Density-dependent band-gap renormalization of one-component plasma in ${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$As/${\mathrm{Al}}_{\mathit{y}}$${\mathrm{In}}_{1\mathrm{-}\mathit{y}}$As single quantum wells

We report the results of a photoluminescence investigation on n-type modulation-doped ${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{In}}_{1\mathrm{-}\mathit{x}}$As/${\mathrm{Al}}_{\mathit{y}}$${\mathrm{In}}_{1\mathrm{-}\mathit{y}}$As single quantum wells which are intentionally doped in the well center with Be acceptors. Strong collective recombinations of the two-dimensional electron gas with different k states up to the Fermi edge and localized holes bound to ionized acceptors are observed. By using an electron-transfer effect, the density-depdendent band-gap renormalization of an electron one-component plasma in a quantum well is quantitatively measured. Experimental results are compared with existing theory.