Band-gap renormalization of modulation-doped quantum wires

We measure the photoluminescence spectra for an array of modulation doped, T-shaped quantum wires as a function of the one-dimensional density $n_e,$ which is modulated with a surface gate. We present self-consistent electronic structure calculations for this device which show a band-gap renormalization which, when corrected for excitonic energy and its screening, are largely insensitive to $n_e$ and which are in quantitatively excellent agreement with the data. The calculations show that electron and hole remain bound up to $\sim 3\times {10}^6\hspace{0.5em}{\mathrm{cm}}^{-1}$ and that, therefore, the stability of the exciton far exceeds the conservative Mott criterion, as determined from the Bethe-Salpeter equation.