Semiclassical theory of surface plasmons in spheroidal clusters

TL;DR

This paper develops a semiclassical microscopic theory for surface plasmons in spheroidal clusters, revealing how shape deformation influences plasmon response and excitation coupling, with specific results for prolate and oblate geometries.

Contribution

It extends the Vlasov-based linear response theory to spheroidal systems, incorporating shape-induced excitation coupling and providing explicit calculations for deformed cluster plasmon responses.

Findings

Prolate clusters show a double-peaked photoabsorption structure.

Oblate clusters exhibit fragmentation of the high-frequency plasmon component.

The theory suggests scaling behavior with electron number and density.

Abstract

A microscopic theory of linear response based on the Vlasov equation is extended to systems having spheroidal equilibrium shape. The solution of the linearized Vlasov equation, which gives a semiclassical version of the random phase approximation, is studied for electrons moving in a deformed equilibrium mean field. The deformed field has been approximated by a cavity of spheroidal shape, both prolate and oblate. Contrary to spherical systems, there is now a coupling among excitations of different multipolarity induced by the interaction among constituents. Explicit calculations are performed for the dipole response of deformed clusters of different size. In all cases studied here the photoabsorption strength for prolate clusters always displays a typical double-peaked structure. For oblate clusters we find that the high--frequency component of the plasmon doublet can get fragmented in the medium size region ($N \sim 250$). This fragmentation is related to the presence of two kinds of three-dimensional electron orbits in oblate cavities. The possible scaling of our semiclassical equations with the valence electron number and density is investigated.