Modification of the electronic oscillation spectrum in metallic clusters, caused by the presence of a large spatial scale of inhomogeneity

Abstract

This work presents a theoretical analysis of the oscillations of a system of degenerate electrons in metallic submicron clusters, taking into account the presence of a large-scale spatial inhomogeneity caused by quantum shell effects. The analysis was carried out in a model formulation in which the large-scale effect was taken into account by the presence of an effective external field acting on the electrons. Two approaches to the description of electron dynamics were considered: kinetic and hydrodynamic. The results obtained within these approaches are in good qualitative and quantitative agreement with each other and demonstrate that for certain cluster sizes, a spectrum of oscillations of the electronic system appears with frequencies differing by the value Δω ∼ ω0/R20 and localized in the vicinity of plasmon frequency ω0 (R0, radius of cluster). The impact of the large-scale effect on the processes of light and electron scattering by metal clusters is estimated. It is shown that maxima appear in the absorption spectrum of the electromagnetic waves, and they turn out to be shifted from the plasmon frequency by value Δω ∼ ω0/R20. Within the framework of the Born approximation, it is shown that a maximum at kR0 ∼ 4π appears in the cross section of elastic scattering of electrons on a metal cluster. The results obtained are important from the point of view of interpreting experiments on plasmonic structures, in particular, on metal films.