A theory of electrodynamic response for bounded metals: Surface capacitive effects

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. This work is expected to find broad applications in optics, plasmonics and other areas such as electron energy loss spectroscopy and accelerator design.

Hydrodynamic effects on the energy transfer from dipoles to metal slab

“…Equation (15) shows that the QD probes the quantity P s,ω (k) rather than χ kω . This accords with the general observation 34 that entities (e.g. the QD here) residing outside a metal can only probe P s kω .…”

“…(4) to the charge densitydensity response function, denoted by χ ω (x, y) of the metal. Physically, χ ω (x, y) gives the charge density at x induced by an external oscillatory (at frequency ω) electrostatic potential localized at y. Quantum linear response theory gives 34,38…”

“…HDM treats the electrons in a metal as a fluid, governed by the linearized Euler's momentum equation incorporating momentum damping, [31][32][33][34]…”

“…In the present work, we systematically explore the nonlocal effects, by means of a hydrodynamic model (HDM) [31][32][33][34] , on the energy transfer rate as a function of the dipole-metal distance and the slab thickness. We find that hydrodynamic effects -together with size effects -can significantly impact the energy transfer process, entailing a very different picture than ignoring the effects.…”

Surface plasmons on Pd(110): An ab initio calculation

“…From the theoretical side, a description of the collective electronic excitations on this surface would perhaps require to go beyond the dipole approximation based on the use of a surface loss function [5]. In this respect, probably the kinematics of the incident probing electron should be taken into account [83][84][85].…”