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Jat MK, Tiwari P, Bajaj R, Shitut I, Mandal S, Watanabe K, Taniguchi T, Krishnamurthy HR, Jain M, Bid A. Higher order gaps in the renormalized band structure of doubly aligned hBN/bilayer graphene moiré superlattice. Nat Commun 2024; 15:2335. [PMID: 38485946 PMCID: PMC10940307 DOI: 10.1038/s41467-024-46672-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2023] [Accepted: 02/27/2024] [Indexed: 03/18/2024] Open
Abstract
This paper presents our findings on the recursive band gap engineering of chiral fermions in bilayer graphene doubly aligned with hBN. Using two interfering moiré potentials, we generate a supermoiré pattern that renormalizes the electronic bands of the pristine bilayer graphene, resulting in higher order fractal gaps even at very low energies. These Bragg gaps can be mapped using a unique linear combination of periodic areas within the system. To validate our findings, we use electronic transport measurements to identify the position of these gaps as a function of the carrier density. We establish their agreement with the predicted carrier densities and corresponding quantum numbers obtained using the continuum model. Our study provides strong evidence of the quantization of the momentum-space area of quasi-Brillouin zones in a minimally incommensurate lattice. It fills important gaps in the understanding of band structure engineering of Dirac fermions with a doubly periodic superlattice spinor potential.
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Affiliation(s)
- Mohit Kumar Jat
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India
| | - Priya Tiwari
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Robin Bajaj
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India
| | - Ishita Shitut
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India
| | - Shinjan Mandal
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - H R Krishnamurthy
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India
| | - Manish Jain
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India.
| | - Aveek Bid
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India.
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2
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Reproducibility in the fabrication and physics of moiré materials. Nature 2022; 602:41-50. [PMID: 35110759 DOI: 10.1038/s41586-021-04173-z] [Citation(s) in RCA: 52] [Impact Index Per Article: 26.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2021] [Accepted: 10/21/2021] [Indexed: 11/08/2022]
Abstract
Overlaying two atomic layers with a slight lattice mismatch or at a small rotation angle creates a moiré superlattice, which has properties that are markedly modified from (and at times entirely absent in) the 'parent' materials. Such moiré materials have progressed the study and engineering of strongly correlated phenomena and topological systems in reduced dimensions. The fundamental understanding of the electronic phases, such as superconductivity, requires a precise control of the challenging fabrication process, involving the rotational alignment of two atomically thin layers with an angular precision below 0.1 degrees. Here we review the essential properties of moiré materials and discuss their fabrication and physics from a reproducibility perspective.
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Che S, Stepanov P, Ge S, Zhu M, Wang D, Lee Y, Myhro K, Shi Y, Chen R, Pi Z, Pan C, Cheng B, Taniguchi T, Watanabe K, Barlas Y, Lake RK, Bockrath M, Hwang J, Lau CN. Substrate-Dependent Band Structures in Trilayer Graphene/h-BN Heterostructures. PHYSICAL REVIEW LETTERS 2020; 125:246401. [PMID: 33412071 DOI: 10.1103/physrevlett.125.246401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2018] [Revised: 04/19/2019] [Accepted: 11/03/2020] [Indexed: 06/12/2023]
Abstract
The tight-binding model has been spectacularly successful in elucidating the electronic and optical properties of a vast number of materials. Within the tight-binding model, the hopping parameters that determine much of the band structure are often taken as constants. Here, using ABA-stacked trilayer graphene as the model system, we show that, contrary to conventional wisdom, the hopping parameters and therefore band structures are not constants, but are systematically variable depending on their relative alignment angle between h-BN. Moreover, the addition or removal of the h-BN substrate results in an inversion of the K and K^{'} valley in trilayer graphene's lowest Landau level. Our work illustrates the oft-ignored and rather surprising impact of the substrates on band structures of 2D materials.
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Affiliation(s)
- Shi Che
- Department of Physics, The Ohio State University, Columbus, Ohio 43221, USA
| | - Petr Stepanov
- Department of Physics, The Ohio State University, Columbus, Ohio 43221, USA
| | - Supeng Ge
- Department of Electrical and Computer Engineering, University of California, Riverside, California 92521, USA
| | - Menglin Zhu
- Department of Materials Science and Engineering, The Ohio State University, Columbus, Ohio 43221, USA
| | - Dongying Wang
- Department of Physics, The Ohio State University, Columbus, Ohio 43221, USA
| | - Yongjin Lee
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Kevin Myhro
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Yanmeng Shi
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Ruoyu Chen
- Department of Physics, The Ohio State University, Columbus, Ohio 43221, USA
| | - Ziqi Pi
- 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
| | - Bin Cheng
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
| | - Yafis Barlas
- Department of Electrical and Computer Engineering, University of California, Riverside, California 92521, USA
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
| | - Roger K Lake
- Department of Electrical and Computer Engineering, University of California, Riverside, California 92521, USA
| | - Marc Bockrath
- Department of Physics, The Ohio State University, Columbus, Ohio 43221, USA
| | - Jinwoo Hwang
- Department of Materials Science and Engineering, The Ohio State University, Columbus, Ohio 43221, USA
| | - Chun Ning Lau
- Department of Physics, The Ohio State University, Columbus, Ohio 43221, USA
- Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
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4
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Herzog-Arbeitman J, Song ZD, Regnault N, Bernevig BA. Hofstadter Topology: Noncrystalline Topological Materials at High Flux. PHYSICAL REVIEW LETTERS 2020; 125:236804. [PMID: 33337182 DOI: 10.1103/physrevlett.125.236804] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2020] [Accepted: 10/21/2020] [Indexed: 06/12/2023]
Abstract
The Hofstadter problem is the lattice analog of the quantum Hall effect and is the paradigmatic example of topology induced by an applied magnetic field. Conventionally, the Hofstadter problem involves adding ∼10^{4} T magnetic fields to a trivial band structure. In this Letter, we show that when a magnetic field is added to an initially topological band structure, a wealth of possible phases emerges. Remarkably, we find topological phases that cannot be realized in any crystalline insulators. We prove that threading magnetic flux through a Hamiltonian with a nonzero Chern number or mirror Chern number enforces a phase transition at fixed filling and that a 2D Hamiltonian with a nontrivial Kane-Mele invariant can be classified as a 3D topological insulator (TI) or 3D weak TI phase in periodic flux. We then study fragile topology protected by the product of twofold rotation and time reversal and show that there exists a higher order TI phase where corner modes are pumped by flux. We show that a model of twisted bilayer graphene realizes this phase. Our results rely primarily on the magnetic translation group that exists at rational values of the flux. The advent of Moiré lattices renders our work relevant experimentally. Due to the enlarged Moiré unit cell, it is possible for laboratory-strength fields to reach one flux per plaquette and allow access to our proposed Hofstadter topological phase.
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Affiliation(s)
| | - Zhi-Da Song
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Nicolas Regnault
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris 75005, France
| | - B Andrei Bernevig
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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5
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Wang X, Wang H, Chen L, He L, Chen C, Jiang C, Qiu Z, Wang H, Xie X. Weak localization in graphene sandwiched by aligned h-BN flakes. NANOTECHNOLOGY 2020; 31:215712. [PMID: 32038038 DOI: 10.1088/1361-6528/ab7444] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Charge carriers in graphene exhibit distinct characteristics from those in other two-dimensional materials because of their chiral nature. Additionally, multiple Dirac cones that emerge in graphene superlattices have been regarded as an interesting point in condensed-matter physics in recent years. Here, we report an investigation of the magneto-conductance in graphene encapsulated on the top and bottom by aligned h-BN. The bottom h-BN is precisely aligned with graphene, while the top h-BN is rotated a very small angle relative to it. Such a heterostructure could spoil the commensurate state existing in precisely aligned graphene while the giant moiré superlattice remains. A clear signature of weak localization and weak anti-localization is observed at multiple Dirac cones. Both the weak (anti)localization and the universal conductance fluctuations exhibit strong dependencies on the carrier density, temperature and channel length. This artificial heterostructure allows one to explore quantum interference in graphene with a wide spectrum of electronic properties.
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Affiliation(s)
- Xiujun Wang
- State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050, People's Republic of China. Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China. CAS Center for Excellence in Superconducting Electronics (CENSE), Shanghai 200050, People's Republic of China
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6
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Datta B, Adak PC, Shi LK, Watanabe K, Taniguchi T, Song JCW, Deshmukh MM. Nontrivial quantum oscillation geometric phase shift in a trivial band. SCIENCE ADVANCES 2019; 5:eaax6550. [PMID: 31667347 PMCID: PMC6799982 DOI: 10.1126/sciadv.aax6550] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/11/2019] [Accepted: 09/20/2019] [Indexed: 06/10/2023]
Abstract
Quantum oscillations provide a notable visualization of the Fermi surface of metals, including associated geometrical phases such as Berry's phase, that play a central role in topological quantum materials. Here we report the existence of a new quantum oscillation phase shift in a multiband system. In particular, we study the ABA-trilayer graphene, the band structure of which is composed of a weakly gapped linear Dirac band, nested within a quadratic band. We observe that Shubnikov-de Haas (SdH) oscillations of the quadratic band are shifted by a phase that sharply departs from the expected 2π Berry's phase and is inherited from the nontrivial Berry's phase of the linear band. We find this arises due to an unusual filling enforced constraint between the quadratic band and linear band Fermi surfaces. Our work indicates how additional bands can be exploited to tease out the effect of often subtle quantum mechanical geometric phases.
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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
| | - Pratap Chandra Adak
- Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
| | - Li-kun Shi
- Institute of High Performance Computing, Agency for Science, Technology, and Research, Singapore 138632, Singapore
| | - 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
| | - Justin C. W. Song
- Institute of High Performance Computing, Agency for Science, Technology, and Research, Singapore 138632, Singapore
- Division of Physics and Applied Physics, Nanyang Technological University, Singapore 637371, Singapore
| | - 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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7
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Cheng B, Pan C, Che S, Wang P, Wu Y, Watanabe K, Taniguchi T, Ge S, Lake R, Smirnov D, Lau CN, Bockrath M. Fractional and Symmetry-Broken Chern Insulators in Tunable Moiré Superlattices. NANO LETTERS 2019; 19:4321-4326. [PMID: 31204812 DOI: 10.1021/acs.nanolett.9b00811] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We study dual-gated graphene bilayer/hBN moiré superlattices. Under zero magnetic field, we observe additional resistance peaks as the charge density varies. The peaks' resistivities vary approximately quadratically with an applied perpendicular displacement field D. Data fit to a continuum model yield a bilayer/hBN interaction energy scale ∼30 ± 10 meV. Under a perpendicular magnetic field, we observe Hofstadter butterfly spectra as well as symmetry-broken and fractional Chern insulator states. Their topology and lattice symmetry breaking is D-tunable, enabling the realization of new topological states in this system.
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Affiliation(s)
- Bin Cheng
- Department of Physics and Astronomy , University of California , Riverside , California 92521 , United States
| | - Cheng Pan
- Department of Physics and Astronomy , University of California , Riverside , California 92521 , United States
| | - Shi Che
- Department of Physics and Astronomy , University of California , Riverside , California 92521 , United States
- Department of Physics , The Ohio State University , Columbus , Ohio 43221 , United States
| | - Peng Wang
- Department of Physics and Astronomy , University of California , Riverside , California 92521 , United States
| | - Yong Wu
- Department of Physics and Astronomy , University of California , Riverside , California 92521 , United States
| | - Kenji Watanabe
- National Institute for Materials Science , 1-1 Namiki Tsukuba , Ibaraki 305-0044 , Japan
| | - Takashi Taniguchi
- National Institute for Materials Science , 1-1 Namiki Tsukuba , Ibaraki 305-0044 , Japan
| | - Supeng Ge
- Department of Electrical and Computer Engineering , University of California , Riverside , California 92521 , United States
| | - Roger Lake
- Department of Electrical and Computer Engineering , University of California , Riverside , California 92521 , United States
| | - Dmitry Smirnov
- National High Magnetic Field Laboratory , Tallahassee , Florida 32310 , United States
| | - Chun Ning Lau
- Department of Physics , The Ohio State University , Columbus , Ohio 43221 , United States
| | - Marc Bockrath
- Department of Physics , The Ohio State University , Columbus , Ohio 43221 , United States
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8
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Wu Y, Zhai D, Pan C, Cheng B, Taniguchi T, Watanabe K, Sandler N, Bockrath M. Quantum Wires and Waveguides Formed in Graphene by Strain. NANO LETTERS 2018; 18:64-69. [PMID: 29207241 DOI: 10.1021/acs.nanolett.7b03167] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Confinement of electrons in graphene to make devices has proven to be a challenging task. Electrostatic methods fail because of Klein tunneling, while etching into nanoribbons requires extreme control of edge terminations, and bottom-up approaches are limited in size to a few nanometers. Fortunately, its mechanical flexibility raises the possibility of using strain to alter graphene's properties and create novel straintronic devices. Here, we report transport studies of nanowires created by linearly-shaped strained regions resulting from individual folds formed by layer transfer onto hexagonal boron nitride. Conductance measurements across the folds reveal Coulomb blockade signatures, indicating confined charges within these structures, which act as quantum dots. Along folds, we observe sharp features in traverse resistivity measurements, attributed to an amplification of the dot conductance modulations by a resistance bridge incorporating the device. Our data indicates ballistic transport up to ∼1 μm along the folds. Calculations using the Dirac model including strain are consistent with measured bound state energies and predict the existence of valley-polarized currents. Our results show that graphene folds can act as straintronic quantum wires.
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Affiliation(s)
- Y Wu
- Department of Physics and Astronomy, University of California , Riverside, California 92521, United States
| | - D Zhai
- Department of Physics and Astronomy, Ohio University , Athens, Ohio 45701-2979, United States
| | - C Pan
- 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
| | - 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
| | - N Sandler
- Department of Physics and Astronomy, Ohio University , Athens, Ohio 45701-2979, United States
| | - M Bockrath
- Department of Physics, The Ohio State University , Columbus, Ohio 43210, United States
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9
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Handschin C, Makk P, Rickhaus P, Liu MH, Watanabe K, Taniguchi T, Richter K, Schönenberger C. Fabry-Pérot Resonances in a Graphene/hBN Moiré Superlattice. NANO LETTERS 2017; 17:328-333. [PMID: 27960257 DOI: 10.1021/acs.nanolett.6b04137] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
While Fabry-Pérot (FP) resonances and Moiré superlattices are intensively studied in graphene on hexagonal boron nitride (hBN), the two effects have not been discussed in their coexistence. Here we investigate the FP oscillations in a ballistic pnp-junctions in the presence and absence of a Moiré superlattice. First, we address the effect of the smoothness of the confining potential on the visibility of the FP resonances and carefully map the evolution of the FP cavity size as a function of densities inside and outside the cavity in the absence of a superlattice, when the cavity is bound by regular pn-junctions. Using a sample with a Moiré superlattice, we next show that an FP cavity can also be formed by interfaces that mimic a pn-junction but are defined through a satellite Dirac point due to the superlattice. We carefully analyze the FP resonances, which can provide insight into the band-reconstruction due to the superlattice.
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Affiliation(s)
- Clevin Handschin
- Department of Physics, University of Basel , Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Péter Makk
- Department of Physics, University of Basel , Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Peter Rickhaus
- Department of Physics, University of Basel , Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Ming-Hao Liu
- Institut für Theoretische Physik, Universität Regensburg , D-93040 Regensburg, Germany
| | - K Watanabe
- National Institute for Material Science , 1-1 Namiki, Tsukuba 305-0044, Japan
| | - T Taniguchi
- National Institute for Material Science , 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Klaus Richter
- Institut für Theoretische Physik, Universität Regensburg , D-93040 Regensburg, Germany
| | - Christian Schönenberger
- Department of Physics, University of Basel , Klingelbergstrasse 82, CH-4056 Basel, Switzerland
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10
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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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