Robust Subnanometric Plasmon Ruler by Rescaling of the Nonlocal Optical Response

Abstract

We present the optical response of two interacting metallic nanowires calculated for separation distances down to angstrom range. State-of-the-art local and nonlocal approaches are compared with full quantum time-dependent density functional theory calculations that give an exact account of nonlocal and tunneling effects. We find that the quantum results are equivalent to those from classical approaches when the nanoparticle separation is defined as the separation between centroids of the screening charges. This establishes a universal plasmon ruler for subnanometric distances. Such a ruler not only impacts the basis of many applications of plasmonics, but also provides a robust rule for subnanometric metrology. DOI: 10.1103/PhysRevLett.110.263901 PACS numbers: 42.25.Bs, 36.40.Gk, 73.20.Mf, 78.67.Bf The exact calculation of the optical response of a nanosystems is a challenging task. In metallic nanostructures the complex nonlocal interactions between conduction electrons modify the standard local classical response, typically characterized by the presence of surface plasmon resonances [1]. This effect is more pronounced in small particles and in strongly coupled systems where the nonlocal nature of electronic interactions is emphasized. To establish an exact and accurate model to describe the spectral features of plasmonic resonances in such systems is thus of paramount importance from both fundamental and practical points of view [2,3]. A variety of theoretical approaches that incorporate different levels of sophistication have been adopted to address the optical response, but certain lack of unification still persists. In particular, the community of surface physics has elaborated accurate nonlocal treatments to address the surface response of conduction electrons of metal surfaces and small metallic objects [1,[4][5][6][7][8][9], whereas the community of nano-optics has focused on developing practical local and nonlocal treatments where the emphasis is placed on the geometrical aspects of the metal boundaries rather than on the actual response of the electrons [2,3,[10][11][12][13][14][15][16]. This Letter bridges both fields, providing a unified and practical picture of the optical response in coupled metallic nanoparticles located at subnanometric proximity.We calculate the optical response of two interacting metallic nanowires in vacuum using a full quantum timedependent density functional theory (TDDFT) approach [17] as well as using macroscopic theory based on solution of classical Maxwell equations with local and nonlocal descriptions of the system. The comparison between quantum and classical results on coupled nanowires provides a perfect basis to unravel the limitations, tendencies, and physics of the optical response under different levels of approximation. By doing so, we are able to relate the results of the optical response from different approximations and predict the influence of nonlocality in the limit of subnanometric distances where nonlocal effects are pronounced. In elucidating the m...

A generalized non-local optical response theory for plasmonic nanostructures

“…Ab initio approaches show a crossing from the classical hybridization of localized surface plasmon resonances to tunnelling-mediated charge-transfer plasmons (CTPs) 36,[48][49][50] . Being able to push experiments into this intriguing regime 13,30,51 , commonly associated with expectations of quantum physics, leaves an open question: Can this regime be adequately described with semiclassical models?…”

A classical treatment of optical tunneling in plasmonic gaps: extending the quantum corrected model to practical situations

“…87 The model predicts an electron density that decays considerably before the jellium edge dening the limit of the particles, i.e., the centroid of charge is displaced towards the interior within this approach. In contrast, full quantum simulations reveal that, for these free electron metals, the electron density is pushed a short distance towards the outside of the particles, i.e.…”

“…This choice is not unique, and one can also consider the classical metal boundary dened by the position of the centroid of the screening charge at the surface. 86,87 For the implementation of the QCM, however, it is important that the classical denition of ' corresponds to the one used in the quantum calculations of the tunneling current. This denition will be also relevant when comparing experiments and calculations with the aim of establishing a criterion of absolute separation distances.…”

“…While in the local classical calculations the plasmon-induced screening charges are located at the geometrical surfaces of the metal, using the nonlocal hydrodynamic model results in a displacement of the screening charges into the metal, inwards from the metal surface. 80,86,87,123,124 Thus, when the distance between the geometrical surfaces is zero, the screening charges across the junction are separated by a distance d n , where d n /2 is the position of the centroid of the screening charge with respect to the geometrical surface (jellium edge) of the individual nanoparticles. Since the screened charges do not abruptly overlap when contact is established, the electrostatic interactions in the system do not diverge, in clear contrast to the classical model where innite localization of the charges is produced.…”

“…The NLHD results are adequate for metals such as silver and gold, whose optical response is signicantly affected by d-electrons, but the blueshi obtained for simple free-electron metals is in contradiction with full quantum results. 86,87 Some approaches have proposed the recovery of nonlocal results by a convenient rescaling of the local distances 86,87 and thicknesses 88 at the metal interfaces, providing good descriptions of the plasmon energies and dispersions in nanometric gaps. Recently, the inclusion of the realistic density prole above the surface into the NLHD description has allowed the retrieval of full quantum and experimental results both for d-electron and simple metals, 89 at an increased computational cost.…”