Optical response of noble metal nanostructures: Quantum surface effects in crystallographic facets

Noble metal nanostructures are ubiquitous elements in nano-optics, supporting plasmon modes that can focus light down to length scales commensurate with nonlocal effects arising from quantum confinement and spatial dispersion in the underlying electron gas. Quantum and nonlocal effects can be more prominent in crystalline noble metals, due to their lower intrinsic loss (when compared with their polycrystalline counterparts), and because particular crystal facets give rise to distinct electronic surface states whose signatures can be imprinted in the optical response of a structure. Here, we employ an atomistic method to describe nonclassical effects impacting the optical response of crystalline noble metal surfaces and demonstrate that these effects can be well captured using a set of surface-response functions known as Feibelman $d$-parameters determined from such quantum-mechanical models. In particular, we characterize the $d$-parameters associated with the (111) and (100) crystal facets of gold, silver, and copper, emphasizing the importance of quantum surface effects associated with electron wave function spill-out/spill-in and with the surface-projected band gap emerging from the atomic-layer corrugation. Furthermore, we show that the extracted $d$-parameters can be straightforwardly applied to describe the optical response of various nanoscale metal morphologies of interest, including metallic ultrathin films, graphene–metal heterostructures hosting ultraconfined acoustic graphene plasmons, and crystallographic faceted metallic nanoparticles supporting localized surface plasmons. We envision that the $d$-parameters presented here, along with the prescription to extract and apply them, could help circumvent computationally expensive first-principles atomistic calculations to describe quantum nonlocal effects in the optical response of mesoscopic crystalline metal surfaces, which are becoming widely available with increasing control over morphology down to atomic length scales for state-of-the-art experiments in nano-optics.