Coulomb Excitations for a Short Linear Chain of Metallic Shells

TL;DR

This paper develops a self-consistent-field theory to analyze Coulomb excitations in a finite chain of metallic spherical electron gases, revealing complex coupling effects influenced by geometry and polarization.

Contribution

It introduces a novel theoretical framework for Coulomb excitations in a linear chain of metallic shells, accounting for angular momentum coupling and geometric effects.

Findings

Next-nearest-neighbor Coulomb coupling exceeds that of a right-angle triad.

Plasma excitation frequencies depend on the chain's orientation relative to the quantization axis.

Angular momenta $L$ and $M$ are coupled due to spherical confinement.

Abstract

A self-consistent-field theory is given for the electronic collective modes of a chain containing a finite number, $N$, of Coulomb-coupled spherical two-dimensional electron gases (S2DE's) arranged with their centers along a straight line, simulating a narrow micro-ribbon of metallic shells. The separation between nearest-neighbor shells is arbitrary and because of the quantization of the electron energy levels due to their confinement to the spherical surface, all angular momenta $L$ of the Coulomb excitations and their projections $M$ on the quantization axis are coupled. However, for incoming light with a specific polarization, only one angular momentum quantum number is chosen. We show that when $N=3$ the next-nearest-neighbor Coulomb coupling is larger than its value if they are located at opposite ends of a right-angle triangle forming the triad. Additionally, the frequencies of the plasma excitations depend on the orientation of the line joining them with respect to the axis of quantization since the magnetic field generated from the induced oscillating electric dipole moment on one sphere can couple to the induced magnetic dipole moment on another.