1
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Manna S, Das A, Goldstein M, Gefen Y. Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise. PHYSICAL REVIEW LETTERS 2024; 132:136502. [PMID: 38613281 DOI: 10.1103/physrevlett.132.136502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2023] [Revised: 12/01/2023] [Accepted: 02/26/2024] [Indexed: 04/14/2024]
Abstract
The nature of the bulk topological order of the 5/2 non-Abelian fractional quantum Hall state and the steady state of its edge are long-studied questions. The most promising non-Abelian model bulk states are the Pfaffian (Pf), anti-Pffafian (APf), and particle-hole symmetric Pfaffian (PHPf). Here, we propose to employ a set of dc current-current correlations (electrical shot noise) in order to distinguish among the Pf, APf, and PHPf candidate states, as well as to determine their edge thermal equilibration regimes: full vs partial. Using other tools, measurements of GaAs platforms have already indicated consistency with the PHPf state. Our protocol, realizable with available experimental tools, is based on fully electrical measurements.
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Affiliation(s)
- Sourav Manna
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel Aviv 6997801, Israel
| | - Ankur Das
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Moshe Goldstein
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel Aviv 6997801, Israel
| | - Yuval Gefen
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
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2
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Assouline A, Wang T, Zhou H, Cohen LA, Yang F, Zhang R, Taniguchi T, Watanabe K, Mong RSK, Zaletel MP, Young AF. Energy Gap of the Even-Denominator Fractional Quantum Hall State in Bilayer Graphene. PHYSICAL REVIEW LETTERS 2024; 132:046603. [PMID: 38335366 DOI: 10.1103/physrevlett.132.046603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Revised: 12/10/2023] [Accepted: 01/04/2024] [Indexed: 02/12/2024]
Abstract
Bernal bilayer graphene hosts even-denominator fractional quantum Hall states thought to be described by a Pfaffian wave function with non-Abelian quasiparticle excitations. Here, we report the quantitative determination of fractional quantum Hall energy gaps in bilayer graphene using both thermally activated transport and by direct measurement of the chemical potential. We find a transport activation gap of 5.1 K at B=12 T for a half filled N=1 Landau level, consistent with density matrix renormalization group calculations for the Pfaffian state. However, the measured thermodynamic gap of 11.6 K is smaller than theoretical expectations for the clean limit by approximately a factor of 2. We analyze the chemical potential data near fractional filling within a simplified model of a Wigner crystal of fractional quasiparticles with long-wavelength disorder, explaining this discrepancy. Our results quantitatively establish bilayer graphene as a robust platform for probing the non-Abelian anyons expected to arise as the elementary excitations of the even-denominator state.
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Affiliation(s)
- Alexandre Assouline
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Taige Wang
- Department of Physics, University of California, Berkeley, California 94720, USA
- Material Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Haoxin Zhou
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Liam A Cohen
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Fangyuan Yang
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Ruining Zhang
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Roger S K Mong
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Michael P Zaletel
- Department of Physics, University of California, Berkeley, California 94720, USA
- Material Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Andrea F Young
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
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3
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Xiang F, Gupta A, Chaves A, Krix ZE, Watanabe K, Taniguchi T, Fuhrer MS, Peeters FM, Neilson D, Milošević MV, Hamilton AR. Intra-Zero-Energy Landau Level Crossings in Bilayer Graphene at High Electric Fields. NANO LETTERS 2023; 23:9683-9689. [PMID: 37883804 DOI: 10.1021/acs.nanolett.3c01456] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/28/2023]
Abstract
The highly tunable band structure of the zero-energy Landau level (zLL) of bilayer graphene makes it an ideal platform for engineering novel quantum states. However, the zero-energy Landau level at high electric fields has remained largely unexplored. Here we present magnetotransport measurements of bilayer graphene in high transverse electric fields. We observe previously undetected Landau level crossings at filling factors ν = -2, 1, and 3 at high electric fields. These crossings provide constraints for theoretical models of the zero-energy Landau level and show that the orbital, valley, and spin character of the quantum Hall states at high electric fields is very different from low electric fields. At high E, new transitions between states at ν = -2 with different orbital and spin polarization can be controlled by the gate bias, while the transitions between ν = 0 → 1 and ν = 2 → 3 show anomalous behavior.
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Affiliation(s)
- Feixiang Xiang
- School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Abhay Gupta
- School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Andrey Chaves
- Universidade Federal do Ceará, Departamento de Física, Caixa Postal 6030, 60455-760 Fortaleza, Ceará Brazil
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium
| | - Zeb E Krix
- School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Kenji Watanabe
- National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan
| | - Takashi Taniguchi
- National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan
| | - Michael S Fuhrer
- School of Physics and Astronomy and ARC Centre of Excellence in Future Low-Energy Electronics Technologies (FLEET), Monash University, Clayton, Victoria 3800, Australia
| | - François M Peeters
- Universidade Federal do Ceará, Departamento de Física, Caixa Postal 6030, 60455-760 Fortaleza, Ceará Brazil
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium
| | - David Neilson
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, University of New South Wales, Sydney, New South Wales 2052, Australia
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium
| | - Milorad V Milošević
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium
- NANOlab Center of Excellence, University of Antwerp, B-2020 Antwerp, Belgium
| | - Alexander R Hamilton
- School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, University of New South Wales, Sydney, New South Wales 2052, Australia
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4
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Fu H, Huang K, Watanabe K, Taniguchi T, Zhu J. Charge Oscillations in Bilayer Graphene Quantum Confinement Devices. NANO LETTERS 2023; 23:9726-9732. [PMID: 37862439 DOI: 10.1021/acs.nanolett.3c02253] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/22/2023]
Abstract
Quantum confinement structures are building blocks of quantum devices in fundamental physics exploration and technological applications. In this work, we fabricate dual-gated bilayer graphene Fabry-Pérot quantum Hall interferometers employing two different gating strategies and conduct finite element simulations to understand the electrostatics of the confinement structures and to guide device design and fabrication. We observe two types of resistance oscillations arising from the charging of quantum dots formed inside the interferometers. We obtain the size, location, and charging energy of the dots by measuring the dependence of the oscillations on the magnetic field, gate voltages, and dc bias. We analyze and discuss the origin of the quantum dots and their impact on quantum Hall edge state backscattering and interference. Insights gained in these studies shed light on the construction of van der Waals quantum confinement devices.
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Affiliation(s)
- Hailong Fu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
- School of Physics, Zhejiang University, Hangzhou 310058, China
| | - Ke Huang
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Jun Zhu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
- Center for Two-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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5
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Cohen LA, Samuelson NL, Wang T, Taniguchi T, Watanabe K, Zaletel MP, Young AF. Universal chiral Luttinger liquid behavior in a graphene fractional quantum Hall point contact. Science 2023; 382:542-547. [PMID: 37917688 DOI: 10.1126/science.adf9728] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 09/29/2023] [Indexed: 11/04/2023]
Abstract
One-dimensional conductors are described by Luttinger liquid theory, which predicts a power-law suppression of the single-electron tunneling density of states at low voltages. The scaling exponent is predicted to be quantized when tunneling into a single isolated chiral edge state of the fractional quantum Hall effect. We report conductance measurements across a point contact linking integer and fractional quantum Hall edge states (at fillings 1 and [Formula: see text], respectively). At weak coupling, we observe the predicted universal quadratic scaling with temperature and voltage. At strong coupling, we demonstrate perfect Andreev reflection of fractionalized quasiparticles at the point contact. We use the strong coupling physics to realize a nearly dissipationless direct current voltage step-up transformer, whose gain arises directly from topological fractionalization of electrical charge.
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Affiliation(s)
- Liam A Cohen
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| | - Noah L Samuelson
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
| | - Taige Wang
- Department of Physics, University of California, Berkeley, CA 94720, USA
- Material Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Michael P Zaletel
- Department of Physics, University of California, Berkeley, CA 94720, USA
- Material Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Andrea F Young
- Department of Physics, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
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6
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Kim S, Kim D, Watanabe K, Taniguchi T, Smet JH, Kim Y. Orbitally Controlled Quantum Hall States in Decoupled Two-Bilayer Graphene Sheets. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2023; 10:e2300574. [PMID: 37259684 PMCID: PMC10427396 DOI: 10.1002/advs.202300574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2023] [Revised: 04/29/2023] [Indexed: 06/02/2023]
Abstract
The authors report on integer and fractional quantum Hall states in a stack of two twisted Bernal bilayer graphene sheets. By exploiting the momentum mismatch in reciprocal space, the single-particle tunneling between both bilayers is suppressed. Since the bilayers are spatially separated by only 0.34 nm, the stack benefits from strong interlayer Coulombic interactions. These interactions can cause the formation of a Bose-Einstein condensate. Indeed, such a condensate is observed for half-filling in each bilayer sheet. However, only when the partially filled levels have orbital index 1. It is absent for partially filled levels with orbital index 0. This discrepancy is tentatively attributed to the role of skyrmion/anti-skyrmion pair excitations and the dependence of the energy of these excitations on the orbital index. The application of asymmetric top and bottom gate voltages enables to influence the orbital nature of the electronic states of the graphene bilayers at the chemical potential and to navigate in orbital mixed space. The latter hosts an even denominator fractional quantum Hall state at total filling of -3/2. These observations suggest a unique edge reconstruction involving both electrons and chiral p-wave composite fermions.
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Affiliation(s)
- Soyun Kim
- Department of Physics and ChemistryDaegu Gyeongbuk Institute of Science and Technology (DGIST)Daegu42988Republic of Korea
| | - Dohun Kim
- Department of Physics and ChemistryDaegu Gyeongbuk Institute of Science and Technology (DGIST)Daegu42988Republic of Korea
| | - Kenji Watanabe
- Research Center for Functional MaterialsNational Institute for Materials ScienceTsukuba305‐0044Japan
| | - Takashi Taniguchi
- International Center for Materials NanoarchitectonicsNational Institute for Materials ScienceTsukuba305‐0044Japan
| | - Jurgen H. Smet
- Max Planck Institute for Solid State Research70569StuttgartGermany
| | - Youngwook Kim
- Department of Physics and ChemistryDaegu Gyeongbuk Institute of Science and Technology (DGIST)Daegu42988Republic of Korea
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7
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Yazdani A, von Oppen F, Halperin BI, Yacoby A. Hunting for Majoranas. Science 2023; 380:eade0850. [PMID: 37347870 DOI: 10.1126/science.ade0850] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Accepted: 05/22/2023] [Indexed: 06/24/2023]
Abstract
Over the past decade, there have been considerable efforts to observe non-abelian quasiparticles in novel quantum materials and devices. These efforts are motivated by the goals of demonstrating quantum statistics of quasiparticles beyond those of fermions and bosons and of establishing the underlying science for the creation of topologically protected quantum bits. In this Review, we focus on efforts to create topological superconducting phases that host Majorana zero modes. We consider the lessons learned from existing experimental efforts, which are motivating both improvements to present platforms and the exploration of new approaches. Although the experimental detection of non-abelian quasiparticles remains challenging, the knowledge gained thus far and the opportunities ahead offer high potential for discovery and advances in this exciting area of quantum physics.
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Affiliation(s)
- Ali Yazdani
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08540, USA
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | | | - Amir Yacoby
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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8
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Fu H, Huang K, Watanabe K, Taniguchi T, Kayyalha M, Zhu J. Aharonov-Bohm Oscillations in Bilayer Graphene Quantum Hall Edge State Fabry-Pérot Interferometers. NANO LETTERS 2023; 23:718-725. [PMID: 36622939 DOI: 10.1021/acs.nanolett.2c05004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Bernal-stacked bilayer graphene exhibits a wealth of interaction-driven phenomena, including robust even-denominator fractional quantum Hall states. We construct Fabry-Pérot interferometers using a split-gate design and present measurements of the Aharonov-Bohm oscillations. The edge state velocity is found to be approximately 6 × 104 m/s at filling factor ν = 2 and decreases with increasing filling factor. The dc bias and temperature dependence of the interference point to electron-electron interaction induced decoherence mechanisms. These results pave the way for the quest of fractional and non-Abelian braiding statistics in this promising device platform.
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Affiliation(s)
- Hailong Fu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania16802, United States
- School of Physics, Zhejiang University, Hangzhou310058, People's Republic of China
| | - Ke Huang
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania16802, United States
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba305-0044, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba305-0044, Japan
| | - Morteza Kayyalha
- Department of Electrical Engineering, The Pennsylvania State University, University Park, Pennsylvania16802, United States
| | - Jun Zhu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania16802, United States
- Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania16802, United States
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9
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Kim D, Kang B, Choi YB, Watanabe K, Taniguchi T, Lee GH, Cho GY, Kim Y. Robust Interlayer-Coherent Quantum Hall States in Twisted Bilayer Graphene. NANO LETTERS 2023; 23:163-169. [PMID: 36524972 DOI: 10.1021/acs.nanolett.2c03836] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
We introduce a novel two-dimensional electronic system with ultrastrong interlayer interactions, namely, twisted bilayer graphene with a large twist angle, as an ideal ground for realizing interlayer-coherent excitonic condensates. In these systems, sub-nanometer atomic separation between the layers allows significant interlayer interactions, while interlayer electron tunneling is geometrically suppressed due to the large twist angle. By fully exploiting these two features we demonstrate that a sequence of odd-integer quantum Hall states with interlayer coherence appears at the second Landau level (N = 1). Notably the energy gaps for these states are of order 1 K, which is several orders of magnitude greater than those in GaAs. Furthermore, a variety of quantum Hall phase transitions are observed experimentally. All the experimental observations are largely consistent with our phenomenological model calculations. Hence, we establish that a large twist angle system is an excellent platform for high-temperature excitonic condensation.
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Affiliation(s)
- Dohun Kim
- Department of Physics and Chemistry, Daegu Gyeongbuk Institute of Science and Technology (DGIST), Daegu 42988, Republic of Korea
| | - Byungmin Kang
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
| | - Yong-Bin Choi
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang 37673, Republic of Korea
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba 305-0044, Japan
| | - Gil-Ho Lee
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang 37673, Republic of Korea
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea
| | - Gil Young Cho
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang 37673, Republic of Korea
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea
- Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Pohang 37673, Republic of Korea
| | - Youngwook Kim
- Department of Physics and Chemistry, Daegu Gyeongbuk Institute of Science and Technology (DGIST), Daegu 42988, Republic of Korea
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10
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Quantum cascade of correlated phases in trigonally warped bilayer graphene. Nature 2022; 608:298-302. [PMID: 35948716 DOI: 10.1038/s41586-022-04937-1] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2021] [Accepted: 06/07/2022] [Indexed: 11/08/2022]
Abstract
Divergent density of states offers an opportunity to explore a wide variety of correlated electron physics. In the thinnest limit, this has been predicted and verified in the ultraflat bands of magic-angle twisted bilayer graphene1-5, the band touching points of few-layer rhombohedral graphite6-8 and the lightly doped rhombohedral trilayer graphene9-11. The simpler and seemingly better understood Bernal bilayer graphene is also susceptible to orbital magnetism at charge neutrality7 leading to layer antiferromagnetic states12 or quantum anomalous Hall states13. Here we report the observation of a cascade of correlated phases in the vicinity of electric-field-controlled Lifshitz transitions14,15 and van Hove singularities16 in Bernal bilayer graphene. We provide evidence for the observation of Stoner ferromagnets in the form of half and quarter metals10,11. Furthermore, we identify signatures consistent with a topologically non-trivial Wigner-Hall crystal17 at zero magnetic field and its transition to a trivial Wigner crystal, as well as two correlated metals whose behaviour deviates from that of standard Fermi liquids. Our results in this reproducible, tunable, simple system open up new horizons for studying strongly correlated electrons.
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11
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Geisenhof FR, Winterer F, Seiler AM, Lenz J, Xu T, Zhang F, Weitz RT. Quantum anomalous Hall octet driven by orbital magnetism in bilayer graphene. Nature 2021; 598:53-58. [PMID: 34616059 DOI: 10.1038/s41586-021-03849-w] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2021] [Accepted: 07/22/2021] [Indexed: 11/09/2022]
Abstract
The quantum anomalous Hall (QAH) effect-a macroscopic manifestation of chiral band topology at zero magnetic field-has been experimentally realized only by the magnetic doping of topological insulators1-3 and the delicate design of moiré heterostructures4-8. However, the seemingly simple bilayer graphene without magnetic doping or moiré engineering has long been predicted to host competing ordered states with QAH effects9-11. Here we explore states in bilayer graphene with a conductance of 2 e2 h-1 (where e is the electronic charge and h is Planck's constant) that not only survive down to anomalously small magnetic fields and up to temperatures of five kelvin but also exhibit magnetic hysteresis. Together, the experimental signatures provide compelling evidence for orbital-magnetism-driven QAH behaviour that is tunable via electric and magnetic fields as well as carrier sign. The observed octet of QAH phases is distinct from previous observations owing to its peculiar ferrimagnetic and ferrielectric order that is characterized by quantized anomalous charge, spin, valley and spin-valley Hall behaviour9.
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Affiliation(s)
- Fabian R Geisenhof
- Physics of Nanosystems, Department of Physics, Ludwig-Maximilians-Universität München, Munich, Germany
| | - Felix Winterer
- Physics of Nanosystems, Department of Physics, Ludwig-Maximilians-Universität München, Munich, Germany
| | - Anna M Seiler
- Physics of Nanosystems, Department of Physics, Ludwig-Maximilians-Universität München, Munich, Germany
| | - Jakob Lenz
- Physics of Nanosystems, Department of Physics, Ludwig-Maximilians-Universität München, Munich, Germany
| | - Tianyi Xu
- Department of Physics, University of Texas at Dallas, Richardson, TX, USA
| | - Fan Zhang
- Department of Physics, University of Texas at Dallas, Richardson, TX, USA.
| | - R Thomas Weitz
- Physics of Nanosystems, Department of Physics, Ludwig-Maximilians-Universität München, Munich, Germany. .,Center for Nanoscience (CeNS), Munich, Germany. .,Munich Center for Quantum Science and Technology (MCQST), Munich, Germany. .,1st Physical Institute, Faculty of Physics, University of Göttingen, Göttingen, Germany.
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12
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Joucken F, Bena C, Ge Z, Quezada-Lopez E, Pinon S, Kaladzhyan V, Taniguchi T, Watanabe K, Ferreira A, Velasco J. Direct Visualization of Native Defects in Graphite and Their Effect on the Electronic Properties of Bernal-Stacked Bilayer Graphene. NANO LETTERS 2021; 21:7100-7108. [PMID: 34415771 DOI: 10.1021/acs.nanolett.1c01442] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Graphite crystals used to prepare graphene-based heterostructures are generally assumed to be defect free. We report here scanning tunneling microscopy results that show graphite commonly used to prepare graphene devices can contain a significant amount of native defects. Extensive scanning of the surface allows us to determine the concentration of native defects to be 6.6 × 108 cm-2. We further study the effects of these native defects on the electronic properties of Bernal-stacked bilayer graphene. We observe gate-dependent intravalley scattering and successfully compare our experimental results to T-matrix-based calculations, revealing a clear carrier density dependence in the distribution of the scattering vectors. We also present a technique for evaluating the spatial distribution of short-scale scattering. Finally, we present a theoretical analysis based on the Boltzmann transport equation that predicts that the dilute native defects identified in our study are an important extrinsic source of scattering, ultimately setting the charge carrier mobility at low temperatures.
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Affiliation(s)
- Frédéric Joucken
- Department of Physics, University of California, Santa Cruz, California 95064, United States
- Department of Physics, Arizona State University, Tempe, Arizona 85287, United States
| | - Cristina Bena
- Institut de Physique Théorique, Université Paris Saclay, CEA CNRS, Orme des Merisiers, 91190 Gif-sur-Yvette Cedex, France
| | - Zhehao Ge
- Department of Physics, University of California, Santa Cruz, California 95064, United States
| | - Eberth Quezada-Lopez
- Department of Physics, University of California, Santa Cruz, California 95064, United States
| | - Sarah Pinon
- Institut de Physique Théorique, Université Paris Saclay, CEA CNRS, Orme des Merisiers, 91190 Gif-sur-Yvette Cedex, France
| | - Vardan Kaladzhyan
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Aires Ferreira
- Department of Physics and York Centre for Quantum Technologies, University of York, York YO10 5DD, United Kingdom
| | - Jairo Velasco
- Department of Physics, University of California, Santa Cruz, California 95064, United States
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13
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Jacak JE. Limits of Applicability of the Composite Fermion Model. MATERIALS (BASEL, SWITZERLAND) 2021; 14:4267. [PMID: 34361462 PMCID: PMC8348463 DOI: 10.3390/ma14154267] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/30/2021] [Revised: 07/18/2021] [Accepted: 07/24/2021] [Indexed: 11/16/2022]
Abstract
The popular model of composite fermions, proposed in order to rationalize FQHE, were insufficient in view of recent experimental observations in graphene monolayer and bilayer, in higher Landau levels in GaAs and in so-called enigmatic FQHE states in the lowest Landau level of GaAs. The specific FQHE hierarchy in double Hall systems of GaAs 2DES and graphene also cannot be explained in the framework of composite fermions. We identify the limits of the usability of the composite fermion model by means of topological methods, which elucidate the phenomenological assumptions in composite fermion structure and admit further development of FQHE understanding. We demonstrate how to generalize these ideas in order to explain experimentally observed FQHE phenomena, going beyond the explanation ability of the conventional composite fermion model.
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Affiliation(s)
- Janusz E Jacak
- Department of Quantum Technologies, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
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14
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Feldman DE, Halperin BI. Fractional charge and fractional statistics in the quantum Hall effects. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2021; 84:076501. [PMID: 34015771 DOI: 10.1088/1361-6633/ac03aa] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Accepted: 05/20/2021] [Indexed: 06/12/2023]
Abstract
Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be observed. In addition to theoretical foundations, we review the present status of the experiments in the area. We also discuss the notions of non-Abelian statistics and attempts to find experimental evidence for the existence of non-Abelian quasiparticles in certain quantum Hall systems.
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Affiliation(s)
- D E Feldman
- Brown Theoretical Physics Center and Department of Physics, Brown University, Providence, RI 02912, United States of America
| | - Bertrand I Halperin
- Department of Physics, Harvard University, Cambridge, MA 02138, United States of America
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15
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Ma KKW, Wang R, Yang K. Realization of Supersymmetry and Its Spontaneous Breaking in Quantum Hall Edges. PHYSICAL REVIEW LETTERS 2021; 126:206801. [PMID: 34110185 DOI: 10.1103/physrevlett.126.206801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2021] [Accepted: 04/28/2021] [Indexed: 06/12/2023]
Abstract
Supersymmetry (SUSY) relating bosons and fermions plays an important role in unifying different fundamental interactions in particle physics. Since no superpartners of elementary particles have been observed, SUSY, if present, must be broken at low-energy. This makes it important to understand how SUSY is realized and broken, and study their consequences. We show that an N=(1,0) SUSY, arguably the simplest type, can be realized at the edge of the Moore-Read quantum Hall state. Depending on the absence or presence of edge reconstruction, both SUSY-preserving and SUSY broken phases can be realized in the same system, allowing for their unified description. The significance of the gapless fermionic Goldstino mode in the SUSY broken phase is discussed.
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Affiliation(s)
- Ken K W Ma
- National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
| | - Ruojun Wang
- National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
| | - Kun Yang
- National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
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16
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Shi Q, Shih EM, Gustafsson MV, Rhodes DA, Kim B, Watanabe K, Taniguchi T, Papić Z, Hone J, Dean CR. Odd- and even-denominator fractional quantum Hall states in monolayer WSe 2. NATURE NANOTECHNOLOGY 2020; 15:569-573. [PMID: 32632320 DOI: 10.1038/s41565-020-0685-6] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2019] [Accepted: 04/05/2020] [Indexed: 06/11/2023]
Abstract
Monolayer semiconducting transition-metal dichalcogenides (TMDs) represent a unique class of two-dimensional (2D) electron systems. Their atomically thin structure facilitates gate tunability just like graphene does, but unlike graphene, TMDs have the advantage of a sizable band gap and strong spin-orbit coupling. Measurements under large magnetic fields have revealed an unusual Landau level (LL) structure1-3, distinct from other 2D electron systems. However, owing to the limited sample quality and poor electrical contact, probing the lowest LLs has been challenging, and observation of electron correlations within the fractionally filled LL regime has not been possible. Here, through bulk electronic compressibility measurements, we investigate the LL structure of monolayer WSe2 in the extreme quantum limit, and observe fractional quantum Hall states in the lowest three LLs. The odd-denominator fractional quantum Hall sequences demonstrate a systematic evolution with the LL orbital index, consistent with generic theoretical expectations. In addition, we observe an even-denominator state in the second LL that is expected to host non-Abelian statistics. Our results suggest that the 2D semiconductors can provide an experimental platform that closely resembles idealized theoretical models in the quantum Hall regime.
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Affiliation(s)
- Qianhui Shi
- Department of Physics, Columbia University, New York, NY, USA
| | - En-Min Shih
- Department of Physics, Columbia University, New York, NY, USA
| | - Martin V Gustafsson
- Department of Physics, Columbia University, New York, NY, USA
- Raytheon BBN Technologies, Cambridge, MA, USA
| | - Daniel A Rhodes
- Department of Mechanical Engineering, Columbia University, New York, NY, USA
| | - Bumho Kim
- Department of Mechanical Engineering, Columbia University, New York, NY, USA
| | - Kenji Watanabe
- National Institute for Materials Science, Tsukuba, Japan
| | | | - Zlatko Papić
- School of Physics and Astronomy, University of Leeds, Leeds, UK
| | - James Hone
- Department of Mechanical Engineering, Columbia University, New York, NY, USA
| | - Cory R Dean
- Department of Physics, Columbia University, New York, NY, USA.
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17
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Jacak JE. Homotopy Phases of FQHE with Long-Range Quantum Entanglement in Monolayer and Bilayer Hall Systems. NANOMATERIALS (BASEL, SWITZERLAND) 2020; 10:E1286. [PMID: 32629942 PMCID: PMC7408279 DOI: 10.3390/nano10071286] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/09/2020] [Revised: 06/08/2020] [Accepted: 06/19/2020] [Indexed: 06/11/2023]
Abstract
Correlated phases in Hall systems have topological character. Multilayer configurations of planar electron systems create the opportunity to change topological phases on demand using macroscopic factors, such as vertical voltage. We present an analysis of such phenomena in close relation to recent experiments with multilayer Hall setups including GaAs and graphene multi-layers. The consequences of the blocking or not of the inter-layer electron tunneling in stacked Hall configurations are analyzed and presented in detail. Multilayer Hall systems are thus tunable topological composite nanomaterials, in the case of graphene-stacked systems by both intra- and inter-layer voltage.
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Affiliation(s)
- Janusz Edward Jacak
- Department of Quantum Technologies, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
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18
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Zhu Z, Sheng DN, Sodemann I. Widely Tunable Quantum Phase Transition from Moore-Read to Composite Fermi Liquid in Bilayer Graphene. PHYSICAL REVIEW LETTERS 2020; 124:097604. [PMID: 32202902 DOI: 10.1103/physrevlett.124.097604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2019] [Accepted: 02/11/2020] [Indexed: 06/10/2023]
Abstract
We develop a proposal to realize a widely tunable and clean quantum phase transition in bilayer graphene between two paradigmatic fractionalized phases of matter: the Moore-Read fractional quantum Hall state and the composite Fermi liquid metal. This transition can be realized at total fillings ν=±3+1/2 and the critical point can be controllably accessed by tuning either the interlayer electric bias or the perpendicular magnetic field values over a wide range of parameters. We study the transition numerically within a model that contains all leading single particle corrections to the band structure of bilayer graphene and includes the fluctuations between the n=0 and n=1 cyclotron orbitals of its zeroth Landau level to delineate the most favorable region of parameters to experimentally access this unconventional critical point. We also find evidence for a new anisotropic gapless phase stabilized near the level crossing of n=0/1 orbits.
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Affiliation(s)
- Zheng Zhu
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - D N Sheng
- Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
| | - Inti Sodemann
- Max-Planck Institute for the Physics of Complex Systems, D-01187 Dresden, Germany
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19
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Veyrat L, Déprez C, Coissard A, Li X, Gay F, Watanabe K, Taniguchi T, Han Z, Piot BA, Sellier H, Sacépé B. Helical quantum Hall phase in graphene on SrTiO
3. Science 2020; 367:781-786. [DOI: 10.1126/science.aax8201] [Citation(s) in RCA: 39] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2019] [Accepted: 01/14/2020] [Indexed: 12/24/2022]
Affiliation(s)
- Louis Veyrat
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | - Corentin Déprez
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | - Alexis Coissard
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | - Xiaoxi Li
- Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, P. R. China
- School of Material Science and Engineering, University of Science and Technology of China, Anhui 230026, P. R. China
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, P. R. China
| | - Frédéric Gay
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | - Kenji Watanabe
- National Institute for Materials Science, 1-1 Namiki, Tsukuba 306-0044, Japan
| | - Takashi Taniguchi
- National Institute for Materials Science, 1-1 Namiki, Tsukuba 306-0044, Japan
| | - Zheng Han
- Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, P. R. China
- School of Material Science and Engineering, University of Science and Technology of China, Anhui 230026, P. R. China
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, P. R. China
| | - Benjamin A. Piot
- Université Grenoble Alpes, UPS-INSA-EMFL-CNRS-LNCMI, 38000 Grenoble, France
| | - Hermann Sellier
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | - Benjamin Sacépé
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
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20
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Wagner G, Nguyen DX, Simon SH. Transport in Bilayer Graphene near Charge Neutrality: Which Scattering Mechanisms Are Important? PHYSICAL REVIEW LETTERS 2020; 124:026601. [PMID: 32004029 DOI: 10.1103/physrevlett.124.026601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2019] [Indexed: 06/10/2023]
Abstract
Using the semiclassical quantum Boltzmann equation (QBE), we numerically calculate the dc transport properties of bilayer graphene near charge neutrality. We find, in contrast to prior discussions, that phonon scattering is crucial even at temperatures below 40 K. Nonetheless, electron-electron scattering still dominates over phonon collisions allowing a hydrodynamic approach. We introduce a simple two-fluid hydrodynamic model of electrons and holes interacting via Coulomb drag and compare our results to the full QBE calculation. We show that the two-fluid model produces quantitatively accurate results for conductivity, thermopower, and thermal conductivity.
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Affiliation(s)
- Glenn Wagner
- Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Dung X Nguyen
- Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Steven H Simon
- Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford OX1 3PU, United Kingdom
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21
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Kim Y, Herlinger P, Taniguchi T, Watanabe K, Smet JH. Reliable Postprocessing Improvement of van der Waals Heterostructures. ACS NANO 2019; 13:14182-14190. [PMID: 31775000 DOI: 10.1021/acsnano.9b06992] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The successful assembly of heterostructures consisting of several layers of different 2D materials in arbitrary order by exploiting van der Waals forces has truly been a game changer in the field of low-dimensional physics. For instance, the encapsulation of graphene or MoS2 between atomically flat hexagonal boron nitride (hBN) layers with strong affinity and graphitic gates that screen charge impurity disorder provided access to a plethora of interesting physical phenomena by drastically boosting the device quality. The encapsulation is accompanied by a self-cleansing effect at the interfaces. The otherwise predominant charged impurity disorder is minimized, and random strain fluctuations ultimately constitute the main source of residual disorder. Despite these advances, the fabricated heterostructures still vary notably in their performance. Although some achieve record mobilities, others only possess mediocre quality. Here, we report a reliable method to improve fully completed van der Waals heterostructure devices with a straightforward postprocessing surface treatment based on thermal annealing and contact mode atomic force microscopy (AFM). The impact is demonstrated by comparing magnetotransport measurements before and after the AFM treatment on one and the same device as well as on a larger set of treated and untreated devices to collect device statistics. Both the low-temperature properties and the room temperature electrical characteristics, as relevant for applications, improve on average substantially. We surmise that the main beneficial effect arises from reducing nanometer scale corrugations at the interfaces, that is, the detrimental impact of random strain fluctuations.
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Affiliation(s)
- Youngwook Kim
- Max-Planck-Institut für Festkörperforschung , 70569 Stuttgart , Germany
- Department of Emerging Materials Science , DGIST , 42988 Daegu , Korea
| | - Patrick Herlinger
- Max-Planck-Institut für Festkörperforschung , 70569 Stuttgart , Germany
| | - Takashi Taniguchi
- National Institute for Materials Science , 1-1 Namiki , Tsukuba 305-0044 , Japan
| | - Kenji Watanabe
- National Institute for Materials Science , 1-1 Namiki , Tsukuba 305-0044 , Japan
| | - Jurgen H Smet
- Max-Planck-Institut für Festkörperforschung , 70569 Stuttgart , Germany
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22
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García-Ruiz A, Slizovskiy S, Mucha-Kruczyński M, Fal’ko VI. Spectroscopic Signatures of Electronic Excitations in Raman Scattering in Thin Films of Rhombohedral Graphite. NANO LETTERS 2019; 19:6152-6156. [PMID: 31361497 PMCID: PMC7007278 DOI: 10.1021/acs.nanolett.9b02196] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/29/2019] [Revised: 07/22/2019] [Indexed: 06/10/2023]
Abstract
Rhombohedral graphite features peculiar electronic properties, including persistence of low-energy surface bands of a topological nature. Here, we study the contribution of electron-hole excitations toward inelastic light scattering in thin films of rhombohedral graphite. We show that, in contrast to the featureless electron-hole contribution toward Raman spectrum of graphitic films with Bernal stacking, the inelastic light scattering accompanied by electron-hole excitations in crystals with rhombohedral stacking produces distinct features in the Raman signal which can be used both to identify the stacking and to determine the number of layers in the film.
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Affiliation(s)
- Aitor García-Ruiz
- Department
of Physics, University of Bath, Claverton Down, Bath BA2 3FL, United Kingdom
| | - Sergey Slizovskiy
- National
Graphene Institute, University of Manchester, Booth Street E, Manchester M13 9PL, United
Kingdom
- Department
of Physics and Astronomy, University of
Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
| | - Marcin Mucha-Kruczyński
- Department
of Physics, University of Bath, Claverton Down, Bath BA2 3FL, United Kingdom
- Centre
for Nanoscience and Nanotechnology, University
of Bath, Claverton Down, Bath BA2 3FL, United Kingdom
| | - Vladimir I. Fal’ko
- National
Graphene Institute, University of Manchester, Booth Street E, Manchester M13 9PL, United
Kingdom
- Department
of Physics and Astronomy, University of
Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
- Henry
Royce Institute, Manchester M13 9PL, United Kingdom
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23
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Zeng Y, Li JIA, Dietrich SA, Ghosh OM, Watanabe K, Taniguchi T, Hone J, Dean CR. High-Quality Magnetotransport in Graphene Using the Edge-Free Corbino Geometry. PHYSICAL REVIEW LETTERS 2019; 122:137701. [PMID: 31012609 DOI: 10.1103/physrevlett.122.137701] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2018] [Indexed: 06/09/2023]
Abstract
We report fabrication of graphene devices in a Corbino geometry consisting of concentric circular electrodes with no physical edge connecting the inner and outer electrodes. High device mobility is realized using boron nitride encapsulation together with a dual-graphite gate structure. Bulk conductance measurement in the quantum Hall effect (QHE) regime outperforms previously reported Hall bar measurements, with improved resolution observed for both the integer and fractional QHE states. We identify apparent phase transitions in the fractional sequence in both the lowest and first excited Landau levels (LLs) and observe features consistent with electron solid phases in higher LLs.
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Affiliation(s)
- Y Zeng
- Department of Physics, Columbia University, New York, New York 10025, USA
| | - J I A Li
- Department of Physics, Columbia University, New York, New York 10025, USA
| | - S A Dietrich
- Department of Physics, Columbia University, New York, New York 10025, USA
| | - O M Ghosh
- Department of Physics, Columbia University, New York, New York 10025, USA
| | - K Watanabe
- National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - T Taniguchi
- National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - J Hone
- Department of Mechanical Engineering, Columbia University, New York, New York 10025, USA
| | - C R Dean
- Department of Physics, Columbia University, New York, New York 10025, USA
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24
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Lee CH, Ho WW, Yang B, Gong J, Papić Z. Floquet Mechanism for Non-Abelian Fractional Quantum Hall States. PHYSICAL REVIEW LETTERS 2018; 121:237401. [PMID: 30576179 DOI: 10.1103/physrevlett.121.237401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2018] [Revised: 09/17/2018] [Indexed: 06/09/2023]
Abstract
Three-body correlations, which arise between spin-polarized electrons in the first excited Landau level, are believed to play a key role in the emergence of enigmatic non-Abelian fractional quantum Hall (FQH) effects. Inspired by recent advances in Floquet engineering, we investigate periodic driving of anisotropic two-body interactions as a route for controllably creating and tuning effective three-body interactions in the FQH regime. We develop an analytic formalism to describe this Floquet-FQH protocol, which is distinct from previous approaches that instead focus on band structure engineering via modulation of single-particle hopping terms. By systematically analyzing the resulting interactions using generalized pseudopotentials, we show that our Floquet-FQH approach leads to repulsive as well as attractive three-body interactions that are highly tunable and support a variety of non-Abelian multicomponent FQH states. Finally, we propose an implementation of the protocol in optically dressed ultracold polar molecules with modulated Rabi frequencies.
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Affiliation(s)
- Ching Hua Lee
- Institute of High Performance Computing, A*STAR, Singapore, 138632
- Department of Physics, National University of Singapore, Singapore, 117542
| | - Wen Wei Ho
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Bo Yang
- Institute of High Performance Computing, A*STAR, Singapore, 138632
- Division of Physics and Applied Physics, Nanyang Technological University, Singapore, 637371
| | - Jiangbin Gong
- Department of Physics, National University of Singapore, Singapore, 117542
| | - Zlatko Papić
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
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25
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Polshyn H, Zhou H, Spanton EM, Taniguchi T, Watanabe K, Young AF. Quantitative Transport Measurements of Fractional Quantum Hall Energy Gaps in Edgeless Graphene Devices. PHYSICAL REVIEW LETTERS 2018; 121:226801. [PMID: 30547606 DOI: 10.1103/physrevlett.121.226801] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2018] [Revised: 10/19/2018] [Indexed: 06/09/2023]
Abstract
Owing to their wide tunability, multiple internal degrees of freedom, and low disorder, graphene heterostructures are emerging as a promising experimental platform for fractional quantum Hall (FQH) studies. Here, we report FQH thermal activation gap measurements in dual graphite-gated monolayer graphene devices fabricated in an edgeless Corbino geometry. In devices with substrate-induced sublattice splitting, we find a tunable crossover between single- and multicomponent FQH states in the zero energy Landau level. Activation gaps in the single-component regime show excellent agreement with numerical calculations using a single broadening parameter Γ≈7.2 K. In the first excited Landau level, in contrast, FQH gaps are strongly influenced by Landau level mixing, and we observe an unexpected valley-ordered state at integer filling ν=-4.
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Affiliation(s)
- H Polshyn
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - H Zhou
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - E M Spanton
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - T Taniguchi
- Advanced Materials Laboratory, National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan
| | - K Watanabe
- Advanced Materials Laboratory, National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan
| | - A F Young
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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26
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Nam Y, Ki DK, Soler-Delgado D, Morpurgo AF. A family of finite-temperature electronic phase transitions in graphene multilayers. Science 2018; 362:324-328. [PMID: 30337406 DOI: 10.1126/science.aar6855] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2017] [Accepted: 08/28/2018] [Indexed: 12/24/2022]
Abstract
Suspended Bernal-stacked graphene multilayers up to an unexpectedly large thickness exhibit a broken-symmetry ground state whose origin remains to be understood. We show that a finite-temperature second-order phase transition occurs in multilayers whose critical temperature (T c) increases from 12 kelvins (K) in bilayers to 100 K in heptalayers. A comparison of the data with a phenomenological model inspired by a mean-field approach suggests that the transition is associated with the appearance of a self-consistent valley- and spin-dependent staggered potential that changes sign from one layer to the next, appearing at T c and increasing upon cooling. The systematic evolution with thickness of several measured quantities imposes constraints on any microscopic theory aiming to analyze the nature of electronic correlations in this system.
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Affiliation(s)
- Youngwoo Nam
- Department of Quantum Matter Physics (DQMP) and Group of Applied Physics (GAP), University of Geneva, 24 Quai Ernest-Ansermet, CH1211 Genéve 4, Switzerland.,Department of Physics, Gyeongsang National University, Jinju-daero 501, Jinju-si, South Korea
| | - Dong-Keun Ki
- Department of Quantum Matter Physics (DQMP) and Group of Applied Physics (GAP), University of Geneva, 24 Quai Ernest-Ansermet, CH1211 Genéve 4, Switzerland.,Department of Physics, The University of Hong Kong, Hong Kong, China
| | - David Soler-Delgado
- Department of Quantum Matter Physics (DQMP) and Group of Applied Physics (GAP), University of Geneva, 24 Quai Ernest-Ansermet, CH1211 Genéve 4, Switzerland
| | - Alberto F Morpurgo
- Department of Quantum Matter Physics (DQMP) and Group of Applied Physics (GAP), University of Geneva, 24 Quai Ernest-Ansermet, CH1211 Genéve 4, Switzerland.
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27
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Łydżba P, Jacak J. Many-body wave functions for correlated systems in magnetic fields: Monte Carlo simulations in the lowest Landau level. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:365601. [PMID: 30051880 DOI: 10.1088/1361-648x/aad653] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We put forward possible wave functions for quantum Hall states in the lowest Landau level. These were deduced from the topological approach based on the relation between braid groups and the quantum statistics, as well as the commensurability condition unavoidable for collective states in magnetic fields. In this paper we demonstrate that the [Formula: see text]-field imposes restrictions on braid trajectories (i.e. elements of the full braid group). This results in the appearance of cyclotron subgroups, instead of the full braid group, for certain filling factors. The fermion representation of cyclotron subgroups defines transformations of wave functions in the quantum Hall regime. Hence, it sets quantum statistics (transformations of [Formula: see text] under exchanges of arguments), which is unavoidable for collective states (in compliance with the framework of Feynman's path integrals). Finally, the topological approach allows to define the hierarchy of fillings in the lowest Landau level, which agree with the hierarchy observed in quantum Hall devices (i.e. in transport measurements). The symmetry of a many-body wave function (i.e. quantum statistics) is always determined by a 1D unitary representation of the system's braid group. Using this topologically-originated property, we demonstrate that many-body wave functions for selected fillings of the lowest Landau level may not be purely antisymmetric. Only systems composed of fermions are investigated. Additionally, we present Monte Carlo calculations in a disc geometry, which remain in a nice agreement with predictions of exact diagonalizations (expected values of potential energy and pair distribution functions are presented). No boundary potential is assumed.
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Affiliation(s)
- P Łydżba
- Department of Quantum Technologies, Faculty of Fundamental Problems of Technology, Wroclaw University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370, Wrocław, Poland
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28
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Falson J, Tabrea D, Zhang D, Sodemann I, Kozuka Y, Tsukazaki A, Kawasaki M, von Klitzing K, Smet JH. A cascade of phase transitions in an orbitally mixed half-filled Landau level. SCIENCE ADVANCES 2018; 4:eaat8742. [PMID: 30225370 PMCID: PMC6140610 DOI: 10.1126/sciadv.aat8742] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/16/2018] [Accepted: 08/02/2018] [Indexed: 06/08/2023]
Abstract
Half-filled Landau levels host an emergent Fermi liquid that displays instability toward pairing, culminating in a gapped even-denominator fractional quantum Hall ground state. While this pairing may be probed by tuning the polarization of carriers in competing orbital and spin degrees of freedom, sufficiently high quality platforms offering such tunability remain few. We explore the ground states at filling factor ν = 5/2 in ZnO-based two-dimensional electron systems through a forced intersection of opposing spin branches of Landau levels taking quantum numbers N = 1 and 0. We reveal a cascade of phases with distinct magnetotransport features including a gapped phase polarized in the N = 1 level and a compressible phase in N = 0, along with an unexpected Fermi liquid, a second gapped, and a strongly anisotropic nematic-like phase at intermediate polarizations when the levels are near degeneracy. The phase diagram is produced by analyzing the proximity of the intersecting levels and highlights the excellent reproducibility and controllability that ZnO offers for exploring exotic fractionalized electronic phases.
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Affiliation(s)
- Joseph Falson
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
| | - Daniela Tabrea
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
| | - Ding Zhang
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
| | - Inti Sodemann
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
| | - Yusuke Kozuka
- Department of Applied Physics and Quantum-Phase Electronics Center, University of Tokyo, Tokyo 113-8656, Japan
- Japan Science and Technology Agency, Precursory Research for Embryonic Science and Technology, Kawaguchi, Saitama 332-0012, Japan
| | - Atsushi Tsukazaki
- Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
| | - Masashi Kawasaki
- Department of Applied Physics and Quantum-Phase Electronics Center, University of Tokyo, Tokyo 113-8656, Japan
- RIKEN Center for Emergent Matter Science, Wako 351-0198, Japan
| | - Klaus von Klitzing
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
| | - Jurgen H. Smet
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
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Barkeshli M, Nayak C, Papić Z, Young A, Zaletel M. Topological Exciton Fermi Surfaces in Two-Component Fractional Quantized Hall Insulators. PHYSICAL REVIEW LETTERS 2018; 121:026603. [PMID: 30085706 DOI: 10.1103/physrevlett.121.026603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2016] [Indexed: 06/08/2023]
Abstract
A wide variety of two-dimensional electron systems allow for independent control of the total and relative charge density of two-component fractional quantum Hall (FQH) states. In particular, a recent experiment on bilayer graphene (BLG) observed a continuous transition between a compressible and incompressible phase at total filling ν_{T}=1/2 as charge is transferred between the layers, with the remarkable property that the incompressible phase has a finite interlayer polarizability. We argue that this occurs because the topological order of ν_{T}=1/2 systems supports a novel type of interlayer exciton that carries Fermi statistics. If the fermionic excitons are lower in energy than the conventional bosonic excitons (i.e., electron-hole pairs), they can form an emergent neutral Fermi surface, providing a possible explanation of an incompressible yet polarizable state at ν_{T}=1/2. We perform exact diagonalization studies that demonstrate that fermionic excitons are indeed lower in energy than bosonic excitons. This suggests that a "topological exciton metal" hidden inside a FQH insulator may have been realized experimentally in BLG. We discuss several detection schemes by which the topological exciton metal can be experimentally probed.
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Affiliation(s)
- Maissam Barkeshli
- Department of Physics, Condensed Matter Theory Center, University of Maryland, College Park, Maryland 20742, USA
- Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - Chetan Nayak
- Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA
| | - Zlatko Papić
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Andrea Young
- Department of Physics, University of California, Santa Barbara, California 93106-6105, USA
| | - Michael Zaletel
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
- Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA
- Department of Physics, Princeton University, Princeton, New Jersey 08540, USA
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30
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Falson J, Kawasaki M. A review of the quantum Hall effects in MgZnO/ZnO heterostructures. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:056501. [PMID: 29353814 DOI: 10.1088/1361-6633/aaa978] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
This review visits recent experimental efforts on high mobility two-dimensional electron systems (2DES) hosted at the Mg x Zn[Formula: see text]O/ZnO heterointerface. We begin with the growth of these samples, and highlight the key characteristics of ozone-assisted molecular beam epitaxy required for their production. The transport characteristics of these structures are found to rival that of traditional semiconductor material systems, as signified by the high electron mobility ([Formula: see text] cm2 Vs-1) and rich quantum Hall features. Owing to a large effective mass and small dielectric constant, interaction effects are an order of magnitude stronger in comparison with the well studied GaAs-based 2DES. The strong correlation physics results in robust Fermi-liquid renormalization of the effective mass and spin susceptibility of carriers, which in turn dictates the parameter space for the quantum Hall effect. Finally, we explore the quantum Hall effect with a particular emphasis on the spin degree of freedom of carriers, and how their large spin splitting allows control of the ground states encountered at ultra-low temperatures within the fractional quantum Hall regime. We discuss in detail the physics of even-denominator fractional quantum Hall states, whose observation and underlying character remain elusive and exotic.
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Affiliation(s)
- Joseph Falson
- Max-Planck-Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
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31
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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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32
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Li J, Tupikov Y, Watanabe K, Taniguchi T, Zhu J. Effective Landau Level Diagram of Bilayer Graphene. PHYSICAL REVIEW LETTERS 2018; 120:047701. [PMID: 29437431 DOI: 10.1103/physrevlett.120.047701] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2017] [Revised: 11/18/2017] [Indexed: 06/08/2023]
Abstract
The E=0 octet of bilayer graphene in the filling factor range of -4<ν<4 is a fertile playground for many-body phenomena, yet a Landau level diagram is missing due to strong interactions and competing quantum degrees of freedom. We combine measurements and modeling to construct an empirical and quantitative spectrum. The single-particlelike diagram incorporates interaction effects effectively and provides a unified framework to understand the occupation sequence, gap energies, and phase transitions observed in the octet. It serves as a new starting point for more sophisticated calculations and experiments.
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Affiliation(s)
- Jing Li
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Yevhen Tupikov
- 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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33
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Zhu Z, Fu L, Sheng DN. Numerical Study of Quantum Hall Bilayers at Total Filling ν_{T}=1: A New Phase at Intermediate Layer Distances. PHYSICAL REVIEW LETTERS 2017; 119:177601. [PMID: 29219462 DOI: 10.1103/physrevlett.119.177601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2017] [Indexed: 06/07/2023]
Abstract
We study the phase diagram of quantum Hall bilayer systems with total filing ν_{T}=1/2+1/2 of the lowest Landau level as a function of layer distances d. Based on numerical exact diagonalization calculations, we obtain three distinct phases, including an exciton superfluid phase with spontaneous interlayer coherence at small d, a composite Fermi liquid at large d, and an intermediate phase for 1.1<d/l_{B}<1.8 (l_{B} is the magnetic length). The transition from the exciton superfluid to the intermediate phase is identified by (i) a dramatic change in the Berry curvature of the ground state under twisted boundary conditions on the two layers and (ii) an energy level crossing of the first excited state. The transition from the intermediate phase to the composite Fermi liquid is identified by the vanishing of the exciton superfluid stiffness. Furthermore, from our finite-size study, the energy cost of transferring one electron between the layers shows an even-odd effect and possibly extrapolates to a finite value in the thermodynamic limit, indicating the enhanced intralayer correlation. Our identification of an intermediate phase and its distinctive features shed new light on the theoretical understanding of the quantum Hall bilayer system at total filling ν_{T}=1.
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Affiliation(s)
- Zheng Zhu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - D N Sheng
- Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
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34
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Li JIA, Tan C, Chen S, Zeng Y, Taniguchi T, Watanabe K, Hone J, Dean CR. Even-denominator fractional quantum Hall states in bilayer graphene. Science 2017; 358:648-652. [DOI: 10.1126/science.aao2521] [Citation(s) in RCA: 65] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2017] [Accepted: 09/25/2017] [Indexed: 12/13/2022]
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35
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Zibrov AA, Kometter C, Zhou H, Spanton EM, Taniguchi T, Watanabe K, Zaletel MP, Young AF. Tunable interacting composite fermion phases in a half-filled bilayer-graphene Landau level. Nature 2017; 549:360-364. [DOI: 10.1038/nature23893] [Citation(s) in RCA: 128] [Impact Index Per Article: 18.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2016] [Accepted: 07/26/2017] [Indexed: 11/09/2022]
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36
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Jacak JE. Unconventional fractional quantum Hall effect in bilayer graphene. Sci Rep 2017; 7:8720. [PMID: 28821795 PMCID: PMC5562899 DOI: 10.1038/s41598-017-09166-5] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2017] [Accepted: 07/24/2017] [Indexed: 12/05/2022] Open
Abstract
Recent experimental progress in Hall measurements in bilayer graphene in the so-called open-face configuration of boron nitride encapsulated samples, together with the earlier technique of suspended samples, allows for precise observation of the fractional quantum Hall effect (FQHE) in all 4 subbands of the Lowest Landau level (with n = 0 and n = 1) and in the next LL subbands (with n = 2) in the bilayer system. Many newly observed FQHE features do not agree with a conventional model of composite fermions and reveal a different hierarchy in comparison to monolayer graphene or GaAs 2DEG. We explain the peculiarity of the FQHE hierarchy in the bilayer system in the framework of a topological approach, which includes the composite fermion model as its special case. Inclusion of a topological effect caused by the hopping of electrons between the two sheets in the bilayer system allowed for an explanation of the FQHE hierarchy in the graphene bilayer in satisfactory accordance with the experimental observations.
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Affiliation(s)
- Janusz Edward Jacak
- Department of Quantum Technologies, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, Wyb. Wyspianskiego 27, 50-370, Wrocław, Poland.
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37
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Isobe H, Fu L. Interlayer Pairing Symmetry of Composite Fermions in Quantum Hall Bilayers. PHYSICAL REVIEW LETTERS 2017; 118:166401. [PMID: 28474921 DOI: 10.1103/physrevlett.118.166401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2016] [Indexed: 06/07/2023]
Abstract
We study the pairing symmetry of the interlayer paired state of composite fermions in quantum Hall bilayers. Based on the Halperin-Lee-Read (HLR) theory, the effect of the long-range Coulomb interaction and the internal Chern-Simons gauge fluctuation is analyzed with the random-phase approximation beyond the leading order contribution in small momentum expansion, and we observe that the interlayer paired states with a relative angular momentum l=+1 are energetically favored for filling ν=1/2+1/2 and 1/4+1/4. The degeneracy between states with ±l is lifted by the interlayer density-current interaction arising from the interplay of the long-range Coulomb interaction and the Chern-Simons term in the HLR theory.
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Affiliation(s)
- Hiroki Isobe
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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38
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Robust fractional quantum Hall effect in the N=2 Landau level in bilayer graphene. Nat Commun 2016; 7:13908. [PMID: 28000663 PMCID: PMC5187585 DOI: 10.1038/ncomms13908] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2016] [Accepted: 11/11/2016] [Indexed: 11/09/2022] Open
Abstract
The fractional quantum Hall effect is a canonical example of electron-electron interactions producing new ground states in many-body systems. Most fractional quantum Hall studies have focussed on the lowest Landau level, whose fractional states are successfully explained by the composite fermion model. In the widely studied GaAs-based system, the composite fermion picture is thought to become unstable for the N≥2 Landau level, where competing many-body phases have been observed. Here we report magneto-resistance measurements of fractional quantum Hall states in the N=2 Landau level (filling factors 4<|ν|<8) in bilayer graphene. In contrast with recent observations of particle-hole asymmetry in the N=0/N=1 Landau levels of bilayer graphene, the fractional quantum Hall states we observe in the N=2 Landau level obey particle-hole symmetry within the fully symmetry-broken Landau level. Possible alternative ground states other than the composite fermions are discussed.
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39
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Broken-Symmetry Quantum Hall States in Twisted Bilayer Graphene. Sci Rep 2016; 6:38068. [PMID: 27905496 PMCID: PMC5131475 DOI: 10.1038/srep38068] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2016] [Accepted: 11/04/2016] [Indexed: 01/29/2023] Open
Abstract
Twisted bilayer graphene offers a unique bilayer two-dimensional-electron system where the layer separation is only in sub-nanometer scale. Unlike Bernal-stacked bilayer, the layer degree of freedom is disentangled from spin and valley, providing eight-fold degeneracy in the low energy states. We have investigated broken-symmetry quantum Hall (QH) states and their transitions due to the interplay of the relative strength of valley, spin and layer polarizations in twisted bilayer graphene. The energy gaps of the broken-symmetry QH states show an electron-hole asymmetric behaviour, and their dependence on the induced displacement field are opposite between even and odd filling factor states. These results strongly suggest that the QH states with broken valley and spin symmetries for individual layer become hybridized via interlayer tunnelling, and the hierarchy of the QH states is sensitive to both magnetic field and displacement field due to charge imbalance between layers.
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40
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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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41
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Zucker PT, Feldman DE. Stabilization of the Particle-Hole Pfaffian Order by Landau-Level Mixing and Impurities That Break Particle-Hole Symmetry. PHYSICAL REVIEW LETTERS 2016; 117:096802. [PMID: 27610872 DOI: 10.1103/physrevlett.117.096802] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2016] [Indexed: 06/06/2023]
Abstract
Numerical results suggest that the quantum Hall effect at ν=5/2 is described by the Pfaffian or anti-Pfaffian state in the absence of disorder and Landau-level mixing. Those states are incompatible with the observed transport properties of GaAs heterostructures, where disorder and Landau-level mixing are strong. We show that the recent proposal of a particle-hole (PH)-Pfaffian topological order by Son is consistent with all experiments. The absence of particle-hole symmetry at ν=5/2 is not an obstacle to the existence of the PH-Pfaffian order since the order is robust to symmetry breaking.
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Affiliation(s)
- P T Zucker
- Department of Physics, Brown University, Providence, Rhode Island 02912, USA
| | - D E Feldman
- Department of Physics, Brown University, Providence, Rhode Island 02912, USA
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42
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Kim Y, Herlinger P, Moon P, Koshino M, Taniguchi T, Watanabe K, Smet JH. Charge Inversion and Topological Phase Transition at a Twist Angle Induced van Hove Singularity of Bilayer Graphene. NANO LETTERS 2016; 16:5053-5059. [PMID: 27387484 DOI: 10.1021/acs.nanolett.6b01906] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
van Hove singularities (VHS's) in the density of states play an outstanding and diverse role for the electronic and thermodynamic properties of crystalline solids. At the critical point the Fermi surface connectivity changes, and topological properties undergo a transition. Opportunities to systematically pass a VHS at the turn of a voltage knob and study its diverse impact are however rare. With the advent of van der Waals heterostructures, control over the atomic registry of neighboring graphene layers offers an unprecedented tool to generate a low energy VHS easily accessible with conventional gating. Here we have addressed magnetotransport when the chemical potential crosses the twist angle induced VHS in twisted bilayer graphene. A topological phase transition is experimentally disclosed in the abrupt conversion of electrons to holes or vice versa, a loss of a nonzero Berry phase and distinct sequences of integer quantum Hall states above and below the singularity.
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Affiliation(s)
- Youngwook Kim
- Max-Planck-Institut für Festköperforschung , 70569 Stuttgart, Germany
| | - Patrick Herlinger
- Max-Planck-Institut für Festköperforschung , 70569 Stuttgart, Germany
| | - Pilkyung Moon
- New York University , Shanghai 200120, China
- NYU-ECNU Institute of Physics at NYU Shanghai , Shanghai 200062, China
| | - Mikito Koshino
- Department of Physics, Tohoku University , Sendai 980-8578, Japan
| | - Takashi Taniguchi
- National Institute for Materials Science , 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Kenji Watanabe
- National Institute for Materials Science , 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Jurgen H Smet
- Max-Planck-Institut für Festköperforschung , 70569 Stuttgart, Germany
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43
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Jacak J, Jacak L. Unconventional fractional quantum Hall effect in monolayer and bilayer graphene. SCIENCE AND TECHNOLOGY OF ADVANCED MATERIALS 2016; 17:149-165. [PMID: 27877866 PMCID: PMC5102017 DOI: 10.1080/14686996.2016.1145531] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/14/2015] [Revised: 12/20/2015] [Accepted: 12/22/2015] [Indexed: 06/06/2023]
Abstract
The commensurability condition is applied to determine the hierarchy of fractional fillings of Landau levels in monolayer and in bilayer graphene. The filling rates for fractional quantum Hall effect (FQHE) in graphene are found in the first three Landau levels in one-to-one agreement with the experimental data. The presence of even denominator filling fractions in the hierarchy for FQHE in bilayer graphene is explained. Experimentally observed hierarchy of FQHE in the first and second Landau levels in monolayer graphene and in the zeroth Landau level in bilayer graphene is beyond the conventional composite fermion interpretation but fits to the presented nonlocal topology commensurability condition.
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Affiliation(s)
- Janusz Jacak
- Institute of Physics, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370, Wrocław, Poland
| | - Lucjan Jacak
- Institute of Physics, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370, Wrocław, Poland
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44
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Shi Y, Lee Y, Che S, Pi Z, Espiritu T, Stepanov P, Smirnov D, Lau CN, Zhang F. Energy Gaps and Layer Polarization of Integer and Fractional Quantum Hall States in Bilayer Graphene. PHYSICAL REVIEW LETTERS 2016; 116:056601. [PMID: 26894724 DOI: 10.1103/physrevlett.116.056601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2015] [Indexed: 06/05/2023]
Abstract
Owing to the spin, valley, and orbital symmetries, the lowest Landau level in bilayer graphene exhibits multicomponent quantum Hall ferromagnetism. Using transport spectroscopy, we investigate the energy gaps of integer and fractional quantum Hall (QH) states in bilayer graphene with controlled layer polarization. The state at filling factor ν=1 has two distinct phases: a layer polarized state that has a larger energy gap and is stabilized by high electric field, and a hitherto unobserved interlayer coherent state with a smaller gap that is stabilized by large magnetic field. In contrast, the ν=2/3 quantum Hall state and a feature at ν=1/2 are only resolved at finite electric field and large magnetic field. These results underscore the importance of controlling layer polarization in understanding the competing symmetries in the unusual QH system of BLG.
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Affiliation(s)
- Yanmeng Shi
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 91765, USA
| | - Yongjin Lee
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 91765, USA
| | - Shi Che
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 91765, USA
| | - Ziqi Pi
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 91765, USA
| | - Timothy Espiritu
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 91765, USA
| | - Petr Stepanov
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 91765, USA
| | - Dmitry Smirnov
- National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
| | - Chun Ning Lau
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 91765, USA
| | - Fan Zhang
- Department of Physics, University of Texas at Dallas, Richardson, Texas 75080, USA
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45
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Jacak J, Jacak L. Explanation of [Formula: see text] fractional quantum Hall state in bilayer graphene. Proc Math Phys Eng Sci 2016; 472:20150330. [PMID: 27118883 PMCID: PMC4841648 DOI: 10.1098/rspa.2015.0330] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2015] [Accepted: 01/07/2016] [Indexed: 11/12/2022] Open
Abstract
The commensurability condition is applied to determine the hierarchy of fractional filling of Landau levels for fractional quantum Hall effect (FQHE) in monolayer and bilayer graphene. Good agreement with experimental data is achieved. The presence of even-denominator filling fractions in the hierarchy of the FQHE in bilayer graphene is explained, including the state at [Formula: see text].
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Affiliation(s)
- J. Jacak
- Department Quantum Technologies, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
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Kim Y, Lee DS, Jung S, Skákalová V, Taniguchi T, Watanabe K, Kim JS, Smet JH. Fractional Quantum Hall States in Bilayer Graphene Probed by Transconductance Fluctuations. NANO LETTERS 2015; 15:7445-7451. [PMID: 26479836 DOI: 10.1021/acs.nanolett.5b02876] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We have investigated fractional quantum Hall (QH) states in Bernal-stacked bilayer graphene using transconductance fluctuation measurements. A variety of odd-denominator fractional QH states with νQH → νQH + 2 symmetry, as previously reported, are observed. However, surprising is that also particle-hole symmetric states are clearly resolved in the same measurement set. We attribute their emergence to the reversal of orbital states in the octet level scheme induced by a strong local charge imbalance, which can be captured by the transconductance fluctuations. Also the even-denominator fractional QH state at filling -1/2 is observed. However, contrary to a previous study on a suspended graphene layer [ Ki et al. Nano Lett. 2014, 14 , 2135 ], the particle-hole symmetric state at filling 1/2 is detected as well. These observations suggest that the stability of both odd and even denominator fractional QH states is very sensitive to local transverse electric fields in bilayer graphene.
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Affiliation(s)
- Youngwook Kim
- Department of Physics, Pohang University of Science and Technology , Pohang 790-784, Korea
- Max-Planck-Institut für Festköperforschung , 70569 Stuttgart, Germany
| | - Dong Su Lee
- KIST Jeonbuk Institute of Advanced Composite Materials , Jeonbuk 565-905, Korea
| | - Suyong Jung
- Center for Quantum Measurement Science, Korea Research Institute of Standards and Science , Daejeon, 305-340, Korea
| | - Viera Skákalová
- Faculty of Physics, University of Vienna , Boltzmanngasse 5, 1090 Vienna, Austria
- STU Center for Nanodiagnostics , Vazovova 5, 812 43 Bratislava, Slovakia
| | - T Taniguchi
- Advanced Materials Laboratory, National Institute for Materials Science , 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - K Watanabe
- Advanced Materials Laboratory, National Institute for Materials Science , 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Jun Sung Kim
- Department of Physics, Pohang University of Science and Technology , Pohang 790-784, Korea
| | - Jurgen H Smet
- Max-Planck-Institut für Festköperforschung , 70569 Stuttgart, Germany
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Insulating state in tetralayers reveals an even-odd interaction effect in multilayer graphene. Nat Commun 2015; 6:6419. [PMID: 25732058 PMCID: PMC4366515 DOI: 10.1038/ncomms7419] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2014] [Accepted: 01/27/2015] [Indexed: 11/08/2022] Open
Abstract
Close to charge neutrality, the electronic properties of graphene and its multilayers are sensitive to electron-electron interactions. In bilayers, for instance, interactions are predicted to open a gap between valence and conduction bands, turning the system into an insulator. In mono and (Bernal-stacked) trilayers, which remain conducting at low temperature, interactions do not have equally drastic consequences. It is expected that interaction effects become weaker for thicker multilayers, whose behaviour should converge to that of graphite. Here we show that this expectation does not correspond to reality by revealing the occurrence of an insulating state close to charge neutrality in Bernal-stacked tetralayer graphene. The phenomenology-incompatible with the behaviour expected from the single-particle band structure-resembles that observed in bilayers, but the insulating state in tetralayers is visible at higher temperature. We explain our findings, and the systematic even-odd effect of interactions in Bernal-stacked layers of different thickness that emerges from experiments, in terms of a generalization of the interaction-driven, symmetry-broken states proposed for bilayers.
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48
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Lin X, Du R, Xie X. Recent experimental progress of fractional quantum Hall effect: 5/2 filling state and graphene. Natl Sci Rev 2014. [DOI: 10.1093/nsr/nwu071] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
Abstract
The phenomenon of fractional quantum Hall effect (FQHE) was first experimentally observed 33 years ago. FQHE involves strong Coulomb interactions and correlations among the electrons, which leads to quasiparticles with fractional elementary charge. Three decades later, the field of FQHE is still active with new discoveries and new technical developments. A significant portion of attention in FQHE has been dedicated to filling factor 5/2 state, for its unusual even denominator and possible application in topological quantum computation. Traditionally, FQHE has been observed in high-mobility GaAs heterostructure, but new materials such as graphene also open up a new area for FQHE. This review focuses on recent progress of FQHE at 5/2 state and FQHE in graphene.
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Affiliation(s)
- Xi Lin
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Ruirui Du
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Xincheng Xie
- International Center for Quantum Materials, Peking University, Beijing 100871, China
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Peterson MR, Nayak C. Effects of Landau level mixing on the fractional quantum Hall effect in monolayer graphene. PHYSICAL REVIEW LETTERS 2014; 113:086401. [PMID: 25192110 DOI: 10.1103/physrevlett.113.086401] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2014] [Indexed: 06/03/2023]
Abstract
We report results of exact diagonalization studies of the spin- and valley-polarized fractional quantum Hall effect in the N = 0 and N = 1 Landau levels in graphene. We use an effective model that incorporates Landau level mixing to lowest order in the parameter κ = ((e(2)/εℓ)/(ħv(F)/ℓ)) = (e(2)/εv(F)ħ), which is magnetic field independent and can only be varied through the choice of substrate. We find Landau level mixing effects are negligible in the N = 0 Landau level for κ ≲ 2. In fact, the lowest Landau level projected Coulomb Hamiltonian is a better approximation to the real Hamiltonian for graphene than it is for semiconductor based quantum wells. Consequently, the principal fractional quantum Hall states are expected in the N = 0 Landau level over this range of κ. In the N = 1 Landau level, fractional quantum Hall states are expected for a smaller range of κ and Landau level mixing strongly breaks particle-hole symmetry, producing qualitatively different results compared to the N = 0 Landau level. At half filling of the N = 1 Landau level, we predict the anti-Pfaffian state will occur for κ ∼ 0.25-0.75.
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Affiliation(s)
- Michael R Peterson
- Department of Physics & Astronomy, California State University Long Beach, Long Beach, California 90840, USA
| | - Chetan Nayak
- Department of Physics, University of California, Santa Barbara, California 93106, USA and Microsoft Research, Station Q, Elings Hall, University of California, Santa Barbara, California 93106, USA
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Kou A, Feldman BE, Levin AJ, Halperin BI, Watanabe K, Taniguchi T, Yacoby A. Electron-hole asymmetric integer and fractional quantum Hall effect in bilayer graphene. Science 2014; 345:55-7. [DOI: 10.1126/science.1250270] [Citation(s) in RCA: 84] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- A. Kou
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Department of Applied Physics, Yale University, New Haven, CT 06520, USA
| | - B. E. Feldman
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A. J. Levin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - B. I. Halperin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - K. Watanabe
- National Institute for Materials Science, Tsukuba, Japan
| | - T. Taniguchi
- National Institute for Materials Science, Tsukuba, Japan
| | - A. Yacoby
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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