Absence of surface plasma waves on hard-wall surfaces

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.