Quantum Surface-Response of Metals Probed by Graphene Plasmons

Graphene supports electrically tunable plasmon excitations capable of confining electromagnetic radiation into deeply subwavelength volumes. Moreover, when a graphene sheet is placed near a metal substrate, graphene plasmons are screened by the metal thereby giving rise to acoustic graphene plasmons (AGPs) with nearly linear dispersion and superlative field confinement [1] , [2] . For this reason, plasmons in such heterostructures make ideal candidates to probe the quantum nonlocal electrodynamic response of the nearby metal in the THz and infrared spectral ranges. With that in mind, here we describe the quantum response of the metal using a formalism of mesoscopic electrodynamics based on microscopic surface-response functions, known as Feibelman d -parameters, which encode the metal’s quantum-surface response [2] , [3] , [4] . Specifically, we present a theory for calculating the spectrum of acoustic plasmons in graphene–dielectric–metal (GDM) heterostructures ( Fig. 1a ), and show that the AGP’s resonances exhibit nonclassical spectral shifts due to the quantum surface-response of the metal: toward the red for Re d ⊥ > 0 (associated with electronic spill-out) and toward the blue for Re d ⊥ < 0 (associated with an inward spill of the induced charges); this is accompanied by a slight increase of plasmon damping (due to electron-hole pair excitations). Importantly, these findings [4] explain and contextualize recent experimental observations of nonclassical optical response in GDM structures [1] . Crucially, using out theory and the concept set forth here, the metal’s quantum surface-response—embodied through the d -parameters—can be directly inferred from the experimental measurements of AGP’s dispersion ( Fig. 1b ). Based on this work [4] , we envision that by harnessing the record-high light confinement brought about by AGPs one could shed light about the physics governing the complex electron dynamics of metals, and, possibly, of strongly-correlated systems.