Static and dynamic properties of coupled electron-electron and electron-hole layers

We have investigated coupled layers of electron and hole liquids in semiconductor heterostructures in zero magnetic field for densities r(x) less than or similar to 20 using the Singwi-Tosi-Land-Sjolander self-consistent formalism generalized for layers of unequal density. We calculate susceptibilities, local fields, pair correlation functions, and the dispersion of the collective modes for a range of layer spacings. We include cases where the densities in the two layers are not equal. We find generally that static correlations acting between layers do not have a large effect; on the correlations within the layers, For coupled electron-hole layers we find that as the spacing between the layers decreases there is a divergence in the static susceptibility of the liquid that signals an instability towards a charge-density-wave ground state. When the layer spacing approaches the effective Bohr radius the electron-hole correlation function starts to diverge at small interparticle separations. This effect is a precursor to the onset of excitonic bound states but this is preempted by the charge-density-wave instability. The acoustic plasmon exhibits a crossover in behavior from a coupled mode to a mode that is confined to a single layer. Correlations sometimes push the acoustic plasmon dispersion curve completely into the single-particle excitation spectrum. For layers with different densities the Landau damping within the single-particle excitation region is sometimes so weak that the acoustic plasmon can exist inside the region asa sharp resonance. We find for the electron-hole case that proximity to the charge-density-wave instability has an unusual effect on the dispersion of the optical plasmon mode.