Excitation modes of neutral jellium slabs.

Abstract

The excitation modes of electrons in symmetric, neutral jellium slabs are studied within the time-dependent local density and related approximations, in the regime when there are several bound states below the Fermi level. Unlike most previous calculations, the present ones do not require all single-particle wave functions to vanish at some small distance from the slab. This modification of the boundary conditions significantly affects the excitation spectra, generally reducing the number of peaks that appear. In particular, from our calculations modeling excitation by longitudinal near fields with nonzero surface-parallel wave vector, we do not find resolvable peaks above the bulk plasmon frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$ which could be interpreted as standing plasma waves resonating across the neutral slab. This is in contrast to the case of a symmetric but non-neutral jellium slab (wide parabolic quantum well or embedded electron gas) where we do predict distinct (but weak) standing plasmon resonances above ${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$ at nonzero surface-parallel wave vector, even for a well with only a few occupied bound states. Although bulk plasmon resonances seem to be unobservable in the relatively narrow, symmetric, neutral jellium slabs studied here, we do find the following peaks consistently at low surface-parallel wave vector: an ``intraband'' mode near the two-dimensional-plasmon frequency and a ``multipole surface plasmon'' near 0.8${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$, the latter being amenable also to other interpretations for very thin slabs. Further peaks, including a cluster near ${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$, are harder to interpret. They can be related to single-particle transitions in the case of thin slabs. However, in the intermediate-thickness regime it is difficult to assign a unique physical cause to each peak in a spectrum, and various ways to help sort out ambiguities are illustrated. These do not always resolve matters since for neutral jellium slabs one has a relatively wide transition region between quantum and classical size effects.