmon dispersion of two–dimensional electron liquids. Here we calculate the plasmon properties, applying the 'Dynamic Many-Body Theory', accounting for correlated two–particle–two–hole fluctuations. These dynamic correlations are found to significantly lower the plasmon's energy. For the data obtained numerically, we provide an analytic xpression that is valid across a wide range both of densities and of wave vectors. Finally, we demonstrate how this can be invoked in determining the actual electron densities from measurements on an AlGaAs quantum well.