Abstract
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.
Highlights
Metals support collective oscillations of their conduction electrons, known as plasmons, with light-trapping and light-manipulation capabilities at nanometer length scales
For the Au(111) surface, this is not the case, because the determination of the gold surface plasmon dispersion is complicated by the onset of broadening in the loss function at low Q, as we show in Fig. S2; the situation is further compounded for copper, where no clear maximum emerges in either the response described by Eq (1) with d -parameters or the direct atomic layer potential (ALP)-random-phase approximation (RPA) calculation, with only the simpler specular reflection model (SRM) exhibiting well-defined maxima
The inherently large losses exhibited by noble metals are often regarded as the “Achilles heel” of nano-optical functionalities based on plasmonics, motivating intensive efforts to identify new material platforms that can support long-lived polaritons
Summary
Metals support collective oscillations of their conduction electrons, known as plasmons, with light-trapping and light-manipulation capabilities at nanometer length scales (i.e., well below the diffraction limit imposed by traditional optics [1,2]). The realization of thin crystalline noble metal films [22,23,24,25] is key to cutting-edge explorations of novel plasmonic devices: metallic nanostructures with a high degree of crystallinity are anticipated to exhibit lower Ohmic losses when compared to their polycrystalline kins [26], with the recent observation of plasmons in laterally patterned few-atom-thick crystalline silver films partially confirming this intuition [19] It is well established in surface science that (111) noble metal surfaces possess Shockley surface states (SSs), with features resembling those of a two-dimensional electron gas (2DEG) [27,28,29]. We anticipate that the results presented could be widely deployed to describe ongoing experiments and engineer future nanoscale plasmonic devices at the extreme nanoscale
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
