1
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Kumar R, Srivastav SK, Roy U, Park J, Spånslätt C, Watanabe K, Taniguchi T, Gefen Y, Mirlin AD, Das A. Electrical noise spectroscopy of magnons in a quantum Hall ferromagnet. Nat Commun 2024; 15:4998. [PMID: 38866830 PMCID: PMC11169481 DOI: 10.1038/s41467-024-49446-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2023] [Accepted: 06/05/2024] [Indexed: 06/14/2024] Open
Abstract
Collective spin-wave excitations, magnons, are promising quasi-particles for next-generation spintronics devices, including platforms for information transfer. In a quantum Hall ferromagnets, detection of these charge-neutral excitations relies on the conversion of magnons into electrical signals in the form of excess electrons and holes, but if the excess electron and holes are equal, detecting an electrical signal is challenging. In this work, we overcome this shortcoming by measuring the electrical noise generated by magnons. We use the symmetry-broken quantum Hall ferromagnet of the zeroth Landau level in graphene to launch magnons. Absorption of these magnons creates excess noise above the Zeeman energy and remains finite even when the average electrical signal is zero. Moreover, we formulate a theoretical model in which the noise is produced by equilibration between edge channels and propagating magnons. Our model also allows us to pinpoint the regime of ballistic magnon transport in our device.
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Affiliation(s)
- Ravi Kumar
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India
| | | | - Ujjal Roy
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India
| | - Jinhong Park
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76021, Karlsruhe, Germany
- Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76128, Karlsruhe, Germany
| | - Christian Spånslätt
- Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, S-412 96, Göteborg, Sweden
| | - K Watanabe
- National Institute of Material Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - T Taniguchi
- National Institute of Material Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Yuval Gefen
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
| | - Alexander D Mirlin
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76021, Karlsruhe, Germany
- Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76128, Karlsruhe, Germany
| | - Anindya Das
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India.
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2
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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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3
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Interplay between topological valley and quantum Hall edge transport. Nat Commun 2022; 13:4187. [PMID: 35858959 PMCID: PMC9300606 DOI: 10.1038/s41467-022-31680-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2021] [Accepted: 06/21/2022] [Indexed: 11/08/2022] Open
Abstract
An established way of realising topologically protected states in a two-dimensional electron gas is by applying a perpendicular magnetic field thus creating quantum Hall edge channels. In electrostatically gapped bilayer graphene intriguingly, even in the absence of a magnetic field, topologically protected electronic states can emerge at naturally occurring stacking domain walls. While individually both types of topologically protected states have been investigated, their intriguing interplay remains poorly understood. Here, we focus on the interplay between topological domain wall states and quantum Hall edge transport within the eight-fold degenerate zeroth Landau level of high-quality suspended bilayer graphene. We find that the two-terminal conductance remains approximately constant for low magnetic fields throughout the distinct quantum Hall states since the conduction channels are traded between domain wall and device edges. For high magnetic fields, however, we observe evidence of transport suppression at the domain wall, which can be attributed to the emergence of spectral minigaps. This indicates that stacking domain walls potentially do not correspond to a topological domain wall in the order parameter.
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4
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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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5
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Tang F, Wang P, He M, Isobe M, Gu G, Li Q, Zhang L, Smet JH. Two-Dimensional Quantum Hall Effect and Zero Energy State in Few-Layer ZrTe 5. NANO LETTERS 2021; 21:5998-6004. [PMID: 34251198 PMCID: PMC8397394 DOI: 10.1021/acs.nanolett.1c00958] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2021] [Revised: 06/30/2021] [Indexed: 05/30/2023]
Abstract
Topological matter plays a central role in today's condensed matter research. Zirconium pentatelluride (ZrTe5) has attracted attention as a Dirac semimetal at the boundary of weak and strong topological insulators (TI). Few-layer ZrTe5 is anticipated to exhibit the quantum spin Hall effect due to topological states inside the band gap, but sample degradation inflicted by ambient conditions and processing has so far hampered the fabrication of high quality devices. The quantum Hall effect (QHE), serving as the litmus test for 2D systems to be considered of high quality, has not been observed so far. Only a 3D variant on bulk was reported. Here, we succeeded in preserving the intrinsic properties of thin films lifting the carrier mobility to ∼3500 cm2 V-1 s-1, sufficient to observe the integer QHE and a bulk band gap related zero-energy state. The magneto-transport results offer evidence for the gapless topological states within this gap.
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Affiliation(s)
- Fangdong Tang
- Max
Planck Institute for Solid State Research, Stuttgart 70569, Germany
| | - Peipei Wang
- Department
of Physics and Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Mingquan He
- Low
Temperature Physics Laboratory, College of Physics and Center of Quantum
Materials and Devices, Chongqing University, Chongqing 401331, China
| | - Masahiko Isobe
- Max
Planck Institute for Solid State Research, Stuttgart 70569, Germany
| | - Genda Gu
- Condensed
Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, New York 11973-5000, United States
| | - Qiang Li
- Condensed
Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, New York 11973-5000, United States
- Department
of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, United States
| | - Liyuan Zhang
- Department
of Physics and Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Jurgen H. Smet
- Max
Planck Institute for Solid State Research, Stuttgart 70569, Germany
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6
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Tanaka M, Shimazaki Y, Borzenets IV, Watanabe K, Taniguchi T, Tarucha S, Yamamoto M. Charge Neutral Current Generation in a Spontaneous Quantum Hall Antiferromagnet. PHYSICAL REVIEW LETTERS 2021; 126:016801. [PMID: 33480769 DOI: 10.1103/physrevlett.126.016801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2020] [Revised: 10/12/2020] [Accepted: 12/01/2020] [Indexed: 06/12/2023]
Abstract
The intrinsic Hall effect allows for the generation of a nondissipative charge neutral current, such as a pure spin current generated via the spin Hall effect. Breaking of the spatial inversion or time reversal symmetries, or the spin-orbit interaction is generally considered necessary for the generation of such a charge neutral current. Here, we challenge this general concept and present generation and detection of a charge neutral current in a centrosymmetric material with little spin-orbit interaction. We employ bilayer graphene, and find enhanced nonlocal transport in the quantum Hall antiferromagnetic state, where spontaneous symmetry breaking occurs due to the electronic correlation.
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Affiliation(s)
- Miuko Tanaka
- Department of Applied Physics, University of Tokyo, Tokyo, 113-8656, Japan
| | - Yuya Shimazaki
- Institute of Quantum Electronics, ETH Zurich, CH-8093, Zurich, Switzerland
| | | | - 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
| | - Seigo Tarucha
- Center for Emergent Matter Science, RIKEN, Wako, 351-0198, Japan
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7
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Iwasaki T, Nakaharai S, Wakayama Y, Watanabe K, Taniguchi T, Morita Y, Moriyama S. Single-Carrier Transport in Graphene/hBN Superlattices. NANO LETTERS 2020; 20:2551-2557. [PMID: 32186384 DOI: 10.1021/acs.nanolett.9b05332] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Graphene/hexagonal boron nitride (hBN) moiré superlattices have attracted interest for use in the study of many-body effects and fractal physics in Dirac fermion systems. Many exotic transport properties have been intensively examined in such superlattices, but previous studies have not focused on single-carrier transport. The investigation of the single-carrier behavior in these superlattices would lead to an understanding of the transition of single-particle/correlated phenomena. Here, we show the single-carrier transport in a high-quality bilayer graphene/hBN superlattice-based quantum dot device. We demonstrate remarkable device controllability in the energy range near the charge neutrality point (CNP) and the hole-side satellite point. Under a perpendicular magnetic field, Coulomb oscillations disappear near the CNP, which could be a signature of the crossover between Coulomb blockade and quantum Hall regimes. Our results pave the way for exploring the relationship of single-electron transport and fractal quantum Hall effects with correlated phenomena in two-dimensional quantum materials.
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Affiliation(s)
- Takuya Iwasaki
- International Center for Young Scientists (ICYS), National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0044, Japan
- International Center for Materials Nanoarchitectonics (WPI-MANA), NIMS, Tsukuba, Ibaraki 305-0044, Japan
| | - Shu Nakaharai
- International Center for Materials Nanoarchitectonics (WPI-MANA), NIMS, Tsukuba, Ibaraki 305-0044, Japan
| | - Yutaka Wakayama
- International Center for Materials Nanoarchitectonics (WPI-MANA), NIMS, Tsukuba, Ibaraki 305-0044, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, NIMS, Tsukuba, Ibaraki 305-0044, Japan
| | - Takashi Taniguchi
- Research Center for Functional Materials, NIMS, Tsukuba, Ibaraki 305-0044, Japan
| | - Yoshifumi Morita
- Faculty of Engineering, Gunma University, Kiryu, Gunma 376-8515, Japan
| | - Satoshi Moriyama
- International Center for Materials Nanoarchitectonics (WPI-MANA), NIMS, Tsukuba, Ibaraki 305-0044, Japan
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8
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Wang D, Che S, Cao G, Lyu R, Watanabe K, Taniguchi T, Lau CN, Bockrath M. Quantum Hall Effect Measurement of Spin-Orbit Coupling Strengths in Ultraclean Bilayer Graphene/WSe 2 Heterostructures. NANO LETTERS 2019; 19:7028-7034. [PMID: 31525877 DOI: 10.1021/acs.nanolett.9b02445] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We study proximity-induced spin-orbit coupling (SOC) in bilayer graphene/few-layer WSe2 heterostructure devices. Contact mode atomic force microscopy (AFM) cleaning yields ultraclean interfaces and high-mobility devices. In a perpendicular magnetic field, we measure the quantum Hall effect to determine the Landau level structure in the presence of out-of-plane Ising and in-plane Rashba SOC. A distinct Landau level crossing pattern emerges when tuning the charge density and displacement field independently with dual gates, originating from a layer-selective SOC proximity effect. Analyzing the Landau level crossings and measured inter-Landau level energy gaps yields the proximity-induced SOC energy scale. The Ising SOC is ∼2.2 meV, 100 times higher than the intrinsic SOC in graphene, whereas its sign is consistent with theories predicting a dependence of SOC on interlayer twist angle. The Rashba SOC is ∼15 meV. Finally, we infer the magnetic field dependence of the inter-Landau level Coulomb interactions. These ultraclean bilayer graphene/WSe2 heterostructures provide a high mobility system with the potential to realize novel topological electronic states and manipulate spins in nanostructures.
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Affiliation(s)
- Dongying Wang
- Department of Physics , The Ohio State University , Columbus , Ohio 43210 , United States
| | - Shi Che
- Department of Physics , The Ohio State University , Columbus , Ohio 43210 , United States
| | - Guixin Cao
- Department of Physics , The Ohio State University , Columbus , Ohio 43210 , United States
| | - Rui Lyu
- Department of Physics and Astronomy , University of California , Riverside , California 92521 , United States
| | - Kenji Watanabe
- National Institute for Materials Science , Namiki Tsukuba Ibaraki 305-0044 Japan
| | - Takashi Taniguchi
- National Institute for Materials Science , Namiki Tsukuba Ibaraki 305-0044 Japan
| | - Chun Ning Lau
- Department of Physics , The Ohio State University , Columbus , Ohio 43210 , United States
| | - Marc Bockrath
- Department of Physics , The Ohio State University , Columbus , Ohio 43210 , United States
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9
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Tomarken SL, Cao Y, Demir A, Watanabe K, Taniguchi T, Jarillo-Herrero P, Ashoori RC. Electronic Compressibility of Magic-Angle Graphene Superlattices. PHYSICAL REVIEW LETTERS 2019; 123:046601. [PMID: 31491239 DOI: 10.1103/physrevlett.123.046601] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2019] [Indexed: 06/10/2023]
Abstract
We report the first electronic compressibility measurements of magic-angle twisted bilayer graphene. The evolution of the compressibility with carrier density offers insights into the interaction-driven ground state that have not been accessible in prior transport and tunneling studies. From capacitance measurements, we determine the chemical potential as a function of carrier density and find the widths of the energy gaps at fractional filling of the moiré lattice. In the electron-doped regime, we observe unexpectedly large gaps at quarter- and half-filling and strong electron-hole asymmetry. Moreover, we measure a ∼35 meV minibandwidth that is much wider than most theoretical estimates. Finally, we explore the field dependence up to the quantum Hall regime and observe significant differences from transport measurements.
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Affiliation(s)
- S L Tomarken
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Y Cao
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - A Demir
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - K Watanabe
- National Institute of Materials Science 1-1 Namiki, Tsukuba 305-0044, Japan
| | - T Taniguchi
- National Institute of Materials Science 1-1 Namiki, Tsukuba 305-0044, Japan
| | - P Jarillo-Herrero
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - R C Ashoori
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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10
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Li J, Fu H, Yin Z, Watanabe K, Taniguchi T, Zhu J. Metallic Phase and Temperature Dependence of the ν=0 Quantum Hall State in Bilayer Graphene. PHYSICAL REVIEW LETTERS 2019; 122:097701. [PMID: 30932549 DOI: 10.1103/physrevlett.122.097701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2018] [Indexed: 06/09/2023]
Abstract
The ν=0 quantum Hall state of bilayer graphene is a fertile playground to realize many-body ground states with various broken symmetries. Here we report the experimental observations of a previously unreported metallic phase. The metallic phase resides in the phase space between the previously identified layer polarized state at large transverse electric field and the canted antiferromagnetic state at small transverse electric field. We also report temperature dependence studies of the quantum spin Hall state of ν=0. Complex nonmonotonic behavior reveals concomitant bulk and edge conductions and excitations. These results provide a timely experimental update to understand the rich physics of the ν=0 state.
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Affiliation(s)
- Jing Li
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Hailong Fu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Zhenxi Yin
- 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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11
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Datta B, Agarwal H, Samanta A, Ratnakar A, Watanabe K, Taniguchi T, Sensarma R, Deshmukh MM. Landau Level Diagram and the Continuous Rotational Symmetry Breaking in Trilayer Graphene. PHYSICAL REVIEW LETTERS 2018; 121:056801. [PMID: 30118256 DOI: 10.1103/physrevlett.121.056801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2018] [Revised: 05/03/2018] [Indexed: 06/08/2023]
Abstract
The sequence of the zeroth Landau levels (LLs) between filling factors ν=-6 to 6 in ABA-stacked trilayer graphene (TLG) is unknown because it depends sensitively on the nonuniform charge distribution on the three layers of ABA-stacked TLG. Using the sensitivity of quantum Hall data on the electric field and magnetic field, in an ultraclean ABA-stacked TLG sample, we quantitatively estimate the nonuniformity of the electric field and determine the sequence of the zeroth LLs. We also observe anticrossings between some LLs differing by 3 in LL index, which result from the breaking of the continuous rotational to C_{3} symmetry by the trigonal warping.
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Affiliation(s)
- Biswajit Datta
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Hitesh Agarwal
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Abhisek Samanta
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Amulya Ratnakar
- Department of Physics, UM-DAE Centre for Excellence in Basic Sciences, Mumbai 400098, India
| | - Kenji Watanabe
- National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Rajdeep Sensarma
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Mandar M Deshmukh
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
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12
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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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13
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Hunt BM, Li JIA, Zibrov AA, Wang L, Taniguchi T, Watanabe K, Hone J, Dean CR, Zaletel M, Ashoori RC, Young AF. Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene. Nat Commun 2017; 8:948. [PMID: 29038518 PMCID: PMC5715057 DOI: 10.1038/s41467-017-00824-w] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2017] [Accepted: 07/28/2017] [Indexed: 11/16/2022] Open
Abstract
The high magnetic field electronic structure of bilayer graphene is enhanced by the spin, valley isospin, and an accidental orbital degeneracy, leading to a complex phase diagram of broken symmetry states. Here, we present a technique for measuring the layer-resolved charge density, from which we directly determine the valley and orbital polarization within the zero energy Landau level. Layer polarization evolves in discrete steps across 32 electric field-tuned phase transitions between states of different valley, spin, and orbital order, including previously unobserved orbitally polarized states stabilized by skew interlayer hopping. We fit our data to a model that captures both single-particle and interaction-induced anisotropies, providing a complete picture of this correlated electron system. The resulting roadmap to symmetry breaking paves the way for deterministic engineering of fractional quantum Hall states, while our layer-resolved technique is readily extendable to other two-dimensional materials where layer polarization maps to the valley or spin quantum numbers. The phase diagram of bilayer graphene at high magnetic fields has been an outstanding question, with orders possibly between multiple internal quantum degrees of freedom. Here, Hunt et al. report the measurement of the valley and orbital order, allowing them to directly reconstruct the phase diagram.
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Affiliation(s)
- B M Hunt
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.,Department of Physics, Columbia University, New York, NY, 10027, USA.,Department of Physics, Carnegie Mellon University, Pittsburgh, PA, 15213, USA
| | - J I A Li
- Department of Physics, Columbia University, New York, NY, 10027, USA
| | - A A Zibrov
- Department of Physics, University of California, Santa Barbara, CA, 93106, USA
| | - L Wang
- Department of Mechanical Engineering, Columbia University, New York, NY, 10027, 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
| | - J Hone
- Department of Mechanical Engineering, Columbia University, New York, NY, 10027, USA
| | - C R Dean
- Department of Physics, Columbia University, New York, NY, 10027, USA
| | - M Zaletel
- Station Q, Microsoft Research, Santa Barbara, CA, 93106-6105, USA
| | - R C Ashoori
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - A F Young
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA. .,Department of Physics, University of California, Santa Barbara, CA, 93106, USA.
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14
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Pan C, Wu Y, Cheng B, Che S, Taniguchi T, Watanabe K, Lau CN, Bockrath M. Layer Polarizability and Easy-Axis Quantum Hall Ferromagnetism in Bilayer Graphene. NANO LETTERS 2017; 17:3416-3420. [PMID: 28429942 DOI: 10.1021/acs.nanolett.7b00197] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We report magnetotransport measurements of graphene bilayers at large perpendicular electric displacement fields, up to ∼1.5 V/nm, where we observe crossings between Landau levels with different orbital quantum numbers. The displacement fields at the studied crossings are primarily determined by energy shifts originating from the Landau level layer polarizability or polarization. Despite decreasing Landau level spacing with energy, successive crossings occur at larger displacement fields, resulting from decreasing polarizability with orbital quantum number. For particular crossings we observe resistivity hysteresis in displacement field, indicating the presence of a first-order transition between states exhibiting easy-axis quantum Hall ferromagnetism.
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Affiliation(s)
- C Pan
- Department of Physics and Astronomy, University of California , Riverside, California 92521, United States
| | - Y Wu
- Department of Physics and Astronomy, University of California , Riverside, California 92521, United States
| | - B Cheng
- Department of Physics and Astronomy, University of California , Riverside, California 92521, United States
| | - S Che
- Department of Physics and Astronomy, University of California , Riverside, California 92521, United States
| | - 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
| | - C N Lau
- Department of Physics and Astronomy, University of California , Riverside, California 92521, United States
| | - M Bockrath
- Department of Physics and Astronomy, University of California , Riverside, California 92521, United States
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15
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Datta B, Dey S, Samanta A, Agarwal H, Borah A, Watanabe K, Taniguchi T, Sensarma R, Deshmukh MM. Strong electronic interaction and multiple quantum Hall ferromagnetic phases in trilayer graphene. Nat Commun 2017; 8:14518. [PMID: 28216666 PMCID: PMC5321728 DOI: 10.1038/ncomms14518] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2016] [Accepted: 01/06/2017] [Indexed: 11/09/2022] Open
Abstract
Quantum Hall effect provides a simple way to study the competition between single particle physics and electronic interaction. However, electronic interaction becomes important only in very clean graphene samples and so far the trilayer graphene experiments are understood within non-interacting electron picture. Here, we report evidence of strong electronic interactions and quantum Hall ferromagnetism seen in Bernal-stacked trilayer graphene. Due to high mobility ∼500,000 cm2 V−1 s−1 in our device compared to previous studies, we find all symmetry broken states and that Landau-level gaps are enhanced by interactions; an aspect explained by our self-consistent Hartree–Fock calculations. Moreover, we observe hysteresis as a function of filling factor and spikes in the longitudinal resistance which, together, signal the formation of quantum Hall ferromagnetic states at low magnetic field. Few-layered graphene offers a powerful platform to investigate electronic interactions beyond the non-interacting electron picture approximation. Here, the authors report the signature of strong electronic interactions and quantum Hall ferromagnetism in trilayer graphene with ABA stacking.
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Affiliation(s)
- Biswajit Datta
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Santanu Dey
- Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Abhisek Samanta
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Hitesh Agarwal
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Abhinandan Borah
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Kenji Watanabe
- Advanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- Advanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Rajdeep Sensarma
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Mandar M Deshmukh
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
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16
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Wang Z, Shan J, Mak KF. Valley- and spin-polarized Landau levels in monolayer WSe 2. NATURE NANOTECHNOLOGY 2017; 12:144-149. [PMID: 27798606 DOI: 10.1038/nnano.2016.213] [Citation(s) in RCA: 74] [Impact Index Per Article: 10.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2016] [Accepted: 09/12/2016] [Indexed: 06/06/2023]
Abstract
Electrons in monolayer transition metal dichalcogenides are characterized by valley and spin quantum degrees of freedom, making it possible to explore new physical phenomena and to foresee novel applications in the fields of electronics and optoelectronics. Theoretical proposals further suggest that Berry curvature effects, together with strong spin-orbit interactions, can generate unconventional Landau levels (LLs) under a perpendicular magnetic field. In particular, these would support valley- and spin-polarized chiral edge states in the quantum Hall regime. However, this unique LL structure has not been observed experimentally in transition metal dichalcogenides. Here we report the observation of fully valley- and spin-polarized LLs in high-quality WSe2 monolayers achieved by exploiting a van der Waals heterostructure device platform. We applied handedness-resolved optical reflection spectroscopy to probe the inter-LL transitions at individual valleys and derived the LL structure in turn. We also measured a sizeable doping-induced mass renormalization driven by the strong Coulomb interactions.
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Affiliation(s)
- Zefang Wang
- Department of Physics and Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania 16802-6300, USA
| | - Jie Shan
- Department of Physics and Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania 16802-6300, USA
| | - Kin Fai Mak
- Department of Physics and Center for 2-Dimensional and Layered Materials, The Pennsylvania State University, University Park, Pennsylvania 16802-6300, USA
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17
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Nguyen VL, Perello DJ, Lee S, Nai CT, Shin BG, Kim JG, Park HY, Jeong HY, Zhao J, Vu QA, Lee SH, Loh KP, Jeong SY, Lee YH. Wafer-Scale Single-Crystalline AB-Stacked Bilayer Graphene. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2016; 28:8177-8183. [PMID: 27414480 DOI: 10.1002/adma.201601760] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2016] [Revised: 06/19/2016] [Indexed: 06/06/2023]
Abstract
Single-crystalline artificial AB-stacked bilayer graphene is formed by aligned transfer of two single-crystalline monolayers on a wafer-scale. The obtained bilayer has a well-defined interface and is electronically equivalent to exfoliated or direct-grown AB-stacked bilayers.
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Affiliation(s)
- Van Luan Nguyen
- Center for Integrated Nanostructure Physics, Institute for Basic Science (IBS), Sungkyunkwan University, Suwon, 16419, Republic of Korea
- Department of Energy Science, Sungkyunkwan University, Suwon, 16419, Republic of Korea
- Department of Physics, Sungkyunkwan University, Suwon, 16419, Republic of Korea
| | - David J Perello
- Center for Integrated Nanostructure Physics, Institute for Basic Science (IBS), Sungkyunkwan University, Suwon, 16419, Republic of Korea
| | - Seunghun Lee
- Department of Cogno-mechatronics Engineering, Pusan National University, Busan, 46241, Republic of Korea
| | - Chang Tai Nai
- Department of Chemistry and Centre for Advanced 2D Materials (CA2DM), National University of Singapore, 3 Science Drive 3, Singapore, 117543
| | - Bong Gyu Shin
- Center for Integrated Nanostructure Physics, Institute for Basic Science (IBS), Sungkyunkwan University, Suwon, 16419, Republic of Korea
| | - Joong-Gyu Kim
- Center for Integrated Nanostructure Physics, Institute for Basic Science (IBS), Sungkyunkwan University, Suwon, 16419, Republic of Korea
- Department of Energy Science, Sungkyunkwan University, Suwon, 16419, Republic of Korea
- Department of Physics, Sungkyunkwan University, Suwon, 16419, Republic of Korea
| | - Ho Yeol Park
- Department of Cogno-mechatronics Engineering, Pusan National University, Busan, 46241, Republic of Korea
| | - Hu Young Jeong
- UNIST Central Research Facilities, Ulsan National Institute of Science and Technology (UNIST), Ulsan, 689-798, Republic of Korea
| | - Jiong Zhao
- Center for Integrated Nanostructure Physics, Institute for Basic Science (IBS), Sungkyunkwan University, Suwon, 16419, Republic of Korea
| | - Quoc An Vu
- Center for Integrated Nanostructure Physics, Institute for Basic Science (IBS), Sungkyunkwan University, Suwon, 16419, Republic of Korea
- Department of Energy Science, Sungkyunkwan University, Suwon, 16419, Republic of Korea
- Department of Physics, Sungkyunkwan University, Suwon, 16419, Republic of Korea
| | - Sang Hyub Lee
- Center for Integrated Nanostructure Physics, Institute for Basic Science (IBS), Sungkyunkwan University, Suwon, 16419, Republic of Korea
- Department of Energy Science, Sungkyunkwan University, Suwon, 16419, Republic of Korea
- Department of Physics, Sungkyunkwan University, Suwon, 16419, Republic of Korea
| | - Kian Ping Loh
- Department of Chemistry and Centre for Advanced 2D Materials (CA2DM), National University of Singapore, 3 Science Drive 3, Singapore, 117543
| | - Se-Young Jeong
- Department of Cogno-mechatronics Engineering, Pusan National University, Busan, 46241, Republic of Korea.
| | - Young Hee Lee
- Center for Integrated Nanostructure Physics, Institute for Basic Science (IBS), Sungkyunkwan University, Suwon, 16419, Republic of Korea.
- Department of Energy Science, Sungkyunkwan University, Suwon, 16419, Republic of Korea.
- Department of Physics, Sungkyunkwan University, Suwon, 16419, Republic of Korea.
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18
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Cheng B, Wu Y, Wang P, Pan C, Taniguchi T, Watanabe K, Bockrath M. Gate-Tunable Landau Level Filling and Spectroscopy in Coupled Massive and Massless Electron Systems. PHYSICAL REVIEW LETTERS 2016; 117:026601. [PMID: 27447518 DOI: 10.1103/physrevlett.117.026601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2015] [Indexed: 06/06/2023]
Abstract
We report transport studies on coupled massive and massless electron systems, realized using twisted monolayer-graphene-natural bilayer-graphene stacks. We incorporate the layers in a dual-gated transistor geometry enabling independently tuning their charge density and the perpendicular electric field. In a perpendicular magnetic field, we observe a distinct pattern of gate-tunable Landau level crossings. Screening and interlayer electron-electron interactions yield a nonlinear monolayer gate capacitance. Data analysis enables determination of the monolayer's Fermi velocity and the bilayer's effective mass. The mass obtained is larger than that expected for isolated bilayers, suggesting that the interlayer interactions renormalize the band structure.
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Affiliation(s)
- Bin Cheng
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Yong Wu
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Peng Wang
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Cheng Pan
- Department of Physics and Astronomy, University of California, Riverside, California 92521, 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
| | - M Bockrath
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
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19
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Zhao F, Xu L, Zhang J. Manipulating interface states in monolayer-bilayer graphene planar junctions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:185001. [PMID: 27050943 DOI: 10.1088/0953-8984/28/18/185001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We report on transport properties of monolayer-bilayer graphene planar junctions in a magnetic field. Due to its unique geometry, the edge and interface states can be independently manipulated by either interlayer potential or Zeeman field, and the conductance exhibits interesting quantized behaviors. In the hybrid graphene junction, the quantum Hall (QH) conductance is no longer antisymmetric with respect to the charge neutrality point. When the Zeeman field is considered, a quantum spin Hall (QSH) phase is found in the monolayer region while the weak-QSH phase stays in the bilayer region. In the presence of both interlayer potential and Zeeman field, the bilayer region hosts a QSH phase, whereas the monolayer region is still in a QH phase, leading to a spin-polarized current in the interface. In particular, the QSH phase remains robust against the disorder.
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Affiliation(s)
- Fang Zhao
- School of Physics Science and Technology, Xinjiang University, Urumqi 830046, People's Republic of China
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20
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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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21
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Li X, Zhang F, MacDonald AH. SU(3) Quantum Hall Ferromagnetism in SnTe. PHYSICAL REVIEW LETTERS 2016; 116:026803. [PMID: 26824559 DOI: 10.1103/physrevlett.116.026803] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2015] [Indexed: 06/05/2023]
Abstract
The (111) surface of SnTe hosts one isotropic Γ[over ¯]-centered and three degenerate anisotropic M[over ¯]-centered Dirac surface states. We predict that a nematic phase with spontaneously broken C_{3} symmetry will occur in the presence of a perpendicular magnetic field when the N=0 M[over ¯] Landau levels are 1/3 or 2/3 filled. The nematic state phase boundary is controlled by a competition between intravalley Coulomb interactions that favor a valley-polarized state and weaker intervalley scattering processes that increase in relative strength with magnetic field. An in-plane Zeeman field alters the phase diagram by lifting the threefold M[over ¯] Landau-level degeneracy, yielding a ground state energy with 2π/3 periodicity as a function of Zeeman-field orientation angle.
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Affiliation(s)
- Xiao Li
- Condensed Matter Theory Center and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
| | - Fan Zhang
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - A H MacDonald
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
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22
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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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23
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Kou X, Pan L, Wang J, Fan Y, Choi ES, Lee WL, Nie T, Murata K, Shao Q, Zhang SC, Wang KL. Metal-to-insulator switching in quantum anomalous Hall states. Nat Commun 2015; 6:8474. [PMID: 26442609 PMCID: PMC4633736 DOI: 10.1038/ncomms9474] [Citation(s) in RCA: 55] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2015] [Accepted: 08/25/2015] [Indexed: 12/23/2022] Open
Abstract
After decades of searching for the dissipationless transport in the absence of any external magnetic field, quantum anomalous Hall effect (QAHE) was recently achieved in magnetic topological insulator films. However, the universal phase diagram of QAHE and its relation with quantum Hall effect (QHE) remain to be investigated. Here, we report the experimental observation of the giant longitudinal resistance peak and zero Hall conductance plateau at the coercive field in the six quintuple-layer (Cr0.12Bi0.26Sb0.62)2Te3 film, and demonstrate the metal-to-insulator switching between two opposite QAHE plateau states up to 0.3 K. Moreover, the universal QAHE phase diagram is confirmed through the angle-dependent measurements. Our results address that the quantum phase transitions in both QAHE and QHE regimes are in the same universality class, yet the microscopic details are different. In addition, the realization of the QAHE insulating state unveils new ways to explore quantum phase-related physics and applications. The quantum anomalous Hall effect is a recently demonstrated chiral transport phenomenon arising in magnetically doped topological insulators. Here, the authors study the Hall plateau switching and universal phase diagram of the quantum anomalous Hall effect in thin films of two-dimensional Cr-doped (BiSb)2Te3.
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Affiliation(s)
- Xufeng Kou
- Device Research Laboratory, Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
| | - Lei Pan
- Device Research Laboratory, Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
| | - Jing Wang
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Yabin Fan
- Device Research Laboratory, Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
| | - Eun Sang Choi
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310-3706, USA
| | - Wei-Li Lee
- Institute of Physics, Academia Sinica, Taipei 11529, Taiwan
| | - Tianxiao Nie
- Device Research Laboratory, Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
| | - Koichi Murata
- Device Research Laboratory, Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
| | - Qiming Shao
- Device Research Laboratory, Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
| | - Shou-Cheng Zhang
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Kang L Wang
- Device Research Laboratory, Department of Electrical Engineering, University of California, Los Angeles, California 90095, USA
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24
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Feng Y, Feng X, Ou Y, Wang J, Liu C, Zhang L, Zhao D, Jiang G, Zhang SC, He K, Ma X, Xue QK, Wang Y. Observation of the Zero Hall Plateau in a Quantum Anomalous Hall Insulator. PHYSICAL REVIEW LETTERS 2015; 115:126801. [PMID: 26431002 DOI: 10.1103/physrevlett.115.126801] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2015] [Indexed: 06/05/2023]
Abstract
We report experimental investigations on the quantum phase transition between the two opposite Hall plateaus of a quantum anomalous Hall insulator. We observe a well-defined plateau with zero Hall conductivity over a range of magnetic field around coercivity when the magnetization reverses. The features of the zero Hall plateau are shown to be closely related to that of the quantum anomalous Hall effect, but its temperature evolution exhibits a significant difference from the network model for a conventional quantum Hall plateau transition. We propose that the chiral edge states residing at the magnetic domain boundaries, which are unique to a quantum anomalous Hall insulator, are responsible for the novel features of the zero Hall plateau.
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Affiliation(s)
- Yang Feng
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
| | - Xiao Feng
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
| | - Yunbo Ou
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
| | - Jing Wang
- Department of Physics, Stanford University, Stanford, California 94305-4045, USA
| | - Chang Liu
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
| | - Liguo Zhang
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
| | - Dongyang Zhao
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
| | - Gaoyuan Jiang
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
| | - Shou-Cheng Zhang
- Department of Physics, Stanford University, Stanford, California 94305-4045, USA
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
| | - Ke He
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
| | - Xucun Ma
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
| | - Qi-Kun Xue
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
| | - Yayu Wang
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
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25
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Engels S, Terrés B, Epping A, Khodkov T, Watanabe K, Taniguchi T, Beschoten B, Stampfer C. Limitations to carrier mobility and phase-coherent transport in bilayer graphene. PHYSICAL REVIEW LETTERS 2014; 113:126801. [PMID: 25279637 DOI: 10.1103/physrevlett.113.126801] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2014] [Indexed: 06/03/2023]
Abstract
We present transport measurements on high-mobility bilayer graphene fully encapsulated in hexagonal boron nitride. We show two terminal quantum Hall effect measurements which exhibit full symmetry broken Landau levels at low magnetic fields. From weak localization measurements, we extract gate-tunable phase-coherence times τϕ as well as the inter- and intravalley scattering times τi and τ*, respectively. While τϕ is in qualitative agreement with an electron-electron interaction-mediated dephasing mechanism, electron spin-flip scattering processes are limiting τϕ at low temperatures. The analysis of τi and τ* points to local strain fluctuation as the most probable mechanism for limiting the mobility in high-quality bilayer graphene.
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Affiliation(s)
- S Engels
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074 Aachen, Germany, EU and Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany, EU
| | - B Terrés
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074 Aachen, Germany, EU and Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany, EU
| | - A Epping
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074 Aachen, Germany, EU and Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany, EU
| | - T Khodkov
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074 Aachen, Germany, EU and Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany, EU
| | - 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
| | - B Beschoten
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074 Aachen, Germany, EU
| | - C Stampfer
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074 Aachen, Germany, EU and Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, Germany, EU
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26
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Competing ordered states with filling factor two in bilayer graphene. Nat Commun 2014; 5:4550. [DOI: 10.1038/ncomms5550] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2014] [Accepted: 06/27/2014] [Indexed: 11/09/2022] Open
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27
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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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28
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Tao HS, Chen YH, Lin HF, Liu HD, Liu WM. Layer anti-ferromagnetism on bilayer honeycomb lattice. Sci Rep 2014; 4:5367. [PMID: 24947369 PMCID: PMC4064339 DOI: 10.1038/srep05367] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2013] [Accepted: 05/29/2014] [Indexed: 11/09/2022] Open
Abstract
Bilayer honeycomb lattice, with inter-layer tunneling energy, has a parabolic dispersion relation, and the inter-layer hopping can cause the charge imbalance between two sublattices. Here, we investigate the metal-insulator and magnetic phase transitions on the strongly correlated bilayer honeycomb lattice by cellular dynamical mean-field theory combined with continuous time quantum Monte Carlo method. The procedures of magnetic spontaneous symmetry breaking on dimer and non-dimer sites are different, causing a novel phase transition between normal anti-ferromagnet and layer anti-ferromagnet. The whole phase diagrams about the magnetism, temperature, interaction and inter-layer hopping are obtained. Finally, we propose an experimental protocol to observe these phenomena in future optical lattice experiments.
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Affiliation(s)
- Hong-Shuai Tao
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yao-Hua Chen
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Heng-Fu Lin
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Hai-Di Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Wu-Ming Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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29
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Velasco J, Lee Y, Zhao Z, Jing L, Kratz P, Bockrath M, Lau CN. Transport measurement of Landau level gaps in bilayer graphene with layer polarization control. NANO LETTERS 2014; 14:1324-1328. [PMID: 24484507 DOI: 10.1021/nl4043399] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Landau level (LL) gaps are important parameters for understanding electronic interactions and symmetry-broken processes in bilayer graphene (BLG). Here we present transport spectroscopy measurements of LL gaps in double-gated suspended BLG with high mobilities in the quantum Hall regime. By using bias as a spectroscopic tool, we measure the gap Δ for the quantum Hall (QH) state at filling factors ν = ±4 and -2. The single-particle Δ(ν=4) scales linearly with magnetic field B and is independent of the out-of-plane electric field E⊥. For the symmetry-broken ν = -2 state, the measured values of Δ(ν=-2) are ∼1.1 meV/T and 0.17 meV/T for singly gated geometry and dual-gated geometry at E⊥ = 0, respectively. The difference between the two values arises from the E⊥. dependence of Δ(ν=-2), suggesting that the ν = -2 state is layer polarized. Our studies provide the first measurements of the gaps of the broken symmetry QH states in BLG with well-controlled E⊥ and establish a robust method that can be implemented for studying similar states in other layered materials.
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Affiliation(s)
- J Velasco
- Department of Physics and Astronomy, University of California, Riverside , Riverside, California 92521, United States
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30
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San-Jose P, Gorbachev RV, Geim AK, Novoselov KS, Guinea F. Stacking boundaries and transport in bilayer graphene. NANO LETTERS 2014; 14:2052-2057. [PMID: 24605877 DOI: 10.1021/nl500230a] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Pristine bilayer graphene behaves in some instances as an insulator with a transport gap of a few millielectronvolts. This behavior has been interpreted as the result of an intrinsic electronic instability induced by many-body correlations. Intriguingly, however, some samples of similar mobility exhibit good metallic properties with a minimal conductivity of the order of 2e(2)/h. Here, we propose an explanation for this dichotomy, which is unrelated to electron interactions and based instead on the reversible formation of boundaries between stacking domains ("solitons"). We argue, using a numerical analysis, that the hallmark features of the previously inferred many-body insulating state can be explained by scattering on boundaries between domains with different stacking order (AB and BA). We furthermore present experimental evidence, reinforcing our interpretation, of reversible switching between a metallic and an insulating regime in suspended bilayers when subjected to thermal cycling or high current annealing.
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Affiliation(s)
- P San-Jose
- Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC), Cantoblanco, 28049 Madrid, Spain
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31
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Ki DK, Fal'ko VI, Abanin DA, Morpurgo AF. Observation of even denominator fractional quantum Hall effect in suspended bilayer graphene. NANO LETTERS 2014; 14:2135-2139. [PMID: 24611523 DOI: 10.1021/nl5003922] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We investigate low-temperature magneto-transport in recently developed, high-quality multiterminal suspended bilayer graphene devices, enabling the independent measurement of the longitudinal and transverse resistance. We observe clear signatures of the fractional quantum Hall effect with different states that are either fully developed, and exhibit a clear plateau in the transverse resistance with a concomitant dip in longitudinal resistance or incipient, and exhibit only a longitudinal resistance minimum. All observed states scale as a function of filling factor ν, as expected. An unprecedented even-denominator fractional state is observed at ν = -1/2 on the hole side, exhibiting a clear plateau in Rxy quantized at the expected value of 2h/e(2) with a precision of ∼0.5%. Many of our observations, together with a recent electronic compressibility measurement performed in graphene bilayers on hexagonal boron-nitride (hBN) substrates, are consistent with a recent theory that accounts for the effect of the degeneracy between the N = 0 and N = 1 Landau levels in the fractional quantum Hall effect and predicts the occurrence of a Moore-Read type ν = -1/2 state. Owing to the experimental flexibility of bilayer graphene, which has a gate-dependent band structure, can be easily accessed by scanning probes, and can be contacted with materials such as superconductors, our findings offer new possibilities to explore the microscopic nature of even-denominator fractional quantum Hall effect.
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Affiliation(s)
- Dong-Keun Ki
- Départment de Physique de la Matiére Condensée (DPMC) and Group of Applied Physics (GAP), University of Geneva , 24 Quai Ernest-Ansermet, CH1211 Genéve 4 Switzerland
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32
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Ki DK, Morpurgo AF. High-quality multiterminal suspended graphene devices. NANO LETTERS 2013; 13:5165-5170. [PMID: 24080018 DOI: 10.1021/nl402462q] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We introduce a new scheme to realize suspended, multiterminal graphene structures that can be current annealed successfully to obtain uniform, very high quality devices. A key aspect is that the bulky metallic contacts are not connected directly to the part of graphene probed by transport measurements, but only through etched constriction, which prevents the contacts from acting invasively. The device high quality and uniformity is demonstrated by a reproducibly narrow (δn ~ 10(9) cm(-2)) resistance peak around charge neutrality, by carrier mobility values exceeding 10(6) cm(2) V(-1) s(-1), by the observation of integer quantum Hall plateaus starting at 30 mT and of symmetry broken states at about 200 mT, and by the occurrence of a negative multiterminal resistance directly proving the occurrence of ballistic transport. As these multiterminal devices enable measurements that cannot be done in a simpler two-terminal configuration, we anticipate that their use in future studies of graphene-based systems will be particularly relevant.
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Affiliation(s)
- Dong-Keun Ki
- Départment de Physique de la Matiére Condensée (DPMC) and Group of Applied Physics (GAP), University of Geneva , 24 quai Ernest-Ansermet, CH-1211 Geneva 4, Switzerland
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33
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McCann E, Koshino M. The electronic properties of bilayer graphene. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2013; 76:056503. [PMID: 23604050 DOI: 10.1088/0034-4885/76/5/056503] [Citation(s) in RCA: 201] [Impact Index Per Article: 18.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
We review the electronic properties of bilayer graphene, beginning with a description of the tight-binding model of bilayer graphene and the derivation of the effective Hamiltonian describing massive chiral quasiparticles in two parabolic bands at low energies. We take into account five tight-binding parameters of the Slonczewski-Weiss-McClure model of bulk graphite plus intra- and interlayer asymmetry between atomic sites which induce band gaps in the low-energy spectrum. The Hartree model of screening and band-gap opening due to interlayer asymmetry in the presence of external gates is presented. The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and we also discuss orbital magnetism, phonons and the influence of strain on electronic properties. We conclude with an overview of electronic interaction effects.
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Affiliation(s)
- Edward McCann
- Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
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34
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Lee Y, Velasco J, Tran D, Zhang F, Bao W, Jing L, Myhro K, Smirnov D, Lau CN. Broken symmetry quantum Hall states in dual-gated ABA trilayer graphene. NANO LETTERS 2013; 13:1627-1631. [PMID: 23527578 DOI: 10.1021/nl4000757] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
ABA-stacked trilayer graphene is a unique 2D electron system with mirror reflection symmetry and unconventional quantum Hall effect. We present low-temperature transport measurements on dual-gated suspended trilayer graphene in the quantum Hall (QH) regime. We observe QH plateaus at filling factors ν = -8, -2, 2, 6, and 10, which is in agreement with the full-parameter tight binding calculations. In high magnetic fields, odd-integer plateaus are also resolved, indicating almost complete lifting of the 12-fold degeneracy of the lowest Landau level (LL). Under an out-of-plane electric field E(perpendicular), we observe degeneracy breaking and transitions between QH plateaus. Interestingly, depending on its direction, E(perpendicular) selectively breaks the LL degeneracies in the electron-doped or hole-doped regimes. Our results underscore the rich interaction-induced phenomena in trilayer graphene.
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Affiliation(s)
- Yongjin Lee
- Department of Physics and Astronomy, University of California, Riverside, Riverside, California 92521, United States
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35
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Connolly MR, Puddy RK, Logoteta D, Marconcini P, Roy M, Griffiths JP, Jones GAC, Maksym PA, Macucci M, Smith CG. Unraveling quantum Hall breakdown in bilayer graphene with scanning gate microscopy. NANO LETTERS 2012; 12:5448-5454. [PMID: 23078572 DOI: 10.1021/nl3015395] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Investigating the structure of quantized plateaus in the Hall conductance of graphene is a powerful way of probing its crystalline and electronic structure and will also help to establish whether graphene can be used as a robust standard of resistance for quantum metrology. We use low-temperature scanning gate microscopy to image the interplateau breakdown of the quantum Hall effect in an exfoliated bilayer graphene flake. Scanning gate images captured during breakdown exhibit intricate patterns where the conductance is strongly affected by the presence of the scanning probe tip. The maximum density and intensity of the tip-induced conductance perturbations occur at half-integer filling factors, midway between consecutive quantum Hall plateau, while the intensity of individual sites shows a strong dependence on tip-voltage. Our results are well-described by a model based on quantum percolation which relates the points of high responsivity to tip-induced scattering in a network of saddle points separating localized states.
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Affiliation(s)
- M R Connolly
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, CB3 0HE, United Kingdom.
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36
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Barlas Y, Côté R, Rondeau M. Quantum Hall to charge-density-wave phase transitions in ABC-trilayer graphene. PHYSICAL REVIEW LETTERS 2012; 109:126804. [PMID: 23005974 DOI: 10.1103/physrevlett.109.126804] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2011] [Indexed: 06/01/2023]
Abstract
ABC-stacked trilayer graphene's chiral band structure results in three (n=0, 1, 2) Landau level orbitals with zero kinetic energy. This unique feature has important consequences on the interaction-driven states of the 12-fold degenerate (including spin and valley) N=0 Landau level. In particular, at many filling factors ν(T) = ±5, ±4, ±2, ±1 a quantum phase transition from a quantum Hall liquid state to a triangular charge-density wave occurs as a function of the single particle-induced Landau level orbital splitting Δ(LL). Experimental signatures of this phase transition are also discussed.
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Affiliation(s)
- Yafis Barlas
- Department of Physics and Astronomy, University of California, Riverside, 92521, USA
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37
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Kharitonov M. Canted antiferromagnetic phase of the ν=0 quantum Hall state in bilayer graphene. PHYSICAL REVIEW LETTERS 2012; 109:046803. [PMID: 23006103 DOI: 10.1103/physrevlett.109.046803] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2011] [Indexed: 06/01/2023]
Abstract
Motivated to understand the nature of the strongly insulating ν=0 quantum Hall state in bilayer graphene, we develop the theory of the state in the framework of quantum Hall ferromagnetism. The generic phase diagram, obtained in the presence of the isospin anisotropy, perpendicular electric field, and Zeeman effect, consists of the spin-polarized ferromagnetic (F), canted antiferromagnetic (CAF), and partially (PLP) and fully (FLP) layer-polarized phases. We address the edge transport properties of the phases. Comparing our findings with the recent data on suspended dual-gated devices, we conclude that the insulating ν=0 state realized in bilayer graphene at lower electric field is the CAF phase. We also predict a continuous and a sharp insulator-metal phase transition upon tilting the magnetic field from the insulating CAF and FLP phases, respectively, to the F phase with metallic edge conductance 2e(2)/h, which could be within the reach of available fields and could allow one to identify and distinguish the phases experimentally.
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Affiliation(s)
- Maxim Kharitonov
- Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA
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38
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Gate-defined quantum confinement in suspended bilayer graphene. Nat Commun 2012; 3:934. [DOI: 10.1038/ncomms1945] [Citation(s) in RCA: 146] [Impact Index Per Article: 12.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2012] [Accepted: 05/31/2012] [Indexed: 11/08/2022] Open
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39
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Evidence for a spontaneous gapped state in ultraclean bilayer graphene. Proc Natl Acad Sci U S A 2012; 109:10802-5. [PMID: 22685212 DOI: 10.1073/pnas.1205978109] [Citation(s) in RCA: 97] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
At the charge neutrality point, bilayer graphene (BLG) is strongly susceptible to electronic interactions and is expected to undergo a phase transition to a state with spontaneously broken symmetries. By systematically investigating a large number of single-and double-gated BLG devices, we observe a bimodal distribution of minimum conductivities at the charge neutrality point. Although σ(min) is often approximately 2-3 e(2)/h (where e is the electron charge and h is Planck's constant), it is several orders of magnitude smaller in BLG devices that have both high mobility and low extrinsic doping. The insulating state in the latter samples appears below a transition temperature T(c) of approximately 5 K and has a T = 0 energy gap of approximately 3 meV. Transitions between these different states can be tuned by adjusting disorder or carrier density.
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40
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Cooper DR, D’Anjou B, Ghattamaneni N, Harack B, Hilke M, Horth A, Majlis N, Massicotte M, Vandsburger L, Whiteway E, Yu V. Experimental Review of Graphene. ACTA ACUST UNITED AC 2012. [DOI: 10.5402/2012/501686] [Citation(s) in RCA: 337] [Impact Index Per Article: 28.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
This review examines the properties of graphene from an experimental perspective. The intent is to review the most important experimental results at a level of detail appropriate for new graduate students who are interested in a general overview of the fascinating properties of graphene. While some introductory theoretical concepts are provided, including a discussion of the electronic band structure and phonon dispersion, the main emphasis is on describing relevant experiments and important results as well as some of the novel applications of graphene. In particular, this review covers graphene synthesis and characterization, field-effect behavior, electronic transport properties, magnetotransport, integer and fractional quantum Hall effects, mechanical properties, transistors, optoelectronics, graphene-based sensors, and biosensors. This approach attempts to highlight both the means by which the current understanding of graphene has come about and some tools for future contributions.
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Affiliation(s)
| | | | | | | | | | | | | | | | | | | | - Victor Yu
- McGill University, Montréal, QC, Canada H3A 2T8
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41
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Liao ZM, Wu HC, Kumar S, Duesberg GS, Zhou YB, Cross GLW, Shvets IV, Yu DP. Large magnetoresistance in few layer graphene stacks with current perpendicular to plane geometry. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2012; 24:1862-1866. [PMID: 22407473 DOI: 10.1002/adma.201104796] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2011] [Revised: 02/01/2012] [Indexed: 05/31/2023]
Abstract
A large magnetoresistance (MR) effect of few-layers graphene between two non-magnetic metal electrodes with current perpendicular to graphene plane is studied. A non-saturation and anisotropic MR with the value over 60% at 14 T is observed in a two-layer graphene stack at room temperature. The resistance of the device is only tens of ohms, having the advantage of low power consumption for magnetic device applications.
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Affiliation(s)
- Zhi-Min Liao
- State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing, P.R. China.
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42
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Sanchez-Yamagishi JD, Taychatanapat T, Watanabe K, Taniguchi T, Yacoby A, Jarillo-Herrero P. Quantum Hall effect, screening, and layer-polarized insulating states in twisted bilayer graphene. PHYSICAL REVIEW LETTERS 2012; 108:076601. [PMID: 22401231 DOI: 10.1103/physrevlett.108.076601] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2011] [Indexed: 05/07/2023]
Abstract
We investigate electronic transport in dual-gated twisted-bilayer graphene. Despite the subnanometer proximity between the layers, we identify independent contributions to the magnetoresistance from the graphene Landau level spectrum of each layer. We demonstrate that the filling factor of each layer can be independently controlled via the dual gates, which we use to induce Landau level crossings between the layers. By analyzing the gate dependence of the Landau level crossings, we characterize the finite interlayer screening and extract the capacitance between the atomically spaced layers. At zero filling factor, we observe an insulating state at large displacement fields, which can be explained by the presence of counterpropagating edge states with interlayer coupling.
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43
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Freitag F, Trbovic J, Weiss M, Schönenberger C. Spontaneously gapped ground state in suspended bilayer graphene. PHYSICAL REVIEW LETTERS 2012; 108:076602. [PMID: 22401232 DOI: 10.1103/physrevlett.108.076602] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2011] [Indexed: 05/31/2023]
Abstract
Bilayer graphene bears an eightfold degeneracy due to spin, valley, and layer symmetry, allowing for a wealth of broken symmetry states induced by magnetic or electric fields, by strain, or even spontaneously by interaction. We study the electrical transport in clean current annealed suspended bilayer graphene. We find two kinds of devices. In bilayers of type B1 the eightfold zero-energy Landau level is partially lifted above a threshold field revealing an insulating ν=0 quantum-Hall state at the charge neutrality point. In bilayers of type B2 the Landau level lifting is full and a gap appears in the differential conductance even at zero magnetic field, suggesting an insulating spontaneously broken symmetry state. Unlike B1, the minimum conductance in B2 is not exponentially suppressed, but remains finite with a value G is < or approximately equall to e(2)/h even in a large magnetic field. We suggest that this phase of B2 is insulating in the bulk and bound by compressible edge states.
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Affiliation(s)
- F Freitag
- Department of Physics, University of Basel, Basel, Switzerland
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44
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Barlas Y, Yang K, MacDonald AH. Quantum Hall effects in graphene-based two-dimensional electron systems. NANOTECHNOLOGY 2012; 23:052001. [PMID: 22238249 DOI: 10.1088/0957-4484/23/5/052001] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
In this article we review the quantum Hall physics of graphene-based two-dimensional electron systems, with a special focus on recent experimental and theoretical developments. We explain why graphene and bilayer graphene can be viewed respectively as J D 1 and 2 chiral two-dimensional electron gases (C2DEGs), and why this property frames their quantum Hall physics. The current status of experimental and theoretical work on the role of electron-electron interactions is reviewed at length with an emphasis on unresolved issues in the field, including the role of disorder in current experiments. Special attention is given to the interesting low magnetic field limit, and to the relationship between quantum Hall effects and the spontaneous anomalous Hall effects that might occur in bilayer graphene systems in the absence of a magnetic field.
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Affiliation(s)
- Yafis Barlas
- National High Magnetic Field Laboratory and Department of Physics, Florida State University, FL 32306, USA
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45
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Hyun YH, Kim Y, Sochichiu C, Choi MY. Landau level spectrum for bilayer graphene in a tilted magnetic field. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:045501. [PMID: 22214562 DOI: 10.1088/0953-8984/24/4/045501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We consider a graphene bilayer in a constant magnetic field of arbitrary orientation, i.e., tilted with respect to the graphene plane. In the low energy approximation to the tight-binding model with Peierls substitution, we find the Landau level spectrum analytically in terms of spheroidal functions and the respective eigenvalues. We compare our result to the perpendicular and purely in-plane field cases. In the limit of perpendicular field we reproduce the known equidistant spectrum for Landau levels. In the opposite limit of large in-plane field this spectrum becomes two-fold degenerate, which is a consequence of Dirac point splitting induced by the in-plane field.
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Affiliation(s)
- Young-Hwan Hyun
- Department of Physics, BK21 Physics Research Division, Sungkyunkwan University, Suwon, Korea.
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Velasco J, Jing L, Bao W, Lee Y, Kratz P, Aji V, Bockrath M, Lau CN, Varma C, Stillwell R, Smirnov D, Zhang F, Jung J, MacDonald AH. Transport spectroscopy of symmetry-broken insulating states in bilayer graphene. NATURE NANOTECHNOLOGY 2012; 7:156-160. [PMID: 22266634 DOI: 10.1038/nnano.2011.251] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2011] [Accepted: 12/19/2011] [Indexed: 05/31/2023]
Abstract
Bilayer graphene is an attractive platform for studying new two-dimensional electron physics, because its flat energy bands are sensitive to out-of-plane electric fields and these bands magnify electron-electron interaction effects. Theory predicts a variety of interesting broken symmetry states when the electron density is at the carrier neutrality point, and some of these states are characterized by spontaneous mass gaps, which lead to insulating behaviour. These proposed gaps are analogous to the masses generated by broken symmetries in particle physics, and they give rise to large Berry phase effects accompanied by spontaneous quantum Hall effects. Although recent experiments have provided evidence for strong electronic correlations near the charge neutrality point, the presence of gaps remains controversial. Here, we report transport measurements in ultraclean double-gated bilayer graphene and use source-drain bias as a spectroscopic tool to resolve a gap of ∼2 meV at the charge neutrality point. The gap can be closed by a perpendicular electric field of strength ∼15 mV nm(-1), but it increases monotonically with magnetic field, with an apparent particle-hole asymmetry above the gap. These data represent the first spectroscopic mapping of the ground states in bilayer graphene in the presence of both electric and magnetic fields.
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Affiliation(s)
- J Velasco
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
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Zhang F, Jung J, MacDonald AH. Spontaneous Quantum Hall States and Novel Luttinger Liquids in Chiral Graphene. ACTA ACUST UNITED AC 2011. [DOI: 10.1088/1742-6596/334/1/012002] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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48
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Lee K, Kim S, Points MS, Beechem TE, Ohta T, Tutuc E. Magnetotransport properties of quasi-free-standing epitaxial graphene bilayer on SiC: evidence for Bernal stacking. NANO LETTERS 2011; 11:3624-3628. [PMID: 21797267 DOI: 10.1021/nl201430a] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We investigate the magnetotransport properties of quasi-free-standing epitaxial graphene bilayer on SiC, grown by atmospheric pressure graphitization in Ar, followed by H(2) intercalation. At the charge neutrality point, the longitudinal resistance shows an insulating behavior, which follows a temperature dependence consistent with variable range hopping transport in a gapped state. In a perpendicular magnetic field, we observe quantum Hall states (QHSs) both at filling factors (ν) multiples of four (ν = 4, 8, 12), as well as broken valley symmetry QHSs at ν = 0 and ν = 6. These results unambiguously show that the quasi-free-standing graphene bilayer grown on the Si-face of SiC exhibits Bernal stacking.
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Affiliation(s)
- Kayoung Lee
- Microelectronics Research Center, The University of Texas at Austin, Austin, Texas 78758, United States
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49
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Kim S, Lee K, Tutuc E. Spin-polarized to valley-polarized transition in graphene bilayers at ν=0 in high magnetic fields. PHYSICAL REVIEW LETTERS 2011; 107:016803. [PMID: 21797563 DOI: 10.1103/physrevlett.107.016803] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2011] [Indexed: 05/31/2023]
Abstract
We investigate the transverse electric field (E) dependence of the ν=0 quantum Hall state (QHS) in dual-gated graphene bilayers in high magnetic fields. The longitudinal resistivity ρ(xx) measured at ν=0 shows an insulating behavior which is strongest in the vicinity of E=0, as well as at large E fields. At a fixed perpendicular magnetic field (B), the ν=0 QHS undergoes a transition as a function of the applied E, marked by a minimum, temperature-independent ρ(xx). This observation is explained by a transition from a spin-polarized ν=0 QHS at small E fields to a valley- (layer-)polarized ν=0 QHS at large E fields. The E field value at which the transition occurs follows a linear dependence on B.
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Affiliation(s)
- Seyoung Kim
- Microelectronics Research Center, The University of Texas at Austin, 78758, USA
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Zhang F, Jung J, Fiete GA, Niu Q, MacDonald AH. Spontaneous quantum Hall states in chirally stacked few-layer graphene systems. PHYSICAL REVIEW LETTERS 2011; 106:156801. [PMID: 21568592 DOI: 10.1103/physrevlett.106.156801] [Citation(s) in RCA: 123] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2010] [Indexed: 05/30/2023]
Abstract
Chirally stacked N-layer graphene systems with N≥2 exhibit a variety of distinct broken symmetry states in which charge density contributions from different spins and valleys are spontaneously transferred between layers. We explain how these states are distinguished by their charge, spin, and valley Hall conductivities, by their orbital magnetizations, and by their edge state properties. We argue that valley Hall states have [N/2] edge channels per spin valley.
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Affiliation(s)
- Fan Zhang
- Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA.
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