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 associated with quantum confinement and spatial dispersion in the underlying electron gas. Nonlocal effects are naturally more prominent for crystalline noble metals, which potentially offer lower intrinsic loss than their amorphous counterparts, and with particular crystal facets giving rise to distinct electronic surface states. Here, we employ a quantum-mechanical model to describe nonclassical effects impacting the optical response of crystalline noble-metal films and demonstrate that these can be well-captured using a set of surface-response functions known as Feibelman $d$-parameters. In particular, we characterize the $d$-parameters associated with the (111) and (100) crystal facets of gold, silver, and copper, emphasizing the importance of surface effects arising due to electron wave function spill-out and the surface-projected band gap emerging from atomic-layer corrugation. We then show that the extracted $d$-parameters can be straightforwardly applied to describe the optical response of various nanoscale metal morphologies of interest, including metallic ultra-thin films, graphene-metal heterostructures hosting extremely confined acoustic graphene plasmons, and crystallographic faceted metallic nanoparticles supporting localized surface plasmons. The tabulated $d$-parameters reported here can circumvent computationally expensive first-principles atomistic simulations to describe microscopic 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.