Abstract
Fermi liquids respond differently to perturbations depending on whether their frequency is higher (collisionless regime) or lower (hydrodynamic regime) than the interparticle collision rate. This results in a different phase velocity between the collisionless zero sound and the hydrodynamic first sound. We performed terahertz photocurrent nanoscopy measurements on graphene devices, with a metallic gate close to the graphene layer, to probe the dispersion of propagating acoustic plasmons, the counterpart of sound modes in electronic Fermi liquids. We report the observation of a change in the plasmon phase velocity when the excitation frequency approaches the electron-electron collision rate that is compatible with the transition between the zero and the first sound mode.
| Original language | English |
|---|---|
| Article number | eadi0415 |
| Journal | Science advances |
| Volume | 9 |
| Issue number | 39 |
| DOIs | |
| State | Published - 29 Sep 2023 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:Copyright © 2023 The Authors, some rights reserved.
Funding
This work was supported by the Government of Spain through CEX2019-000910-S (MCIN/AEI/10.13039/501100011033) and European Union NextGenerationEU/PRTR (D.B.R., I.T., N.C.H.H., H.H.S., C.R.M., and F.H.L.K.); the Fundació Cellex (D.B.R., I.T., N.C.H.H., H.H.S., C.R.M., and F.H.L.K.), the Fundació Mir-Puig (D.B.R., I.T., N.C.H.H., H.H.S., C.R.M., and F.H.L.K.); the Generalitat de Catalunya through CERCA (D.B.R., I.T., N.C.H.H., H.H.S., C.R.M., and F.H.L.K.); the Secretaria d’Universitats i Recerca del Departament d’Empresa i Coneixement de la Generalitat de Catalunya and the European Social Fund (L’FSE inverteix en el teu futur)-FEDER (D.B.R.); the European Union’s Horizon 2020 programme under the Marie Skłodowska-Curie grant agreement Ref. 843830 (H.H.S.); the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement ref. 665884 (N.C.H.H.); the Spanish Ministry of Science, Innovation, and Universities (MCIU) and State Research Agency (AEI) via the Juan de la Cierva fellowship ref. FJC2018-037098-I (I.T.); the ERC TOPONANOP (726001) (F.H.L.K.); the Government of Spain (PID2019-106875GB-I00, PHOTOTBG PCI2021-122020-2A) (F.H.L.K.); the Generalitat de Catalunya (AGAUR, SGR 1656) (F.H.L.K.); the European Union’s Horizon 2020 under grant agreement no. 881603 (Graphene flagship Core 3) and ERC-POC PDC2022-138844-100 (F.H.L.K. and M.P.); the European Union’s Horizon 2020 under grant agreement no. 820378 (Quantum flagship) (F.H.L.K.); the The University of Pisa under the “PRA - Progetti di Ricerca di Ateneo” (Institutional Research Grants) (project no. PRA_2020-2021_92) “Quantum Computing, Technologies and Applications” (M.P.); the MUR–Italian Minister of University and Research under the “Research projects of relevant national interest - PRIN 2020” (project no. 2020JLZ52N), titled “Light-matter interactions and the collective behavior of quantum 2D materials (q-LIMA)” (M.P.); the Swiss National Science Foundation (grant no. 172218) (C.M.M.); the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement nos. 873028 (A.P.) and 843830 (H.H.S.); the European Commission EU Horizon 2020 MSCA-RISE-2019 programme (project 873028 HYDROTRONICS) and Leverhulme Trust grant RPG-2019-363 (A.P.); the Leverhulme Trust under the grant agreement no. RPG-2019-363 (A.P.); JSPS KAKENHI (grant nos. 19H05790, 20H00354, and 21H05233; T.T. and K.W.); and the Spanish Ministry of Science and Innovation under the María de Maeztu Units of Excellence Program (CEX2020-001038-M) and the Projects RTI2018-094830-B-100 and PID2021-123949OB-I00. (R.H.). Acknowledgments Funding:ThisworkwassupportedbytheGovernmentofSpainthroughCEX2019-000910-S (MCIN/AEI/10.13039/501100011033)andEuropeanUnionNextGenerationEU/PRTR(D.B.R.,I.T ., N.C.H.H.,H.H.S.,C.R.M.,andF .H.L.K.); theFundacióCellex(D.B.R.,I.T ., N.C.H.H.,H.H.S.,C.R.M.,and F .H.L.K.), theFundacióMir-Puig(D.B.R.,I.T ., N.C.H.H.,H.H.S.,C.R.M.,andF .H.L.K.); theGeneralitat deCatalunyathroughCERCA(D.B.R.,I.T ., N.C.H.H.,H.H.S.,C.R.M.,andF .H.L.K.); theSecretaria d’Universitats i Recerca del Departament d’Empresa i Coneixement de la Generalitat de Catalunya and the European Social Fund (L ’FSE inverteix en el teu futur)-FEDER (D.B.R.); the European Union’s Horizon 2020 programme under the Marie Skłodowska-Curie grant agreement Ref. 843830 (H.H.S.); the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement ref. 665884 (N.C.H.H.); the SpanishMinistryofScience,Innovation,andUniversities(MCIU)andStateResearchAgency (AEI) via the Juan de la Cierva fellowship ref. FJC2018-037098-I (I.T .); the ERC TOP ONANOP (726001)(F .H.L.K.); theGovernmentofSpain(PID2019-106875GB-I00,PHOT OTB GPCI2021-122020-2A)(F .H.L.K.); theGeneralitatdeCatalunya(AGAUR,SGR1656)(F .H.L.K.); theEuropean Union’s Horizon 2020 under grant agreement no. 881603 (Graphene flagship Core 3) and ERC-POC PDC2022-138844-100 (F .H.L.K. and M.P .); the European Union’s Horizon 2020 under grant agreementno.820378(Quantumflagship)(F .H.L.K.); theTheUniversityofPisaunderthe“PRA-ProgettidiRicercadiAteneo ”(InstitutionalResearchGrants)(projectno.PRA_2020-2021_92) “QuantumComputing,T echnologies andApplications”(M.P .); theMUR–ItalianMinisterof UniversityandResearchunderthe“Researchprojectsofrelevantnationalinterest-PRIN2020” (projectno.2020JLZ52N),titled“Light-matterinteractionsandthecollectivebehaviorof quantum2Dmaterials(q-LIMA)”(M.P .); theSwissNationalScienceFoundation(grantno. 172218) (C.M.M.); the European Union’s Horizon 2020 research and innovation progr amme undertheMarieSkłodowska-Curiegrantagreementnos.873028(A.P .) and843830(H.H.S.);the EuropeanCommissionEUHorizon2020MSCA-RISE-2019programme(project873028 HYDROTR ONICS) andLeverhulmeTrustgrantRPG-2019-363(A.P .); theLeverhulmeTrustunder thegrantagreementno.RPG-2019-363(A.P .); JSPSKAKENHI(grantnos.19H05790,20H00354, and21H05233;T .T .andK.W .); andtheSpanishMinistryofScienceandInnovationunderthe MaríadeMaeztuUnitsofExcellenceProgram(CEX2020-001038-M)andtheProjectsRTI2018-094830-B-100andPID2021-123949OB-I00.(R.H.).Authorcontributions:Conceptualization: I.T ., D.B.R.,andF .H.L.K. Samplefabrication:D.B.R.andN.C.H.H.Experiment:D.B.R.,N.C.H.H., H.H.S.,andC.M.M.hBNcrystals:K.W .andT .T .Dataanalysis:D.B.R.,I.T ., andC.R.M.Theoretical calculations:R.A.,A.P ., andI.T .Supervision:I.T ., F .H.L.K., M.P ., andR.H.Writing—originaldraft:I.T ., D.B.R.,andF .H.L.K. Writing—reviewandediting:Allauthors.Competinginterests:R.H.isthe cofounderofNeaspecGmbH,acompanyproducingscattering-typescanningnear-fieldoptical microscopesystems,suchastheoneusedinthisstudy.Allotherauthorsdeclarethattheyhave nocompetinginterests.Dataandmaterialsavailability:Alldataneededtoevaluatethe conclusions in thepaperare presentin the paperand/or theSupplementary Materials. Allraw datageneratedduringthecurrentstudyareavailableat10.5281/zenodo.8298069.
| Funders | Funder number |
|---|---|
| ERC TOPONANOP | 726001, PHOTOTBG PCI2021-122020-2A, PID2019-106875GB-I00 |
| ERC-POC | PDC2022-138844-100 |
| European Commission EU Horizon 2020 | MSCA-RISE-2019 |
| European Union NextGenerationEU/PRTR | |
| European Union’s Horizon 2020 Programme | |
| Government of Spain | MCIN/AEI/10.13039/501100011033, CEX2019-000910-S |
| Italian Minister of University and Research | 2020JLZ52N |
| State Research Agency | |
| Union’s Horizon 2020 | |
| Fundación Cellex | |
| Horizon 2020 Framework Programme | 881603, 665884 |
| H2020 Marie Skłodowska-Curie Actions | 843830 |
| Ministerio de Ciencia, Innovación y Universidades | |
| Leverhulme Trust | RPG-2019-363 |
| Japan Society for the Promotion of Science | 21H05233, 20H00354, 19H05790 |
| Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung | 172218, 873028 |
| Generalitat de Catalunya | |
| Federación Española de Enfermedades Raras | |
| Agència de Gestió d'Ajuts Universitaris i de Recerca | SGR 1656 |
| Ministero dell’Istruzione, dell’Università e della Ricerca | |
| Ministerio de Ciencia e Innovación | RTI2018-094830-B-100, CEX2020-001038-M, PID2021-123949OB-I00 |
| European Social Fund Plus | |
| Università di Pisa | PRA_2020-2021_92 |
| Agencia Estatal de Investigación | FJC2018-037098-I |
| Fundación Mig-Puig |