Probing nonlocal effects in metals with graphene plasmons

In this paper we analyze the effects of nonlocality on the optical properties of a system consisting of a thin metallic film separated from a graphene sheet by a hexagonal boron nitride (hBN) layer. We show that nonlocal effects in the metal have a strong impact on the spectrum of the surface plasmon-polaritons on graphene. If the graphene sheet is shaped into a grating, we show that the extinction curves can be used to shed light on the importance of nonlocal effects in metals. Therefore, graphene surface plasmons emerge as a tool for probing nonlocal effects in metallic nanostructures, including thin metallic films. As a byproduct of our study, we show that nonlocal effects lead to smaller losses for the graphene plasmons than what is predicted by a local calculation. We show that these effects can be very well mimicked using a local theory with an effective spacer thickness larger than its actual value. The authors thank Sébastien Nanot and Itai Epstein for valuable discussions and comments. E.J.C.D., Yu.V.B. and N.M.R.P. acknowledge support from the European Commission through the project GrapheneDriven Revolutions in ICT and Beyond (Ref. No. 785219), and from the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Financing UID/FIS/04650/2013. E.J.C.D. acknowledges FCT for the grant CFUM-BI-14/2016. D.A.I. acknowledges the FPI grant BES-2014-068504. F.H.L.K. acknowledges financial support from the Government of Catalonia trough the SGR grant (2014-SGR-1535), and from the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2015-0522), support by Fundacio Cellex Barcelona, CERCA Programme / Generalitat de Catalunya and the Mineco grants Ramn y Cajal (RYC-2012-12281) and Plan Nacional (FIS201347161-P and FIS2014-59639-JIN). Furthermore, the research leading to these results has received funding from the European Union Seventh Framework Programme under grant agreement no.696656 Graphene Flagship, the ERC starting grant (307806, CarbonLight), and project GRASP (FP7-ICT-2013-613024-GRASP). N. A. M. is a VILLUM Investigator supported by VILLUM FONDEN (grant No. 16498). Center for Nano Optics is financially supported by the University of Southern Denmark (SDU 2020 funding). Center for Nanostructured Graphene is supported by the Danish National Research Foundation (DNRF103).