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Dirac Fermion Optics and Plasmonics in Graphene Microwave Devices This document is downloaded from DR‑NTU (https://dr.ntu.edu.sg) Nanyang Technological University, Singapore. Dirac fermion optics and plasmonics in graphene microwave devices Graef, Holger 2019 Graef, H. (2019). Dirac fermion optics and plasmonics in graphene microwave devices. Doctoral thesis, Nanyang Technological University, Singapore. https://hdl.handle.net/10356/143704 https://doi.org/10.32657/10356/143704 This work is licensed under a Creative Commons Attribution‑NonCommercial 4.0 International License (CC BY‑NC 4.0). Downloaded on 10 Oct 2021 13:04:16 SGT Dirac fermion optics and plasmonics in graphene microwave devices Holger Graef School of Electrical & Electronic Engineering A thesis submitted to Sorbonne Universités and to the Nanyang Technological University in partial fulfillment of the requirement for the degree of Doctor of Philosophy 2019 Statement of Originality I hereby certify that the work embodied in this thesis is the result of original research, is free of plagiarised materials, and has not been submitted for a higher degree to any other University or Institution. 25/07/2019 . Date Holger Graef Supervisor Declaration Statement I have reviewed the content and presentation style of this thesis and declare it is free of plagiarism and of sufficient grammatical clarity to be examined. To the best of my knowledge, the research and writing are those of the candidate except as acknowledged in the Author Attribution Statement. I confirm that the investigations were conducted in accord with the ethics policies and integrity standards of Nanyang Technological University and that the research data are presented honestly and without prejudice. 23/07/2019 . Date Teo Hang Tong Edwin Authorship Attribution Statement This thesis contains material from 3 paper(s) published in the following peer-reviewed journal(s): Chapter 3 is published as H. Graef, Q. Wilmart, M. Rosticher, D. Mele, L. Banszerus, C. Stampfer, T. Taniguchi, K. Watanabe, J.-M. Berroir, E. Bocquillon, G. Fève, E.H.T. Teo, and B. Plaçais. A corner reflector of graphene Dirac fermions as a phonon- scattering sensor. Nature Communications 10, 2428 (2019). DOI: 10.1038/s41467- 019-10326-6. The contributions of the co-authors are as follows: H.G., Q.W., and B.P. conceived the experiment. Q.W. developed the bottom gate fabrication process. L.B., C.S., T.T., K.W., H.G., and M.R. participated to sample fabrication at RWTH University in Aachen, Germany, NIMS in Tsukuba, Japan, and École Normale Supérieure in Paris, France. H.G. conducted the measurements at École Normale Supérieure in Paris, France. H.G., D.M., J.-M.B., G.F., E.B., E.H.T.T., and B.P. participated to the data analysis. Q.W. and H.G. developed the ray-tracing simulations. H.G. and B.P. worked out the analytic model. H.G. and B.P. wrote the manuscript with contributions from the coauthors. Chapter 4 is published as H. Graef, D. Mele, M. Rosticher, L. Banszerus, C. Stampfer, T. Taniguchi, K. Watanabe, E. Bocquillon, G. Fève, J.-M. Berroir, E.H.T. Teo, and B. Plaçais. Ultra-long wavelength Dirac plasmons in graphene capacitors. Journal of Physics Materials 1, 01LT02 (2018). DOI: 10.1088/2515-7639/aadd8c. The contributions of the co-authors are as follows: H.G. and B.P. conceived the experiment. L.B., C.S., T.T., K.W., H.G., D.M. and M.R. participated to sample fabrication at RWTH University in Aachen, Germany, NIMS in Tsukuba, Japan, and École Normale Supérieure in Paris, France. H.G. and D.M. conducted the measurements at École Normale Supérieure in Paris, France. H.G., D.M., J.-M.B., G.F., E.B., E.H.T.T., and B.P. participated to the data analysis. H.G., D.M. and B.P. wrote the manuscript with contributions from the coauthors. Chapter 5 is published as W. Yang, H. Graef, X. Lu, G. Zhang, T. Taniguchi, K. Watanabe, A. Bachthold, E.H.T. Teo, E. Baudin, E. Bocquillon, G. Fève, J.-M. Berroir, D. Carpentier, M.O. Goerbig, B. Plaçais. Landau velocity for collective quantum Hall breakdown in bilayer graphene. Physical Review Letters 121, 136804 (2018). DOI: 10.1103/PhysRevLett.121.136804. The contributions of the co-authors are as follows: W.Y. and B.P. conceived the experiment. X.L., G.Z., T.T., K.W., and W.Y. participated to sample fabrication at Beijing National Laboratory for Condensed Matter Physics and Institute of Physics in Beijing, China, NIMS in Tsukuba, Japan, and École Normale Supérieure in Paris, France. W.Y. conducted the measurements at École Normale Supérieure in Paris, France. W.Y., H.G., A.B., J.-M.B., G.F., E. Baudin, E. Bocquillon., E.H.T.T., and B.P. participated to the data analysis. H.G., D.C., and M.O.G. participated to the theory part. B.P. wrote the manuscript with contributions from the coauthors. 25/07/2019 . Date Holger Graef Abstract This thesis addresses the physics of non-interacting and interacting Dirac fermions in ballistic graphene. Three main phenomena are investigated: Dirac fermion optics in electronic prisms defined by p-n junctions, GHz plasmonics in plasma resonance capacitors, and the breakdown of the integer quantum Hall effect (QHBD) by a magnetoexciton instability. Our technol- ogy relies on h-BN encapsulated graphene devices characterized by DC to GHz electronic transport and noise. We first study the total internal reflection of electrons in a gate-defined corner reflector. Both geometric and coherent electron optics effects are demonstrated and the device is shown to be sensitive to minute phonon scattering rates. It is then used as a proof-of-concept for GHz electron optics experiments in graphene. We introduce top-gated graphene field-effect capacitors as a platform to study ultra- long wavelength plasmons characterized with a vector network analyzer. We simultaneously measure resistivity, capacitance and kinetic inductance. We observe a resonance at 40 GHz with a quality factor of two, corresponding to a plasmon of 100 µm wavelength. This result sets a milestone for the realization of resonant plasmonic devices. We finally move our attention to the QHBD in a bilayer graphene sample. DC transport and GHz noise measurements show that the elusive intrinsic breakdown field can be reached in graphene. Its signature is an abrupt increase of noise, with a super-Poissonian Fano factor. We propose a magnetoexciton instability scenario as the origin of breakdown. These results show how progress in sample fabrication has enabled us to study new classes of ballistic devices, to explore new fundamental phenomena and to envision more complex experiments like: time-of-flight measurements of acoustic phonons, characterization of plasmon propagation in bipolar superlattices, or breakdown in single layer graphene. In terms of applications, this thesis paves the way for room-temperature electron optics devices, plasma-resonance-based THz detectors, and improvement of quantum Hall resistance standards. i ii R´esum´e Cette th`ese porte sur la physique des fermions de Dirac dans le graph`ene balistique, sans et avec interactions. Trois ph´enom`enes principaux sont ´etudi´es: L’optique des fermions de Dirac dans des prismes ´electroniques d´efinis par des jonctions p-n, la plasmonique GHz dans des condensateurs `ar´esonance plasmons, et la rupture de l’effect Hall quantique (en anglais QHBD) dˆu`al’instabilit´ede magnetoexcitons. Notre technique est bas´ee sur la caract´erisation du transport ´electronique et du bruit dans les dispositifs de graph`ene encapsul´edans du nitrure de bore, du continu aux hyperfr´equences. En optique ´electronique, nous ´etudions la r´eflexion totale interne des ´electrons dans un r´eflecteur coin d´efini par des ´electrodes de grille. On d´emontre des effets d’optique ´electron- ique g´eom´etrique et coh´erente. Le dispositif est sensible `a des taux de diffusion minuscules et donc capable de d´etecter des phonons `abasse temp´erature. On l’utilise pour d´emontrer la faisabilit´ed’exp´eriences d’optique de fermions de Dirac en r´egime hyperfr´equences. En plasmonique, nous introduisons les condensateurs graph`ene `aeffet de champs en tant que plateforme pour ´etudier les plasmons de longeur d’onde tr`es grande. Les dispositifs sont caract´eris´es avec un analyseur de r´eseau. Nous mesurons simultan´ement la r´esistivit´e, la capacitance et l’inductance cin´etique et nous observons une r´esonance `a40 GHz avec un facteur de qualit´ede deux, qui correspond `aun plasmon d’une longueur d’onde de 100 µm. Ce r´esultat constitue un pas important vers la r´ealisation de dispositifs plasmoniques r´esonnants. Enfin, `achamps magn´etiques et ´electriques crois´es forts, nous ´etudions la rupture de l’effet Hall quantique entier dans un ´echantillon mod`ele de graph`ene bicouche. Le transport en courant continu et le bruit `a5 GHz d´emontrent que le champ de rupture intrins`eque peut ˆetre atteint dans le graph`ene. La signature du QHBD est un d´ecollage brutal du bruit, avec un facteur de Fano largement superpoissonien. Comme m´ecanisme collectif de rupture, nous proposons l’instabilit´ede magnetoexcitons. Ces r´esultats montrent comment le progr`es dans la fabrication des ´echantillons a permis d’´etudier de nouvelles classes de dispositifs balistiques, d’explorer de nouveaux ph´enom`enes fondamentaux et d’envisager des exp´eriences plus complexes, comme : des mesures du temps de vol des phonons acoustiques, la caract´erisation de la propagation d’un plasmon dans un super-r´eseau bipolaire ou le QHBD dans le graph`ene monocouche. En termes d’applications, cette th`ese ouvre la voie pour l’exploitation de l’optique de fermions de Dirac `atemp´erature ambiante, la conception de d´etecteurs THz utilisant la r´esonance de plasmon, et l’am´elioration des standards de r´esistance bas´esur l’effet Hall quantique.
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