Electron Correlations in an Electron Bilayer at Finite Temperature: Landau Damping of the Acoustic Plasmon

We report angle-resolved Raman scattering observations of the temperature dependent Landau damping of the acoustic plasmon in an electron bilayer system realised in a GaAs double quantum well structure. Corresponding calculations of the charge-density excitation spectrum of the electron bilayer using forms of the random phase approximation (RPA), and the static local field formalism of Singwi, Tosi, Land and Sj\"{o}lander (STLS) extended to incorporate non-zero electron temperature $T_{\rm e}$ and phenomenological damping, are also presented. The STLS calculations include details of the temperature dependence of the intra- and inter-layer local field factors and pair-correlation functions. Good agreement between experiment and the various theories is obtained for the acoustic plasmon energy and damping for $T_{\rm e} \lesssim T_{\rm F}/2$, the Fermi temperature. However, contrary to current expectations, all of the calculations show significant departures from our experimental data for $T_{\rm e} \gtrsim T_{\rm F}/2$. From this, we go on to demonstrate unambiguously that real local field factors fail to provide a physically accurate description of exchange correlation behaviour in low dimensional electron gases. Our results suggest instead that one must resort to a {\em{dynamical}} local field theory, characterised by a {\em{complex}} field factor to provide a more accurate description.