Quantum surface-response of metals revealed by acoustic graphene plasmons

A quantitative understanding of the electromagnetic response of materials is essential for the precise engineering of maximal, versatile, and controllable light-matter interactions. Material surfaces, in particular, are prominent platforms for enhancing electromagnetic interactions and for tailoring chemical processes. However, at the deep nanoscale, the electromagnetic response of electron systems is significantly impacted by quantum surface-response at material interfaces, which is challenging to probe using standard optical techniques. Here, we show how ultraconfined acoustic graphene plasmons in graphene-dielectric-metal structures can be used to probe the quantum surface-response functions of nearby metals, here encoded through the so-called Feibelman d-parameters. Based on our theoretical formalism, we introduce a concrete proposal for experimentally inferring the low-frequency quantum response of metals from quantum shifts of the acoustic graphene plasmons dispersion, and demonstrate that the high field confinement of acoustic graphene plasmons can resolve intrinsically quantum mechanical electronic length-scales with subnanometer resolution. Our findings reveal a promising scheme to probe the quantum response of metals, and further suggest the utilization of acoustic graphene plasmons as plasmon rulers with angstrom-scale accuracy. Knowledge of the quantum response of materials is essential for designing light-matter interactions at the nanoscale. Here, the authors report a theory for understanding the impact of metallic quantum response on acoustic graphene plasmons and how such response could be inferred from measurements.N.A.M. is a VILLUM Investigator supported by VILLUM FONDEN (Grant No. 16498) and Independent Research Fund Denmark (Grant No. 7026-00117B). The Center for Nano Optics is financially supported by the University of Southern Denmark (SDU 2020 funding). The Center for Nanostructured Graphene (CNG) is sponsored by the Danish National Research Foundation (Project No. DNRF103). This work was partly supported by the Army Research Office through the Institute for Soldier Nanotechnologies under Contract No. W911NF-18-2-0048. N.M.R.P. acknowledges support from the European Commission through the project "Graphene-Driven Revolutions in ICT and Beyond" (No. 881603, Core 3), COMPETE 2020, PORTUGAL 2020, FEDER and the Portuguese Foundation for Science and Technology (FCT) through project POCI-01-0145-FEDER028114 and through the framework of the Strategic Financing UID/FIS/04650/2019. F.H. L.K. acknowledges financial support from the Government of Catalonia through the SGR grant and from the Spanish Ministry of Economy and Competitiveness (MINECO) through the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-20150522), support by Fundacio Cellex Barcelona, Generalitat de Catalunya through the CERCA program, and the MINECO grants Plan Nacional (FIS2016-81044-P) and the Agency for Management of University and Research Grants (AGAUR) 2017 SGR 1656. Furthermore, the research leading to these results has received funding from the European Union's Horizon 2020 program under the Graphene Flagship Grant Agreements No. 785219 (Core 2) and no. 881603 (Core 3), and the Quantum Flagship Grant No. 820378. This work was also supported by the ERC TOPONANOP (Grant No. 726001)