Electron-electron interaction and intersubband absorption coefficient in a GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum well

The full random-phase approximation (RPA) spectral function is calculated for an electron gas confined in a modulation-doped GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum well. In the first subband we observe the typical structure of the two-dimensional plasmaron. The renormalization of the chemical potential is smaller than that of the edge of the density of states. In the second subband the single-state broadening and the band renormalization are found to be smaller than in the first subband. When the depolarization effect is neglected, the intersubband absorption line is narrower than the inhomogeneous broadening due to the different effective masses in the two subbands for the noninteracting electron system. This result is explained by the two-dimensional plasmaron structure in the first subband. The theoretical peak is narrower than the experimental one. If in the spectral function the self-energy is taken at the energy of the noninteracting electron, the corresponding absorption line is broader than the experimental one. If the depolarization effect is included, the approximate linewidth is found to be narrower and the full RPA linewidth broader than the experimental one.