Finite-size and quantum effects in plasmonics: manifestations and theoretical modelling [Invited]

The tremendous growth of the field of plasmonics in the past twenty years owes much to the pre-existence of solid theoretical foundations. Rather than calling for the introduction of radically new theory and computational techniques, plasmonics required, to a large extent, application of some of the most fundamental laws in physics, namely Maxwell's equations, albeit adjusted to the nanoscale. The success of this description, which was triggered by the rapid advances in nanofabrication, makes a striking example of new effects and novel applications emerging by applying known physics to a different context. Nevertheless, the prosperous recipe of treating nanostructures within the framework of classical electrodynamics and with use of macroscopic, bulk material response functions (known as the local-response approximation, LRA) has its own limitations, and inevitably fails once the relevant length scales approach the few- to sub-nm regime, dominated by characteristic length scales such as the electron mean free path and the Fermi wavelength. Here we provide a review of the main non-classical effects that emerge when crossing the border between the macroscopic and atomistic worlds. We study the physical mechanisms involved, highlight experimental manifestations thereof and focus on the theoretical efforts developed in the quest for models that implement atomistic descriptions into otherwise classical-electrodynamic calculations for mesoscopic plasmonic nanostructures.