Electron-gas boundary properties in non-neutral jellium (wide-parabolic-quantum-well) systems

We consider a non-neutral system consisting of a broad but finite slab of immobile uniform positive charge interpenetrated by mobile interacting electrons of total charge less than that of the positive background. This idealized configuration, which we here term an ‘‘embedded electron gas,’’ is approximated by the wide parabolic quantum wells now being grown by molecular-beam epitaxy in the GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Al}}_{\mathit{x}}$As system. The continuation of the positive background outside the embedded electron gas leads to a sharper electronic surface density profile than the standard Lang-Kohn jellium edge profile with the same bulk electron density. We find the sharpened surface profile to be largely independent of layer thickness (universality). This sharpening causes significant differences between the surface properties of the embedded electron gas and those of the ‘‘regular’’ jellium surface model long used to study the surface properties of simple metals. In particular, the ‘‘multipole plasmon’’ mode which exists on a jellium slab with ‘‘regular’’ surfaces is absent for the non-neutral slab, although the two-dimensional plasmon and ‘‘sloshing’’ or center-of-mass (c.m.) modes still occur. The c.m. mode frequency goes, in the limit of small surface-parallel wave vector, to the bare oscillator frequency corresponding to unscreened motion in the positive background potential, as demanded by the generalized Kohn theorem due to Brey et al. This theorem has little relevance to the multipole mode at finite surface-parallel wave vector, however: we show that its existence hinges principally on surface properties.