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      Electrical tunability of terahertz nonlinearity in graphene

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          Abstract

          We turn graphene from an inert electronic material to the most nonlinear material for the terahertz range using a small voltage.

          Abstract

          Graphene is conceivably the most nonlinear optoelectronic material we know. Its nonlinear optical coefficients in the terahertz frequency range surpass those of other materials by many orders of magnitude. Here, we show that the terahertz nonlinearity of graphene, both for ultrashort single-cycle and quasi-monochromatic multicycle input terahertz signals, can be efficiently controlled using electrical gating, with gating voltages as low as a few volts. For example, optimal electrical gating enhances the power conversion efficiency in terahertz third-harmonic generation in graphene by about two orders of magnitude. Our experimental results are in quantitative agreement with a physical model of the graphene nonlinearity, describing the time-dependent thermodynamic balance maintained within the electronic population of graphene during interaction with ultrafast electric fields. Our results can serve as a basis for straightforward and accurate design of devices and applications for efficient electronic signal processing in graphene at ultrahigh frequencies.

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          Most cited references44

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          The rise of graphene.

          Graphene is a rapidly rising star on the horizon of materials science and condensed-matter physics. This strictly two-dimensional material exhibits exceptionally high crystal and electronic quality, and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Whereas one can be certain of the realness of applications only when commercial products appear, graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena, some of which are unobservable in high-energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick, and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications.
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            Two-dimensional gas of massless Dirac fermions in graphene.

            Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrödinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.
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              Large-area synthesis of high-quality and uniform graphene films on copper foils.

              X. Li, W Cai, J. An (2009)
              Graphene has been attracting great interest because of its distinctive band structure and physical properties. Today, graphene is limited to small sizes because it is produced mostly by exfoliating graphite. We grew large-area graphene films of the order of centimeters on copper substrates by chemical vapor deposition using methane. The films are predominantly single-layer graphene, with a small percentage (less than 5%) of the area having few layers, and are continuous across copper surface steps and grain boundaries. The low solubility of carbon in copper appears to help make this growth process self-limiting. We also developed graphene film transfer processes to arbitrary substrates, and dual-gated field-effect transistors fabricated on silicon/silicon dioxide substrates showed electron mobilities as high as 4050 square centimeters per volt per second at room temperature.
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                Author and article information

                Journal
                Sci Adv
                Sci Adv
                SciAdv
                advances
                Science Advances
                American Association for the Advancement of Science
                2375-2548
                April 2021
                07 April 2021
                : 7
                : 15
                : eabf9809
                Affiliations
                [1 ]Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, Germany.
                [2 ]Fakultät für Physik, Universität Bielefeld, Universitätsstr. 25, 33615 Bielefeld, Germany.
                [3 ]Catalan Institute of Nanoscience and Nanotechnology (ICN2), BIST and CSIC, Campus UAB, 08193, Bellaterra (Barcelona), Spain.
                [4 ]Institut de Ciencies Fotoniques (ICFO), The Barcelona Institute of Science and Technology, Barcelona, Spain.
                [5 ]Institució Catalana de Recerça i Estudis Avancats (ICREA), 08010 Barcelona, Spain.
                [6 ]Fakultät für Physik, Universität Duisburg-Essen, Lotharstraße 1, 47057 Duisburg, Germany.
                [7 ]Max-Planck-Institut für Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany.
                [8 ]Institut für Optische Sensorsysteme, DLR, Rutherfordstraße 2, 12489 Berlin, Germany
                [9 ]Institut für Optik und Atomare Physik, Technische Universität Berlin, Strasse des 17. Juni 135, 10623 Berlin, Germany.
                Author notes
                Author information
                http://orcid.org/0000-0002-2290-1016
                http://orcid.org/0000-0002-0055-6231
                http://orcid.org/0000-0001-6211-0158
                http://orcid.org/0000-0002-9664-9095
                http://orcid.org/0000-0003-3189-2331
                http://orcid.org/0000-0002-5649-2548
                http://orcid.org/0000-0001-5230-360X
                http://orcid.org/0000-0002-2382-3363
                http://orcid.org/0000-0002-7184-5620
                http://orcid.org/0000-0001-9764-6120
                http://orcid.org/0000-0003-3998-2518
                http://orcid.org/0000-0001-6851-8453
                http://orcid.org/0000-0003-0054-7092
                Article
                abf9809
                10.1126/sciadv.abf9809
                8026126
                33827824
                35923390-17b4-4fdb-aabb-2750e8cde790
                Copyright © 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY).

                This is an open-access article distributed under the terms of the Creative Commons Attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                History
                : 02 December 2020
                : 19 February 2021
                Funding
                Funded by: doi http://dx.doi.org/10.13039/100010661, Horizon 2020 Framework Programme;
                Award ID: Grant Agreement No. 804349 (ERC StG CUHL)
                Funded by: doi http://dx.doi.org/10.13039/100010661, Horizon 2020 Framework Programme;
                Award ID: Grant Agreement No. 964735 — EXTREME-IR
                Funded by: European Cluster of Advanced Laser Light Sources (EUCALL);
                Award ID: 654220
                Funded by: MAINZ Visiting Professorship;
                Funded by: Severo Ochoa program from Spanish MINECO;
                Award ID: Grant No. SEV-2017-0706
                Categories
                Research Article
                Research Articles
                SciAdv r-articles
                Condensed Matter Physics
                Optics
                Condensed Matter Physics
                Custom metadata
                Ella Polintan

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