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Patel DK, Marzano M, Liu CI, Kruskopf M, Elmquist RE, Liang CT, Rigosi AF. Development of gateless quantum Hall checkerboard p-n junction devices. JOURNAL OF PHYSICS D: APPLIED PHYSICS 2020; 53:https://doi.org/10.1088/1361-6463/ab8d6f. [PMID: 33071355 PMCID: PMC7558461] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Measurements of fractional multiples of the ν = 2 plateau quantized Hall resistance (R H ≈ 12906 Ω) were enabled by the utilization of multiple current terminals on millimetre-scale graphene p-n junction devices fabricated with interfaces along both lateral directions. These quantum Hall resistance checkerboard devices have been demonstrated to match quantized resistance outputs numerically calculated with the LTspice circuit simulator. From the devices' functionality, more complex embodiments of the quantum Hall resistance checkerboard were simulated to highlight the parameter space within which these devices could operate. Moreover, these measurements suggest that the scalability of p-n junction fabrication on millimetre or centimetre scales is feasible with regards to graphene device manufacturing by using the far more efficient process of standard ultraviolet lithography.
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Affiliation(s)
- Dinesh K Patel
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States of America
- Department of Physics, National Taiwan University, Taipei 10617, Taiwan
| | - Martina Marzano
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States of America
- Istituto Nazionale di Ricerca Metrologica, Torino 10135, Italy
| | - Chieh-I Liu
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States of America
- Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742, United States of America
| | - Mattias Kruskopf
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States of America
- Joint Quantum Institute, University of Maryland, College Park, MD 20742, United States of America
- Electricity Division, Physikalisch-Technische Bundesanstalt, Braunschweig 38116, Germany
| | - Randolph E Elmquist
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States of America
| | - Chi-Te Liang
- Department of Physics, National Taiwan University, Taipei 10617, Taiwan
| | - Albert F Rigosi
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States of America
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Rigosi AF, Marzano M, Levy A, Hill HM, Patel DK, Kruskopf M, Jin H, Elmquist RE, Newell DB. Analytical determination of atypical quantized resistances in graphene p-n junctions. PHYSICA. B, CONDENSED MATTER 2020; 582:https://doi.org/10.1016/j.physb.2019.411971. [PMID: 32863578 PMCID: PMC7450729] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
A mathematical approach is introduced for predicting quantized resistances in graphene p-n junction devices that utilize more than a single entry and exit point for electron flow. Depending on the configuration of an arbitrary number of terminals, electrical measurements yield nonconventional, fractional multiples of the typical quantized Hall resistance at the v = 2 plateau (R H ≈ 12906 Ω) and take the form:a b R H . This theoretical formulation is independent of material, and applications to other material systems that exhibit quantum Hall behaviors are to be expected. Furthermore, this formulation is supported with experimental data from graphene devices with multiple source and drain terminals.
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Affiliation(s)
- Albert F. Rigosi
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States
| | - Martina Marzano
- Department of Electronics and Telecommunications, Politecnico di Torino, Torino 10129, Italy
- Istituto Nazionale di Ricerca Metrologica, Torino 10135, Italy
| | - Antonio Levy
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States
| | - Heather M. Hill
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States
| | - Dinesh K. Patel
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States
- Department of Physics, National Taiwan University, Taipei 10617, Taiwan
| | - Mattias Kruskopf
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States
- Joint Quantum Institute, University of Maryland, College Park, MD 20742, United States
| | - Hanbyul Jin
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States
- Joint Quantum Institute, University of Maryland, College Park, MD 20742, United States
| | - Randolph E. Elmquist
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States
| | - David B. Newell
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States
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Liu CI, Scaletta DS, Patel DK, Kruskopf M, Levy A, Hill HM, Rigosi AF. Analysing quantized resistance behaviour in graphene Corbino p-n junction devices. JOURNAL OF PHYSICS D: APPLIED PHYSICS 2020; 53:10.1088/1361-6463/ab83bb. [PMID: 32831402 PMCID: PMC7431976 DOI: 10.1088/1361-6463/ab83bb] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Just a few of the promising applications of graphene Corbino pnJ devices include two-dimensional Dirac fermion microscopes, custom programmable quantized resistors, and mesoscopic valley filters. In some cases, device scalability is crucial, as seen in fields like resistance metrology, where graphene devices are required to accommodate currents of the order 100 μA to be compatible with existing infrastructure. However, fabrication of these devices still poses many difficulties. In this work, unusual quantized resistances are observed in epitaxial graphene Corbino p-n junction devices held at the ν = 2 plateau (R H ≈ 12906 Ω) and agree with numerical simulations performed with the LTspice circuit simulator. The formulae describing experimental and simulated data are empirically derived for generalized placement of up to three current terminals and accurately reflects observed partial edge channel cancellation. These results support the use of ultraviolet lithography as a way to scale up graphene-based devices with suitably narrow junctions that could be applied in a variety of subfields.
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Affiliation(s)
- Chieh-I Liu
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States
- Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742, United States
| | - Dominick S Scaletta
- Department of Physics, Mount San Jacinto College, Menifee, CA 92584, United States
| | - Dinesh K Patel
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States
- Department of Physics, National Taiwan University, Taipei 10617, Taiwan
| | - Mattias Kruskopf
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States
- Joint Quantum Institute, University of Maryland, College Park, MD 20742, United States
- Electricity Division, Physikalisch-Technische Bundesanstalt, Braunschweig 38116, Germany
| | - Antonio Levy
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States
| | - Heather M Hill
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States
| | - Albert F Rigosi
- Physical Measurement Laboratory, National Institute of Standards and Technology (NIST), Gaithersburg, MD 20899, United States
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Srivastav SK, Sahu MR, Watanabe K, Taniguchi T, Banerjee S, Das A. Universal quantized thermal conductance in graphene. SCIENCE ADVANCES 2019; 5:eaaw5798. [PMID: 31309156 PMCID: PMC6625820 DOI: 10.1126/sciadv.aaw5798] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/07/2019] [Accepted: 05/31/2019] [Indexed: 06/10/2023]
Abstract
The universal quantization of thermal conductance provides information on a state's topological order. Recent measurements revealed that the observed value of thermal conductance of the 5 2 state is inconsistent with either Pfaffian or anti-Pfaffian model, motivating several theoretical articles. Analysis has been made complicated by the presence of counter-propagating edge channels arising from edge reconstruction, an inevitable consequence of separating the dopant layer from the GaAs quantum well and the resulting soft confining potential. Here, we measured thermal conductance in graphene with atomically sharp confining potential by using sensitive noise thermometry on hexagonal boron-nitride encapsulated graphene devices, gated by either SiO2/Si or graphite back gate. We find the quantization of thermal conductance within 5% accuracy for ν = 1 ; 4 3 ; 2 and 6 plateaus, emphasizing the universality of flow of information. These graphene quantum Hall thermal transport measurements will allow new insight into exotic systems like even-denominator quantum Hall fractions in graphene.
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Affiliation(s)
| | - Manas Ranjan Sahu
- Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - K. Watanabe
- National Institute of Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - T. Taniguchi
- National Institute of Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Sumilan Banerjee
- Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Anindya Das
- Department of Physics, Indian Institute of Science, Bangalore 560012, India
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Li J, Wen H, Watanabe K, Taniguchi T, Zhu J. Gate-Controlled Transmission of Quantum Hall Edge States in Bilayer Graphene. PHYSICAL REVIEW LETTERS 2018; 120:057701. [PMID: 29481178 DOI: 10.1103/physrevlett.120.057701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2017] [Revised: 12/01/2017] [Indexed: 06/08/2023]
Abstract
The edge states of the quantum Hall and fractional quantum Hall effect of a two-dimensional electron gas carry key information of the bulk excitations. Here we demonstrate gate-controlled transmission of edge states in bilayer graphene through a potential barrier with tunable height. The backscattering rate is continuously varied from 0 to close to 1, with fractional quantized values corresponding to the sequential complete backscattering of individual modes. Our experiments demonstrate the feasibility to controllably manipulate edge states in bilayer graphene, thus opening the door to more complex experiments.
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Affiliation(s)
- Jing Li
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Hua Wen
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Kenji Watanabe
- National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Jun Zhu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
- Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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Wei DS, van der Sar T, Sanchez-Yamagishi JD, Watanabe K, Taniguchi T, Jarillo-Herrero P, Halperin BI, Yacoby A. Mach-Zehnder interferometry using spin- and valley-polarized quantum Hall edge states in graphene. SCIENCE ADVANCES 2017; 3:e1700600. [PMID: 28835920 PMCID: PMC5562424 DOI: 10.1126/sciadv.1700600] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2017] [Accepted: 07/14/2017] [Indexed: 05/31/2023]
Abstract
Confined to a two-dimensional plane, electrons in a strong magnetic field travel along the edge in one-dimensional quantum Hall channels that are protected against backscattering. These channels can be used as solid-state analogs of monochromatic beams of light, providing a unique platform for studying electron interference. Electron interferometry is regarded as one of the most promising routes for studying fractional and non-Abelian statistics and quantum entanglement via two-particle interference. However, creating an edge-channel interferometer in which electron-electron interactions play an important role requires a clean system and long phase coherence lengths. We realize electronic Mach-Zehnder interferometers with record visibilities of up to 98% using spin- and valley-polarized edge channels that copropagate along a pn junction in graphene. We find that interchannel scattering between same-spin edge channels along the physical graphene edge can be used to form beamsplitters, whereas the absence of interchannel scattering along gate-defined interfaces can be used to form isolated interferometer arms. Surprisingly, our interferometer is robust to dephasing effects at energies an order of magnitude larger than those observed in pioneering experiments on GaAs/AlGaAs quantum wells. Our results shed light on the nature of edge-channel equilibration and open up new possibilities for studying exotic electron statistics and quantum phenomena.
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Affiliation(s)
- Di S. Wei
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
| | | | - Javier D. Sanchez-Yamagishi
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Kenji Watanabe
- Advanced Materials Laboratory, National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan
| | - Takashi Taniguchi
- Advanced Materials Laboratory, National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan
| | - Pablo Jarillo-Herrero
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | | | - Amir Yacoby
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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Overweg H, Eggimann H, Liu MH, Varlet A, Eich M, Simonet P, Lee Y, Watanabe K, Taniguchi T, Richter K, Fal'ko VI, Ensslin K, Ihn T. Oscillating Magnetoresistance in Graphene p-n Junctions at Intermediate Magnetic Fields. NANO LETTERS 2017; 17:2852-2857. [PMID: 28383919 DOI: 10.1021/acs.nanolett.6b05318] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We report on the observation of magnetoresistance oscillations in graphene p-n junctions. The oscillations have been observed for six samples, consisting of single-layer and bilayer graphene, and persist up to temperatures of 30 K, where standard Shubnikov-de Haas oscillations are no longer discernible. The oscillatory magnetoresistance can be reproduced by tight-binding simulations. We attribute this phenomenon to the modulated densities of states in the n- and p-regions.
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Affiliation(s)
- Hiske Overweg
- Solid State Physics Laboratory, ETH Zürich , CH-8093 Zürich, Switzerland
| | - Hannah Eggimann
- Solid State Physics Laboratory, ETH Zürich , CH-8093 Zürich, Switzerland
| | - Ming-Hao Liu
- Institut für Theoretische Physik, Universität Regensburg , D-93040 Regensburg, Germany
- Department of Physics, National Cheng Kung University , Tainan 70101, Taiwan
| | - Anastasia Varlet
- Solid State Physics Laboratory, ETH Zürich , CH-8093 Zürich, Switzerland
| | - Marius Eich
- Solid State Physics Laboratory, ETH Zürich , CH-8093 Zürich, Switzerland
| | - Pauline Simonet
- Solid State Physics Laboratory, ETH Zürich , CH-8093 Zürich, Switzerland
| | - Yongjin Lee
- Solid State Physics Laboratory, ETH Zürich , CH-8093 Zürich, Switzerland
| | - Kenji Watanabe
- Advanced Materials Laboratory, National Institute for Material Science , 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- Advanced Materials Laboratory, National Institute for Material Science , 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Klaus Richter
- Institut für Theoretische Physik, Universität Regensburg , D-93040 Regensburg, Germany
| | - Vladimir I Fal'ko
- National Graphene Institute, University of Manchester , Manchester M13 9PL, United Kingdom
| | - Klaus Ensslin
- Solid State Physics Laboratory, ETH Zürich , CH-8093 Zürich, Switzerland
| | - Thomas Ihn
- Solid State Physics Laboratory, ETH Zürich , CH-8093 Zürich, Switzerland
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Tóvári E, Makk P, Liu MH, Rickhaus P, Kovács-Krausz Z, Richter K, Schönenberger C, Csonka S. Gate-controlled conductance enhancement from quantum Hall channels along graphene p-n junctions. NANOSCALE 2016; 8:19910-19916. [PMID: 27878177 PMCID: PMC5315021 DOI: 10.1039/c6nr05100f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
The formation of quantum Hall channels inside the bulk of graphene is studied using various contact and gate geometries. p-n junctions are created along the longitudinal direction of samples, and enhanced conductance is observed in the case of bipolar doping due to the new conducting channels formed in the bulk, whose position, propagating direction and, in one geometry, coupling to electrodes are determined by the gate-controlled filling factor across the device. This effect could be exploited to probe the behavior and interaction of quantum Hall channels protected against uncontrolled scattering at the edges.
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Affiliation(s)
- Endre Tóvári
- Department of Physics, Budapest University of Technology and Economics, and Condensed Matter Research Group of the Hungarian Academy of Sciences, Budafoki út 8, 1111 Budapest, Hungary.
| | - Péter Makk
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Ming-Hao Liu
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Peter Rickhaus
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Zoltán Kovács-Krausz
- Department of Physics, Budapest University of Technology and Economics, and Condensed Matter Research Group of the Hungarian Academy of Sciences, Budafoki út 8, 1111 Budapest, Hungary. and Faculty of Physics, Babes-Bolyai University, Str. Mihail Kogalniceanu nr. 1, 400084 Cluj-Napoca, Romania
| | - Klaus Richter
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Christian Schönenberger
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Szabolcs Csonka
- Department of Physics, Budapest University of Technology and Economics, and Condensed Matter Research Group of the Hungarian Academy of Sciences, Budafoki út 8, 1111 Budapest, Hungary.
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Abstract
The control and measurement of local non-equilibrium configurations is of utmost importance in applications on energy harvesting, thermoelectrics and heat management in nano-electronics. This challenging task can be achieved with the help of various local probes, prominent examples including superconducting or quantum dot based tunnel junctions, classical and quantum resistors, and Raman thermography. Beyond time-averaged properties, valuable information can also be gained from spontaneous fluctuations of current (noise). From these perspective, however, a fundamental constraint is set by current conservation, which makes noise a characteristic of the whole conductor, rather than some part of it. Here we demonstrate how to remove this obstacle and pick up a local noise temperature of a current biased diffusive conductor with the help of a miniature noise probe. This approach is virtually noninvasive for the electronic energy distributions and extends primary local measurements towards strongly non-equilibrium regimes.
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KOBAYASHI K. What can we learn from noise? - Mesoscopic nonequilibrium statistical physics. PROCEEDINGS OF THE JAPAN ACADEMY. SERIES B, PHYSICAL AND BIOLOGICAL SCIENCES 2016; 92:204-221. [PMID: 27477456 PMCID: PMC5114290 DOI: 10.2183/pjab.92.204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/27/2016] [Accepted: 05/30/2016] [Indexed: 06/06/2023]
Abstract
Mesoscopic systems - small electric circuits working in quantum regime - offer us a unique experimental stage to explorer quantum transport in a tunable and precise way. The purpose of this Review is to show how they can contribute to statistical physics. We introduce the significance of fluctuation, or equivalently noise, as noise measurement enables us to address the fundamental aspects of a physical system. The significance of the fluctuation theorem (FT) in statistical physics is noted. We explain what information can be deduced from the current noise measurement in mesoscopic systems. As an important application of the noise measurement to statistical physics, we describe our experimental work on the current and current noise in an electron interferometer, which is the first experimental test of FT in quantum regime. Our attempt will shed new light in the research field of mesoscopic quantum statistical physics.
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Affiliation(s)
- Kensuke KOBAYASHI
- Graduate School of Science, Osaka University, Toyonaka, Osaka, Japan
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