Excitonic emission in the presence of a two dimensional electron gas: a microscopic understanding

The near- and far-field photoluminescence spectra of a gated two-dimensional electron gas have been measured. Spatial fluctuations in the electron density are found to be manifested as spatial fluctuations in the emission amplitude of the negatively charged exciton (X$^{-}$) and in the peak energy of the neutral exciton (X). Consequently, the far-field X$^{-}$ spectrum is a homogoneously broadened Lorentzian, while the X lineshape exhibits substantial inhomogenous broadening. We present a novel and simple technique to extract the electron density from the X$^{-}$ spectrum. We show that width of the far-field X line is proportional to the electron density fluctuations; hence it can be used to characterize the inhomogeneity in the electron density.