Interacting intersubband excitations in parabolic semiconductor quantum wells

We calculate the finite wave-vector intersubband collective excitation spectra in wide parabolic wells at low two-dimensional electron densities where only the lowest quantum subband is occupied by electrons. We use a self-consistent time-dependent local-density approximation to calculate the linear response of the system, comparing our density-functional results with the noninteracting time-dependent Hartree approximation to estimate the magnitudes of exchange-correlation corrections to the collective-mode dispersion. We predict a qualitatively new phenomenon at low electron densities where, in the presence of exchange-correlation effects, it becomes possible for the collective charge-density excitation (i.e., the intersubband plasmon mode) to lie below the intersubband quasiparticle continuum. As the electron density is lowered, the charge-density excitation passes through the intersubband single-particle Landau continuum, eventually going below the intersubband single-particle excitations. In this low-density regime (0.1–0.2×${10}^{11}$ ${\mathrm{cm}}^{\mathrm{-}2}$), the collective and the single-particle intersubband excitations are strongly resonantly coupled, leading to an experimentally observable line-splitting phenomenon in the far-infrared-absorption and inelastic-light-scattering spectra. We calculate the far-infrared-absorption spectra self-consistently and find the interesting result that at a critical density even the long-wavelength intersubband charge-density excitation is Landau damped because it is essentially degenerate with the single-particle excitations. We provide detailed numerical results for the intersubband collective charge- and spin-density excitation spectra and the associated far-infrared-absorption spectra for realistic GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As parabolic quantum-well structures, comparing some of our results with the corresponding results for wide square-well structures. We also provide a theoretical comparison between the self-consistent density-functional theory of intersubband linear response with the corresponding diagrammatic perturbation-theory approach.