Surface-plasmon dispersion and size dependence of Mie resonance: Silver versus simple metals

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Abstract
The recently observed blueshift of the surface plasmon of Ag with increasing parallel momentum and of the Mie resonance of small Ag particles with decreasing radius are discussed in terms of a model for the dynamical response of a two-component s-d electron system. In the case of flat Ag surfaces, the 5s conduction electrons are treated as a semi-infinite homogeneous electron gas while the influence of the fully occupied 4d bands is described via a polarizable medium which extends up to a certain distance from the surface. Using the time-dependent density-functional approach it is shown that the absence of the s-d screening interaction in the surface region leads to a positive dispersion of the surface plasmon in agreement with the data. A self-energy approach is introduced which allows us to establish a qualitative relation between the scattering processes at a flat metal surface and those at the surface of a spherical particle. Using this approach it is argued that the blueshift of the Mie resonance of Ag particles can also be understood in terms of a reduced s-d interaction in the region where the s electrons spill out into the vacuum. Finally, it is shown that the polarizability of simple metal particles exhibits above the Mie resonance a collective excitation which is the analogue of the dipolar surface plasmon observed on the flat surfaces of various simple metals. This feature seems to have been observed in recent absorption spectra on large K clusters.