Absence of surface plasma waves on hard-wall surfaces

TL;DR

This paper clarifies that surface plasma waves do not exist on ideal hard-wall metal surfaces, challenging previous assumptions and impacting the interpretation of experimental data in plasmonics.

Contribution

It demonstrates that waves on hard-wall surfaces are not true surface plasma waves, correcting a long-standing misconception in the field.

Findings

Hard-wall surface waves lack surface charge density.

These waves occur at frequency ω_p/√2 but are not SPWs.

The result impacts interpretation of experimental data.

Abstract

It seems having been firmly established that surface plasma waves (SPWs) could exist on any metal surfaces, including those of the ideal hard-wall type frequently employed in \textit{ab initio} studies of the dielectric responses of metals. Here we show that the surface waves hosted on hard-wall surface are not SPWs. Though they possess the celebrated frequency $\omega_p/\sqrt{2}$, where $\omega_p$ is the volume plasma wave frequency, these waves are shown devoid of charges in the infinite wavelength limit. In contrast, SPWs are always associated with a finite density of charges localized on the surface. This finding corrects a historical mistake and calls for a reappraisal of innumerable work that interpret experimental data (e.g. electron energy loss spectroscopy) based on the hard-wall model and related models such as the specular reflection model.