A universal macroscopic theory of surface plasma waves and their losses

Recently, we have revealed an intrinsic instability of metals due to surface plasma waves (SPWs) and raised the prospect of using it to create lossless SPWs. The counter-intuitive nature of this finding prompts one to ask, why had not this instability been disclosed before, given the long history of this subject? If this instability does exist, how far is it from reality? The present work is devoted to answering these questions. To this end, we derive a unified macroscopic theory of SPWs that applies to any type of electron dynamics, be they local or non-local, classical or quantum-mechanical. In light of this theory, we analyze the behaviors of SPWs according to several electron dynamics models, including the widely used local dielectric model (DM), the hydrodynamic model (HDM) and the specular reflection model (SRM), in addition to the less common semi-classical model (SCM). We find that, in order to unveil the instability, one must (i) self-consistently treat surface effects without any of the usually imposed auxiliary conditions and (ii) include translation symmetry breaking effects in electron dynamics. As far as we are concerned, none existing work had fulfilled both (i) and (ii). To assess the possibility of realizing the instability, we analyze two very important factors: the dielectric interfacing the metal and inter-band transitions, which both were ignored in our recent work. Whereas inter-band absorption -- together with Landau damping -- is shown adverse to the instability, a dielectric brings it closer to occurrence. One may even attain it in common plasmonic materials such as silver under not so tough conditions.