Exchange instability of the two-dimensional electron gas in semiconductor quantum wells

A two-dimensional (2D) electron gas formed in a modulation-doped $\mathrm{GaAs}/{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ single quantum well undergoes a first-order transition when the first excited subband is occupied with electrons, as the Fermi level is tuned into resonance with the excited subband by applying a dc voltage. Direct evidence for this effect is obtained from low-temperature photoluminescence spectra that display the sudden renormalization of the intersubband energy ${E}_{01}$ upon the abrupt occupation of the first excited subband. Calculations within density-functional theory, which treat the 2D exchange potential exactly, show that this thermodynamical instability of the electron system is mainly driven by intersubband terms of the exchange Coulomb interaction, thus being a unique but fundamental property of an electron system with more than one occupied subband.