Collective intersubband transitions in quantum wells: A comparative density-functional study

We use linearized time-dependent (current) density-functional theory to study collective transitions between the two lowest subbands in GaAs/Al_xGa_1-xAs quantum wells. We focus on two particular systems, for both of which experimental results are available: a wide single square well and a narrow asymmetric double quantum well. The aim is to calculate the frequency and linewidth of collective electronic modes damped through electron-electron interaction only. Since Landau damping, i.e., creation of single electron-hole pairs, is not effective here, the dominant damping mechanism involves dynamical exchange-correlation effects such as multipair production. To capture these effects, one has to go beyond the widely used adiabatic local-density approximation (ALDA) and include retardation effects. We perform a comparative study of two approaches which fall in this category. The first one is the dynamical extension of the ALDA by Gross and Kohn. The second one is a more recent approach which treats exchange and correlation beyond the ALDA as viscoelastic stresses in the electron liquid. It is found that the former method is more robust: it performs similarly for strongly different degrees of collectivity of the electronic motion. Results for single and double quantum wells compare reasonably to experiment, with a tendency towards overdamping. The viscoelastic approach, on the other hand, is superior for systems where the electron dynamics is predominantly collective, but breaks down if the local velocity field is too rapidly varying, which is the case for single-electron-like behavior such as tunneling through a potential barrier.