Photoabsorption by Volume Plasmons in Metal Nanoclusters

It is well known that plasmons in bulk metals cannot be excited by direct photoabsorption, that is, by coupling of volume plasmons to light. Here we demonstrate that the situation in nanoclusters of the same metals is entirely different. We have carried out a photodepletion measurement for ${\mathrm{Na}}_{20}$ and ${\mathrm{Na}}_{92}$ and identified a broad volume plasmon absorption peak centered slightly above 4 eV, revealing the possibility of optical excitation of volume-type collective electronic modes in a metallic system. The observed phenomenon is related to different selection rules for finite systems.

Figure 1

A depiction of the theoretically predicted evolution of the photoabsorption strength $S$ of surface and volume plasmons in nanoclusters as a function of size (adapted from 6, 11). Microscopically, these collective modes are envelopes of coherent superpositions of electron-hole excitations, and because of the discreteness of electronic states in clusters they are split among several transitions and broadened, as indicated by the dashed lines. The surface and volume labels derive from the fact that the two resonance regions can be shown to correspond to two different types of electron density oscillations—translation vs compression—whose dipolar components are schematically outlined by the diagrams at the top (the gray rectangle represents the positive charge distribution, and the dotted lines the oscillating valence electron density). In finite particles both collective resonances are redshifted with respect to the bulk frequencies (labeled ${\omega }_{\mathrm{Mie}}$ and ${\omega }_p$, respectively), and both can couple to light, whereas in the bulk limit the volume plasmon cannot.

Figure 2

(a) Photoabsorption cross sections per atom of ${\mathrm{Na}}_{20}$ nanoclusters. The thick line is drawn through the individual experimental data points that are shown as diamonds in (b), the squares and circles are data from 31, 32, respectively. (b) Diamonds: photoabsorption cross sections of ${\mathrm{Na}}_{20}$; solid line: fit to the data by means of a sum of Lorentzian profiles (dashed lines). The shaded peak is the volume plasmon which becomes dipole-active in finite particles.

Figure 3

Photoabsorption cross sections and fits for ${\mathrm{Na}}_{92}$, marked as in Fig. 2b.