A Theory of Electrodynamic Responses for Bounded Metals: Surface Capacitive Effects

TL;DR

This paper develops a comprehensive macroscopic theory for the electrodynamic response of semi-infinite metals, highlighting surface capacitive effects and comparing multiple electronic models to understand surface plasma wave behavior.

Contribution

It introduces a unified theoretical framework that incorporates surface capacitive effects and compares various models, including the semi-classical model, for the electrodynamic response of bounded metals.

Findings

Surface plasma wave peaks are sharper in the SCM model.

The response function reveals model-specific charge distributions.

The theory provides analytical expressions for response functions.

Abstract

We report a general macroscopic theory for the electrodynamic response of semi-infinite metals (SIMs). The theory includes the hitherto overlooked capacitive effects due to the finite spatial extension of a surface. The basic structure of this theory is independent of the particulars of electron dynamics. Analytical expressions have been obtained of the charge density-density response function, which is naturally parsed into two parts. One of them represents a bulk property while the other a pure surface property. We apply the theory to study the responses according to several electronic dynamics models and provide a unified view of their validity and limitations. The models studied include the local dielectric model (DM), the dispersive hydrodynamic model (HDM) and specular reflection model (SRM), as well as the less common semi-classical model (SCM) based on Boltzmann's transport equation. We show that, in terms of their basic equations, the SRM is an extension of the HDM, just as the HDM is an extension of the DM. The SCM improves over the SRM critically through the inclusion of translation symmetry breaking and surface roughness effects. We then employ the response function to evaluate the so-called dynamical structure factor, which plays an important role in particle scattering. As expected, this factor reveals a peak due to the excitation of surface plasma waves (SPWs). Surprisingly, however, the peak is shown to be considerably sharper in the SCM than in other models, indicating an incipient instability of the system according to this model. We also study the distribution of charges induced by a charged particle grazing over a SIM surface at constant speed. This distribution is shown to contain model-specific features that are of immediate experimental interest.