1
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Ding P, Yan J, Wang J, Han X, Yang W, Chen H, Zhang D, Huang M, Zhao J, Yang S, Xue TT, Liu L, Dai Y, Hou Y, Zhang S, Xu X, Wang Y, Huang Y. Manipulation of Moiré Superlattice in Twisted Monolayer-multilayer Graphene by Moving Nanobubbles. NANO LETTERS 2024; 24:8208-8215. [PMID: 38913825 DOI: 10.1021/acs.nanolett.4c02548] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/26/2024]
Abstract
In the heterostructure of two-dimensional (2D) materials, many novel physics phenomena are strongly dependent on the Moiré superlattice. How to achieve the continuous manipulation of the Moiré superlattice in the same sample is very important to study the evolution of various physical properties. Here, in minimally twisted monolayer-multilayer graphene, we found that bubble-induced strain has a huge impact on the Moiré superlattice. By employing the AFM tip to dynamically and continuously move the nanobubble, we realized the modulation of the Moiré superlattice, like the evolution of regular triangular domains into long strip domain structures with single or double domain walls. We also achieved controllable modulation of the Moiré superlattice by moving multiple nanobubbles and establishing the coupling of nanobubbles. Our work presents a flexible method for continuous and controllable manipulation of Moiré superlattices, which will be widely used to study novel physical properties in 2D heterostructures.
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Affiliation(s)
- Pengfei Ding
- School of Physics, School of Integrated Circuits and Electronics, Beijing Institute of Technology, Advanced Research Institute of Multidisciplinary Sciences, Beijing 100081, China
| | - Jiahao Yan
- School of Physics, School of Integrated Circuits and Electronics, Beijing Institute of Technology, Advanced Research Institute of Multidisciplinary Sciences, Beijing 100081, China
| | - Jiakai Wang
- School of Physics, School of Integrated Circuits and Electronics, Beijing Institute of Technology, Advanced Research Institute of Multidisciplinary Sciences, Beijing 100081, China
| | - Xu Han
- School of Physics, School of Integrated Circuits and Electronics, Beijing Institute of Technology, Advanced Research Institute of Multidisciplinary Sciences, Beijing 100081, China
| | - Wenchen Yang
- School of Physics, School of Integrated Circuits and Electronics, Beijing Institute of Technology, Advanced Research Institute of Multidisciplinary Sciences, Beijing 100081, China
| | - Hui Chen
- School of Physics, School of Integrated Circuits and Electronics, Beijing Institute of Technology, Advanced Research Institute of Multidisciplinary Sciences, Beijing 100081, China
| | - Decheng Zhang
- School of Integrated Circuits and Electronics, MIIT Key Laboratory for Low-Dimensional Quantum Structure and Devices, Beijing Institute of Technology, Beijing 100081, China
| | - Mengting Huang
- School of Integrated Circuits and Electronics, MIIT Key Laboratory for Low-Dimensional Quantum Structure and Devices, Beijing Institute of Technology, Beijing 100081, China
| | - Jinghan Zhao
- School of Physics, School of Integrated Circuits and Electronics, Beijing Institute of Technology, Advanced Research Institute of Multidisciplinary Sciences, Beijing 100081, China
| | - Shiqi Yang
- School of Physics, School of Integrated Circuits and Electronics, Beijing Institute of Technology, Advanced Research Institute of Multidisciplinary Sciences, Beijing 100081, China
| | - Tong-Tong Xue
- School of Integrated Circuits and Electronics, MIIT Key Laboratory for Low-Dimensional Quantum Structure and Devices, Beijing Institute of Technology, Beijing 100081, China
| | - Liwei Liu
- School of Integrated Circuits and Electronics, MIIT Key Laboratory for Low-Dimensional Quantum Structure and Devices, Beijing Institute of Technology, Beijing 100081, China
| | - Yunyun Dai
- School of Physics, School of Integrated Circuits and Electronics, Beijing Institute of Technology, Advanced Research Institute of Multidisciplinary Sciences, Beijing 100081, China
| | - Yuan Hou
- Department of Mechanical Engineering, City University of Hong Kong, Kowloon 999077, Hong Kong SAR, China
| | - Shuai Zhang
- Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - Xiaolong Xu
- School of Physics, School of Integrated Circuits and Electronics, Beijing Institute of Technology, Advanced Research Institute of Multidisciplinary Sciences, Beijing 100081, China
| | - Yeliang Wang
- School of Physics, School of Integrated Circuits and Electronics, Beijing Institute of Technology, Advanced Research Institute of Multidisciplinary Sciences, Beijing 100081, China
- BIT Chongqing Institute of Microelectronics and Microsystems, Chongqing 100190, China
| | - Yuan Huang
- School of Physics, School of Integrated Circuits and Electronics, Beijing Institute of Technology, Advanced Research Institute of Multidisciplinary Sciences, Beijing 100081, China
- BIT Chongqing Institute of Microelectronics and Microsystems, Chongqing 100190, China
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2
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Wang Y, Wang Z, Cao L, Han Y, Peng H, Wang Z, Xue Y, Watanabe K, Taniguchi T, Lu J, Duan J, Gao HJ, Jiang Y, Mao J. Local Gate Enhanced Correlated Phases in Twisted Monolayer-Bilayer Graphene. ACS NANO 2024. [PMID: 38924709 DOI: 10.1021/acsnano.4c02733] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/28/2024]
Abstract
Manipulating the flat band degeneracy and thus getting the correlated insulating phases has been an ideal thread for realizing the exotic quantum phenomenon in the moiré system. To achieve this goal, the delicately tuned twist angle and a substantial displacement field (D) are rigorously requested. Here, we report our scanning tunneling microscope (STM) work on reaching these correlated insulating states in twisted monolayer-bilayer graphene through a decorated tip. It acts as a local top gate, leading to an enhanced local D, and enables us to fully lift the 8-fold degeneracy of the flat bands. With the aid of this technique, we further expand the correlated insulating states into a more tolerant twist angle that is down to 0.92°. Moreover, the correlated insulating phases in the hole-doping regime are realized. Our tip decoration method allows us to integrate the STM study with the high displacement field for the correlated phases in the twisted moiré systems.
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Affiliation(s)
- Yingbo Wang
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Zhengwen Wang
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Lu Cao
- College of Materials Science and Optoelectronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yingzhuo Han
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Huimin Peng
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100086, China
| | - Zhongrui Wang
- College of Materials Science and Optoelectronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yucheng Xue
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Kenji Watanabe
- Research Center for Electronic and Optical 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
| | - Jianming Lu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Junxi Duan
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100086, China
| | - Hong-Jun Gao
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Beijing National Center for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yuhang Jiang
- College of Materials Science and Optoelectronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Jinhai Mao
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
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3
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Shang N, Huang C, Chen Q, Liu C, Yao G, Sun Z, Meng S, Liu K, Hong H. Evidence of abnormal hot carrier thermalization at van Hove singularity of twisted bilayer graphene. Sci Bull (Beijing) 2024:S2095-9273(24)00444-4. [PMID: 38945751 DOI: 10.1016/j.scib.2024.06.019] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2024] [Revised: 04/22/2024] [Accepted: 06/11/2024] [Indexed: 07/02/2024]
Abstract
Interlayer twist evokes revolutionary changes to the optical and electronic properties of twisted bilayer graphene (TBG) for electronics, photonics and optoelectronics. Although the ground state responses in TBG have been vastly and clearly studied, the dynamic process of its photoexcited carrier states mainly remains elusive. Here, we unveil the photoexcited hot carrier dynamics in TBG by time-resolved ultrafast photoluminescence (PL) autocorrelation spectroscopy. We demonstrate the unconventional ultrafast PL emission between the van Hove singularities (VHSs) with a ∼4 times prolonged relaxation lifetime. This intriguing photoexcited carrier behavior is ascribed to the abnormal hot carrier thermalization brought by bottleneck effects at VHSs and interlayer charge distribution process. Our study on hot carrier dynamics in TBG offers new insights into the excited states and correlated physics of graphene twistronics systems.
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Affiliation(s)
- Nianze Shang
- State Key Laboratory for Mesoscopic Physics, Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China; QTF Centre of Excellence, Department of Electronics and Nanoengineering, Aalto University, Espoo 02150, Finland
| | - Chen Huang
- State Key Laboratory for Mesoscopic Physics, Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China
| | - Qing Chen
- Institute of Physics, Chinese Academy of Science, Beijing 100190, China
| | - Chang Liu
- State Key Laboratory for Mesoscopic Physics, Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China
| | - Guangjie Yao
- State Key Laboratory for Mesoscopic Physics, Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China
| | - Zhipei Sun
- QTF Centre of Excellence, Department of Electronics and Nanoengineering, Aalto University, Espoo 02150, Finland
| | - Sheng Meng
- Institute of Physics, Chinese Academy of Science, Beijing 100190, China.
| | - Kaihui Liu
- State Key Laboratory for Mesoscopic Physics, Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China; Songshan Lake Materials Lab, Institute of Physics, Chinese Academy of Sciences, Dongguan 523808, China.
| | - Hao Hong
- State Key Laboratory for Mesoscopic Physics, Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China; Interdisciplinary Institute of Light-Element Quantum Materials and Research Centre for Light- Element Advanced Materials, Peking University, Beijing 100871, China.
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4
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Pu S, Balram AC, Taylor J, Fradkin E, Papić Z. Microscopic Model for Fractional Quantum Hall Nematics. PHYSICAL REVIEW LETTERS 2024; 132:236503. [PMID: 38905694 DOI: 10.1103/physrevlett.132.236503] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2024] [Accepted: 04/25/2024] [Indexed: 06/23/2024]
Abstract
Geometric fluctuations of the density mode in a fractional quantum Hall (FQH) state can give rise to a nematic FQH phase, a topological state with a spontaneously broken rotational symmetry. While experiments on FQH states in the second Landau level have reported signatures of putative FQH nematics in anisotropic transport, a realistic model for this state has been lacking. We show that the standard model of particles in the lowest Landau level interacting via the Coulomb potential realizes the FQH nematic transition, which is reached by a progressive reduction of the strength of the shortest-range Haldane pseudopotential. Using exact diagonalization and variational wave functions, we demonstrate that the FQH nematic transition occurs when the system's neutral gap closes in the long-wavelength limit while the charge gap remains open. We confirm the symmetry-breaking nature of the transition by demonstrating the existence of a "circular moat" potential in the manifold of states with broken rotational symmetry, while its geometric character is revealed through the strong fluctuations of the nematic susceptibility and Hall viscosity.
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Affiliation(s)
| | | | | | - Eduardo Fradkin
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
- Anthony J. Leggett Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
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5
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Bigeard G, Cresti A. Magic-angle twisted bilayer graphene under orthogonal and in-plane magnetic fields. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:325502. [PMID: 38670079 DOI: 10.1088/1361-648x/ad4431] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2024] [Accepted: 04/26/2024] [Indexed: 04/28/2024]
Abstract
We investigate the effect of a magnetic field on the band structure of bilayer graphene with a magic twist angle of 1.08∘. The coupling of a tight-binding model and the Peierls phase allows the calculation of the energy bands of periodic two-dimensional systems. For an orthogonal magnetic field, the Landau levels are dispersive, particularly for magnetic lengths comparable to or larger than the twisted bilayer cell size. A high in-plane magnetic field modifies the low-energy bands and gap, which we demonstrate to be a direct consequence of the minimal coupling.
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Affiliation(s)
- Gaëlle Bigeard
- Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, Grenoble INP, CROMA, 38000 Grenoble, France
| | - Alessandro Cresti
- Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, Grenoble INP, CROMA, 38000 Grenoble, France
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6
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Zhumagulov Y, Kochan D, Fabian J. Emergent Correlated Phases in Rhombohedral Trilayer Graphene Induced by Proximity Spin-Orbit and Exchange Coupling. PHYSICAL REVIEW LETTERS 2024; 132:186401. [PMID: 38759183 DOI: 10.1103/physrevlett.132.186401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2023] [Revised: 11/28/2023] [Accepted: 03/22/2024] [Indexed: 05/19/2024]
Abstract
The impact of proximity-induced spin-orbit and exchange coupling on the correlated phase diagram of rhombohedral trilayer graphene (RTG) is investigated theoretically. By employing ab initio-fitted effective models of RTG encapsulated by transition metal dichalcogenides (spin-orbit proximity effect) and ferromagnetic Cr_{2}Ge_{2}Te_{6} (exchange proximity effect), we incorporate the Coulomb interactions within the random-phase approximation to explore potential correlated phases at different displacement fields and doping. We find a rich spectrum of spin-valley resolved Stoner and intervalley coherence instabilities induced by the spin-orbit proximity effects, such as the emergence of a spin-valley-coherent phase due to the presence of valley-Zeeman coupling. Similarly, proximity exchange removes the phase degeneracies by biasing the spin direction, enabling a magnetocorrelation effect-strong sensitivity of the correlated phases to the relative magnetization orientations (parallel or antiparallel) of the encapsulating ferromagnetic layers.
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Affiliation(s)
- Yaroslav Zhumagulov
- Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany
| | - Denis Kochan
- Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany
- Institute of Physics, Slovak Academy of Sciences, 84511 Bratislava, Slovakia
- Center for Quantum Frontiers of Research and Technology (QFort), National Cheng Kung University, Tainan 70101, Taiwan
| | - Jaroslav Fabian
- Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany
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7
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Li H, Xiang Z, Naik MH, Kim W, Li Z, Sailus R, Banerjee R, Taniguchi T, Watanabe K, Tongay S, Zettl A, da Jornada FH, Louie SG, Crommie MF, Wang F. Imaging moiré excited states with photocurrent tunnelling microscopy. NATURE MATERIALS 2024; 23:633-638. [PMID: 38172545 DOI: 10.1038/s41563-023-01753-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2023] [Accepted: 11/06/2023] [Indexed: 01/05/2024]
Abstract
Moiré superlattices provide a highly tuneable and versatile platform to explore novel quantum phases and exotic excited states ranging from correlated insulators to moiré excitons. Scanning tunnelling microscopy has played a key role in probing microscopic behaviours of the moiré correlated ground states at the atomic scale. However, imaging of quantum excited states in moiré heterostructures remains an outstanding challenge. Here we develop a photocurrent tunnelling microscopy technique that combines laser excitation and scanning tunnelling spectroscopy to directly visualize the electron and hole distribution within the photoexcited moiré exciton in twisted bilayer WS2. The tunnelling photocurrent alternates between positive and negative polarities at different locations within a single moiré unit cell. This alternating photocurrent originates from the in-plane charge transfer moiré exciton in twisted bilayer WS2, predicted by our GW-Bethe-Salpeter equation calculations, that emerges from the competition between the electron-hole Coulomb interaction and the moiré potential landscape. Our technique enables the exploration of photoexcited non-equilibrium moiré phenomena at the atomic scale.
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Affiliation(s)
- Hongyuan Li
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
- Graduate Group in Applied Science and Technology, University of California Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Ziyu Xiang
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
- Graduate Group in Applied Science and Technology, University of California Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Mit H Naik
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Woochang Kim
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Zhenglu Li
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Renee Sailus
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA
| | - Rounak Banerjee
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Sefaattin Tongay
- School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ, USA
| | - Alex Zettl
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
- Kavli Energy Nano Sciences Institute, University of California Berkeley and Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Felipe H da Jornada
- Department of Materials Science and Engineering, Stanford University, Palo Alto, CA, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
| | - Steven G Louie
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA.
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
| | - Michael F Crommie
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA.
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
- Kavli Energy Nano Sciences Institute, University of California Berkeley and Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
| | - Feng Wang
- Department of Physics, University of California at Berkeley, Berkeley, CA, USA.
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
- Kavli Energy Nano Sciences Institute, University of California Berkeley and Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
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8
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Cortés-Del Río E, Trivini S, Pascual JI, Cherkez V, Mallet P, Veuillen JY, Cuevas JC, Brihuega I. Shaping Graphene Superconductivity with Nanometer Precision. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2024; 20:e2308439. [PMID: 38112230 DOI: 10.1002/smll.202308439] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2023] [Revised: 11/23/2023] [Indexed: 12/21/2023]
Abstract
Graphene holds great potential for superconductivity due to its pure 2D nature, the ability to tune its carrier density through electrostatic gating, and its unique, relativistic-like electronic properties. At present, still far from controlling and understanding graphene superconductivity, mainly because the selective introduction of superconducting properties to graphene is experimentally very challenging. Here, a method is developed that enables shaping at will graphene superconductivity through a precise control of graphene-superconductor junctions. The method combines the proximity effect with scanning tunnelling microscope (STM) manipulation capabilities. Pb nano-islands are first grown that locally induce superconductivity in graphene. Using a STM, Pb nano-islands can be selectively displaced, over different types of graphene surfaces, with nanometre scale precision, in any direction, over distances of hundreds of nanometres. This opens an exciting playground where a large number of predefined graphene-superconductor hybrid structures can be investigated with atomic scale precision. To illustrate the potential, a series of experiments are performed, rationalized by the quasi-classical theory of superconductivity, going from the fundamental understanding of superconductor-graphene-superconductor heterostructures to the construction of superconductor nanocorrals, further used as "portable" experimental probes of local magnetic moments in graphene.
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Affiliation(s)
- Eva Cortés-Del Río
- Departamento Física de la Materia Condensada, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, E-28049, Spain
| | | | - José I Pascual
- CIC nanoGUNE-BRTA, Donostia-San Sebastián, 20018, Spain
- Ikerbasque, Basque Foundation for Science, Bilbao, 48013, Spain
| | - Vladimir Cherkez
- Université Grenoble Alpes, CNRS, Institut Néel, Grenoble, F-38400, France
- CNRS, Institut Neel, Grenoble, F-38042, France
| | - Pierre Mallet
- Université Grenoble Alpes, CNRS, Institut Néel, Grenoble, F-38400, France
- CNRS, Institut Neel, Grenoble, F-38042, France
| | - Jean-Yves Veuillen
- Université Grenoble Alpes, CNRS, Institut Néel, Grenoble, F-38400, France
- CNRS, Institut Neel, Grenoble, F-38042, France
| | - Juan C Cuevas
- Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Departamento Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
| | - Iván Brihuega
- Departamento Física de la Materia Condensada, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
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9
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Li Q, Zhang H, Wang Y, Chen W, Bao C, Liu Q, Lin T, Zhang S, Zhang H, Watanabe K, Taniguchi T, Avila J, Dudin P, Li Q, Yu P, Duan W, Song Z, Zhou S. Evolution of the flat band and the role of lattice relaxations in twisted bilayer graphene. NATURE MATERIALS 2024:10.1038/s41563-024-01858-4. [PMID: 38658674 DOI: 10.1038/s41563-024-01858-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2023] [Accepted: 03/11/2024] [Indexed: 04/26/2024]
Abstract
Magic-angle twisted bilayer graphene exhibits correlated phenomena such as superconductivity and Mott insulating states related to the weakly dispersing flat band near the Fermi energy. Such a flat band is expected to be sensitive to both the moiré period and lattice relaxations. Thus, clarifying the evolution of the electronic structure with the twist angle is critical for understanding the physics of magic-angle twisted bilayer graphene. Here we combine nano-spot angle-resolved photoemission spectroscopy and atomic force microscopy to resolve the fine electronic structure of the flat band and remote bands, as well as their evolution with twist angle from 1.07° to 2.60°. Near the magic angle, the dispersion is characterized by a flat band near the Fermi energy with a strongly reduced band width. Moreover, we observe a spectral weight transfer between remote bands at higher binding energy, which allows to extract the modulated interlayer spacing near the magic angle. Our work provides direct spectroscopic information on flat band physics and highlights the important role of lattice relaxations.
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Affiliation(s)
- Qian Li
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, People's Republic of China
| | - Hongyun Zhang
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, People's Republic of China
| | - Yijie Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing, People's Republic of China
| | - Wanying Chen
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, People's Republic of China
| | - Changhua Bao
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, People's Republic of China
| | - Qinxin Liu
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, People's Republic of China
| | - Tianyun Lin
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, People's Republic of China
| | - Shuai Zhang
- AML, CNMM, Department of Engineering Mechanics, Tsinghua University, Beijing, People's Republic of China
| | - Haoxiong Zhang
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, People's Republic of China
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Jose Avila
- Synchrotron SOLEIL, L'Orme des Merisiers, Gif sur Yvette, France
| | - Pavel Dudin
- Synchrotron SOLEIL, L'Orme des Merisiers, Gif sur Yvette, France
| | - Qunyang Li
- AML, CNMM, Department of Engineering Mechanics, Tsinghua University, Beijing, People's Republic of China
| | - Pu Yu
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, People's Republic of China
- Frontier Science Center for Quantum Information, Beijing, People's Republic of China
| | - Wenhui Duan
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, People's Republic of China
- Frontier Science Center for Quantum Information, Beijing, People's Republic of China
- Institute for Advanced Study, Tsinghua University, Beijing, People's Republic of China
| | - Zhida Song
- International Center for Quantum Materials, School of Physics, Peking University, Beijing, People's Republic of China
| | - Shuyun Zhou
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, People's Republic of China.
- Frontier Science Center for Quantum Information, Beijing, People's Republic of China.
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10
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Hou Y, Zhou J, Xue M, Yu M, Han Y, Zhang Z, Lu Y. Strain Engineering of Twisted Bilayer Graphene: The Rise of Strain-Twistronics. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2024:e2311185. [PMID: 38616775 DOI: 10.1002/smll.202311185] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2023] [Revised: 03/24/2024] [Indexed: 04/16/2024]
Abstract
The layer-by-layer stacked van der Waals structures (termed vdW hetero/homostructures) offer a new paradigm for materials design-their physical properties can be tuned by the vertical stacking sequence as well as by adding a mechanical twist, stretch, and hydrostatic pressure to the atomic structure. In particular, simple twisting and stacking of two layers of graphene can form a uniform and ordered Moiré superlattice, which can effectively modulate the electrons of graphene layers and lead to the discovery of unconventional superconductivity and strong correlations. However, the twist angle of twisted bilayer graphene (tBLG) is almost unchangeable once the interlayer stacking is determined, while applying mechanical elastic strain provides an alternative way to deeply regulate the electronic structure by controlling the lattice spacing and symmetry. In this review, diverse experimental advances are introduced in straining tBLG by in-plane and out-of-plane modes, followed by the characterizations and calculations toward quantitatively tuning the strain-engineered electronic structures. It is further discussed that the structural relaxation in strained Moiré superlattice and its influence on electronic structures. Finally, the conclusion entails prospects for opportunities of strained twisted 2D materials, discussions on existing challenges, and an outlook on the intriguing emerging field, namely "strain-twistronics".
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Affiliation(s)
- Yuan Hou
- Department of Mechanical Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, 999077, China
| | - Jingzhuo Zhou
- Department of Mechanical Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, 999077, China
| | - Minmin Xue
- Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education, State Key Laboratory of Mechanics and Control of Mechanical Structures, and Institute for Frontier Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China
| | - Maolin Yu
- Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education, State Key Laboratory of Mechanics and Control of Mechanical Structures, and Institute for Frontier Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China
| | - Ying Han
- Department of Mechanical Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, 999077, China
| | - Zhuhua Zhang
- Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education, State Key Laboratory of Mechanics and Control of Mechanical Structures, and Institute for Frontier Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China
| | - Yang Lu
- Department of Mechanical Engineering, The University of Hong Kong, Pokfulam, Hong Kong, Hong Kong SAR, 999077, China
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11
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Li K, Yin LJ, Che C, Zhang S, Liu X, Xiao Y, Liu S, Tong Q, Li SY, Pan A. Correlation-Induced Symmetry-Broken States in Large-Angle Twisted Bilayer Graphene on MoS 2. ACS NANO 2024; 18:7937-7944. [PMID: 38441035 DOI: 10.1021/acsnano.3c09993] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/06/2024]
Abstract
Strongly correlated states commonly emerge in twisted bilayer graphene (TBG) with "magic-angle" (1.1°), where the electron-electron (e-e) interaction U becomes prominent relative to the small bandwidth W of the nearly flat band. However, the stringent requirement of this magic angle makes the sample preparation and the further application facing great challenges. Here, using scanning tunneling microscopy (STM) and spectroscopy (STS), we demonstrate that the correlation-induced symmetry-broken states can also be achieved in a 3.45° TBG, via engineering this nonmagic-angle TBG into regimes of U/W > 1. We enhance the e-e interaction through controlling the microscopic dielectric environment by using a MoS2 substrate. Simultaneously, the width of the low-energy van Hove singularity (VHS) peak is reduced by enhancing the interlayer coupling via STM tip modulation. When partially filled, the VHS peak exhibits a giant splitting into two states flanked by the Fermi level and shows a symmetry-broken LDOS distribution with a stripy charge order, which confirms the existence of strong correlation effect in our 3.45° TBG. Our result demonstrates the feasibility of the study and application of the correlation physics in TBGs with a wider range of twist angle.
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Affiliation(s)
- Kaihui Li
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, Hunan Institute of Optoelectronic Integration and College of Materials Science and Engineering, Hunan University, Changsha 410082, People's Republic of China
| | - Long-Jing Yin
- School of Physics and Electronics, Hunan University, Changsha 410082, People's Republic of China
| | - Chenglong Che
- School of Physics and Electronics, Hunan University, Changsha 410082, People's Republic of China
| | - Shihao Zhang
- School of Physics and Electronics, Hunan University, Changsha 410082, People's Republic of China
| | - Xueying Liu
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, Hunan Institute of Optoelectronic Integration and College of Materials Science and Engineering, Hunan University, Changsha 410082, People's Republic of China
| | - Yulong Xiao
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, Hunan Institute of Optoelectronic Integration and College of Materials Science and Engineering, Hunan University, Changsha 410082, People's Republic of China
| | - Songlong Liu
- School of Physics and Electronics, Hunan University, Changsha 410082, People's Republic of China
| | - Qingjun Tong
- School of Physics and Electronics, Hunan University, Changsha 410082, People's Republic of China
| | - Si-Yu Li
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, Hunan Institute of Optoelectronic Integration and College of Materials Science and Engineering, Hunan University, Changsha 410082, People's Republic of China
- Greater Bay Area Institute for Innovation, Hunan University, Guangzhou 511300, People's Republic of China
| | - Anlian Pan
- Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, Hunan Institute of Optoelectronic Integration and College of Materials Science and Engineering, Hunan University, Changsha 410082, People's Republic of China
- School of Physics and Electronics, Hunan Normal University, Changsha 410081, People's Republic of China
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12
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Wang J, Cheng F, Sun Y, Xu H, Cao L. Stacking engineering in layered homostructures: transitioning from 2D to 3D architectures. Phys Chem Chem Phys 2024; 26:7988-8012. [PMID: 38380525 DOI: 10.1039/d3cp04656g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/22/2024]
Abstract
Artificial materials, characterized by their distinctive properties and customized functionalities, occupy a central role in a wide range of applications including electronics, spintronics, optoelectronics, catalysis, and energy storage. The emergence of atomically thin two-dimensional (2D) materials has driven the creation of artificial heterostructures, harnessing the potential of combining various 2D building blocks with complementary properties through the art of stacking engineering. The promising outcomes achieved for heterostructures have spurred an inquisitive exploration of homostructures, where identical 2D layers are precisely stacked. This perspective primarily focuses on the field of stacking engineering within layered homostructures, where precise control over translational or rotational degrees of freedom between vertically stacked planes or layers is paramount. In particular, we provide an overview of recent advancements in the stacking engineering applied to 2D homostructures. Additionally, we will shed light on research endeavors venturing into three-dimensional (3D) structures, which allow us to proactively address the limitations associated with artificial 2D homostructures. We anticipate that the breakthroughs in stacking engineering in 3D materials will provide valuable insights into the mechanisms governing stacking effects. Such advancements have the potential to unlock the full capability of artificial layered homostructures, propelling the future development of materials, physics, and device applications.
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Affiliation(s)
- Jiamin Wang
- Changchun Institute of Optics, Fine Mechanics & Physics (CIOMP), Chinese Academy of Sciences, Changchun 130033, P. R. China.
- University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100049, P. R. China
| | - Fang Cheng
- State Key Laboratory for Organic Electronics and Information Displays & Jiangsu Key Laboratory for Biosensors, Institute of Advanced Materials (IAM), Jiangsu National Synergetic Innovation Center for Advanced Materials (SICAM), Nanjing University of Posts and Telecommunications, Nanjing 210023, P. R. China
| | - Yan Sun
- Institutes of Physical Science and Information Technology, Anhui University, Hefei 230601, P. R. China.
| | - Hai Xu
- Changchun Institute of Optics, Fine Mechanics & Physics (CIOMP), Chinese Academy of Sciences, Changchun 130033, P. R. China.
- University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100049, P. R. China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, P. R. China
| | - Liang Cao
- Anhui Key Laboratory of Low-Energy Quantum Materials and Devices, High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences, Hefei 230031, P. R. China.
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13
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Luo R, Zhou W. Unveiling the intricate moiré of moiré texture. NATURE MATERIALS 2024; 23:304-305. [PMID: 38438617 DOI: 10.1038/s41563-024-01805-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/06/2024]
Affiliation(s)
- Ruichun Luo
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China
| | - Wu Zhou
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China.
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14
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Zhang NJ, Lin JX, Chichinadze DV, Wang Y, Watanabe K, Taniguchi T, Fu L, Li JIA. Angle-resolved transport non-reciprocity and spontaneous symmetry breaking in twisted trilayer graphene. NATURE MATERIALS 2024; 23:356-362. [PMID: 38388731 DOI: 10.1038/s41563-024-01809-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2023] [Accepted: 01/16/2024] [Indexed: 02/24/2024]
Abstract
The identification and characterization of spontaneous symmetry breaking is central to our understanding of strongly correlated two-dimensional materials. In this work, we utilize the angle-resolved measurements of transport non-reciprocity to investigate spontaneous symmetry breaking in twisted trilayer graphene. By analysing the angular dependence of non-reciprocity in both longitudinal and transverse channels, we are able to identify the symmetry axis associated with the underlying electronic order. We report that a hysteretic rotation in the mirror axis can be induced by thermal cycles and a large current bias, supporting the spontaneous breaking of rotational symmetry. Moreover, the onset of non-reciprocity with decreasing temperature coincides with the emergence of orbital ferromagnetism. Combined with the angular dependence of the superconducting diode effect, our findings uncover a direct link between rotational and time-reversal symmetry breaking. These symmetry requirements point towards exchange-driven instabilities in momentum space as a possible origin for transport non-reciprocity in twisted trilayer graphene.
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Affiliation(s)
| | - Jiang-Xiazi Lin
- Department of Physics, Brown University, Providence, RI, USA
| | | | - Yibang Wang
- Department of Physics, Brown University, Providence, RI, USA
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - J I A Li
- Department of Physics, Brown University, Providence, RI, USA.
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15
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Lu X, Xie B, Yang Y, Zhang Y, Kong X, Li J, Ding F, Wang ZJ, Liu J. Magic Momenta and Three-Dimensional Landau Levels from a Three-Dimensional Graphite Moiré Superlattice. PHYSICAL REVIEW LETTERS 2024; 132:056601. [PMID: 38364175 DOI: 10.1103/physrevlett.132.056601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2023] [Revised: 11/17/2023] [Accepted: 01/04/2024] [Indexed: 02/18/2024]
Abstract
In this Letter, we theoretically explore the physical properties of a new type of three-dimensional graphite moiré superlattice, the bulk alternating twisted graphite (ATG) system with homogeneous twist angle, which is grown by in situ chemical vapor decomposition method. Compared to twisted bilayer graphene (TBG), the bulk ATG system is bestowed with an additional wave vector degree of freedom due to the extra dimensionality. As a result, when the twist angle of bulk ATG is smaller than twice of the magic angle of TBG, there always exist "magic momenta" which host topological flat bands with vanishing in-plane Fermi velocities. Most saliently, when the twist angle is relatively large, a dispersionless three-dimensional zeroth Landau level would emerge in the bulk ATG, which may give rise to robust three-dimensional quantum Hall effects and unusual quantum-Hall physics over a large range of twist angles.
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Affiliation(s)
- Xin Lu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 201210, China
| | - Bo Xie
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 201210, China
| | - Yue Yang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
| | - Yiwen Zhang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 201210, China
| | - Xiao Kong
- Institute of Technology for Carbon Neutrality, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
- Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai, China
| | - Jun Li
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 201210, China
| | - Feng Ding
- Institute of Technology for Carbon Neutrality, Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China
- Faculty of Materials Science and Energy Engineering, Shenzhen University of Advanced Technology, Shenzhen, China
| | - Zhu-Jun Wang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
| | - Jianpeng Liu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 201210, China
- Liaoning Academy of Materials, Shenyang 110167, China
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16
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Pandey V, Mishra S, Maity N, Paul S, B AM, Roy AK, Glavin NR, Watanabe K, Taniguchi T, Singh AK, Kochat V. Probing Interlayer Interactions and Commensurate-Incommensurate Transition in Twisted Bilayer Graphene through Raman Spectroscopy. ACS NANO 2024. [PMID: 38295130 DOI: 10.1021/acsnano.3c08344] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/02/2024]
Abstract
Twisted 2D layered materials have garnered much attention recently as a class of 2D materials whose interlayer interactions and electronic properties are dictated by the relative rotation/twist angle between the adjacent layers. In this work, we explore a prototype of such a twisted 2D system, artificially stacked twisted bilayer graphene (TBLG), where we probe, using Raman spectroscopy, the changes in the interlayer interactions and electron-phonon scattering pathways as the twist angle is varied from 0° to 30°. The long-range Moiré potential of the superlattice gives rise to additional intravalley and intervalley scattering of the electrons in TBLG, which has been investigated through their Raman signatures. Density functional theory (DFT) calculations of the electronic band structure of the TBLG superlattices were found to be in agreement with the resonant Raman excitations across the van Hove singularities in the valence and conduction bands predicted for TBLG due to hybridization of bands from the two layers. We also observe that the relative rotation between the graphene layers has a marked influence on the second order overtone and combination Raman modes signaling a commensurate-incommensurate transition in TBLG as the twist angle increases. This serves as a convenient and rapid characterization tool to determine the degree of commensurability in TBLG systems.
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Affiliation(s)
- Vineet Pandey
- Materials Science Centre, Indian Institute of Technology, Kharagpur, West Bengal 721302, India
| | - Subhendu Mishra
- Materials Research Centre, Indian Institute of Science, Bengaluru 560012, India
| | - Nikhilesh Maity
- Materials Research Centre, Indian Institute of Science, Bengaluru 560012, India
| | - Sourav Paul
- Materials Science Centre, Indian Institute of Technology, Kharagpur, West Bengal 721302, India
| | - Abhijith M B
- Materials Science Centre, Indian Institute of Technology, Kharagpur, West Bengal 721302, India
| | - Ajit K Roy
- Air Force Research Laboratory, Wright-Patterson Air Force Base, Dayton, Ohio 45433, United States
| | - Nicholas R Glavin
- Air Force Research Laboratory, Wright-Patterson Air Force Base, Dayton, Ohio 45433, United States
| | - Kenji Watanabe
- Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Abhishek K Singh
- Materials Research Centre, Indian Institute of Science, Bengaluru 560012, India
| | - Vidya Kochat
- Materials Science Centre, Indian Institute of Technology, Kharagpur, West Bengal 721302, India
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17
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Banerjee S, Scheurer MS. Enhanced Superconducting Diode Effect due to Coexisting Phases. PHYSICAL REVIEW LETTERS 2024; 132:046003. [PMID: 38335356 DOI: 10.1103/physrevlett.132.046003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2023] [Accepted: 12/14/2023] [Indexed: 02/12/2024]
Abstract
The superconducting diode effect refers to an asymmetry in the critical supercurrent J_{c}(n[over ^]) along opposite directions, J_{c}(n[over ^])≠J_{c}(-n[over ^]). While the basic symmetry requirements for this effect are known, it is, for junction-free systems, difficult to capture within current theoretical models the large current asymmetries J_{c}(n[over ^])/J_{c}(-n[over ^]) recently observed in experiment. We here propose and develop a theory for an enhancement mechanism of the diode effect arising from spontaneous symmetry breaking. We show-both within a phenomenological and a microscopic theory-that there is a coupling of the supercurrent and the underlying symmetry-breaking order parameter. This coupling can enhance the current asymmetry significantly. Our work might not only provide a possible explanation for recent experiments on trilayer graphene but also pave the way for future realizations of the superconducting diode effect with large current asymmetries.
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Affiliation(s)
- Sayan Banerjee
- Institute for Theoretical Physics III, University of Stuttgart, 70550 Stuttgart, Germany and Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria
| | - Mathias S Scheurer
- Institute for Theoretical Physics III, University of Stuttgart, 70550 Stuttgart, Germany and Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria
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18
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Bocarsly M, Uzan M, Roy I, Grover S, Xiao J, Dong Z, Labendik M, Uri A, Huber ME, Myasoedov Y, Watanabe K, Taniguchi T, Yan B, Levitov LS, Zeldov E. De Haas-van Alphen spectroscopy and magnetic breakdown in moiré graphene. Science 2024; 383:42-48. [PMID: 38175887 DOI: 10.1126/science.adh3499] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2023] [Accepted: 11/23/2023] [Indexed: 01/06/2024]
Abstract
Quantum oscillations originating from the quantization of electron cyclotron orbits provide sensitive diagnostics of electron bands and interactions. We report on nanoscale imaging of the thermodynamic magnetization oscillations caused by the de Haas-van Alphen effect in moiré graphene. Scanning by means of superconducting quantum interference device (SQUID)-on-tip in Bernal bilayer graphene crystal axis-aligned to hexagonal boron nitride reveals large magnetization oscillations with amplitudes reaching 500 Bohr magneton per electron in weak magnetic fields, unexpectedly low frequencies, and high sensitivity to superlattice filling fraction. The oscillations allow us to reconstruct the complex band structure, revealing narrow moiré bands with multiple overlapping Fermi surfaces separated by unusually small momentum gaps. We identified sets of oscillations that violate the textbook Onsager Fermi surface sum rule, signaling formation of broad-band particle-hole superposition states induced by coherent magnetic breakdown.
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Affiliation(s)
- Matan Bocarsly
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Matan Uzan
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Indranil Roy
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Sameer Grover
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Jiewen Xiao
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Zhiyu Dong
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Mikhail Labendik
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Aviram Uri
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Martin E Huber
- Departments of Physics and Electrical Engineering, University of Colorado Denver, Denver, CO 80217, USA
| | - Yuri Myasoedov
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - 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
| | - Binghai Yan
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Leonid S Levitov
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Eli Zeldov
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
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19
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Naumis GG, Herrera SA, Poudel SP, Nakamura H, Barraza-Lopez S. Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2023; 87:016502. [PMID: 37879327 DOI: 10.1088/1361-6633/ad06db] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2023] [Accepted: 10/25/2023] [Indexed: 10/27/2023]
Abstract
This is an update of a previous review (Naumiset al2017Rep. Prog. Phys.80096501). Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials were considered. We surveyed (i) methods to induce valley and sublattice polarisation (P) in graphene, (ii) time-dependent strain and its impact on graphene's electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, (iv) inducing polarisationPon hexagonal boron nitride monolayers via strain, (v) modifying the optoelectronic properties of transition metal dichalcogenide monolayers through strain, (vi) ferroic 2D materials with intrinsic elastic (σ), electric (P) and magnetic (M) polarisation under strain, as well as incipient 2D multiferroics and (vii) moiré bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The update features the experimental realisations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of elemental 2D ferroelectric bismuth, and 2D multiferroic NiI2. The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents an up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.
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Affiliation(s)
- Gerardo G Naumis
- Departamento de Sistemas Complejos, Instituto de Física, Universidad Nacional Autónoma de México (UNAM), Apdo. Postal 20-364, CDMX, 01000, Mexico
| | - Saúl A Herrera
- Departamento de Sistemas Complejos, Instituto de Física, Universidad Nacional Autónoma de México (UNAM), Apdo. Postal 20-364, CDMX, 01000, Mexico
| | - Shiva P Poudel
- Department of Physics, University of Arkansas, Fayetteville, AR 72701, United States of America
- MonArk NSF Quantum Foundry, University of Arkansas, Fayetteville, AR 72701, United States of America
| | - Hiro Nakamura
- Department of Physics, University of Arkansas, Fayetteville, AR 72701, United States of America
- MonArk NSF Quantum Foundry, University of Arkansas, Fayetteville, AR 72701, United States of America
| | - Salvador Barraza-Lopez
- Department of Physics, University of Arkansas, Fayetteville, AR 72701, United States of America
- MonArk NSF Quantum Foundry, University of Arkansas, Fayetteville, AR 72701, United States of America
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20
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Kim H, Choi Y, Lantagne-Hurtubise É, Lewandowski C, Thomson A, Kong L, Zhou H, Baum E, Zhang Y, Holleis L, Watanabe K, Taniguchi T, Young AF, Alicea J, Nadj-Perge S. Imaging inter-valley coherent order in magic-angle twisted trilayer graphene. Nature 2023; 623:942-948. [PMID: 37968401 DOI: 10.1038/s41586-023-06663-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Accepted: 09/21/2023] [Indexed: 11/17/2023]
Abstract
Magic-angle twisted trilayer graphene (MATTG) exhibits a range of strongly correlated electronic phases that spontaneously break its underlying symmetries1,2. Here we investigate the correlated phases of MATTG using scanning tunnelling microscopy and identify marked signatures of interaction-driven spatial symmetry breaking. In low-strain samples, over a filling range of about two to three electrons or holes per moiré unit cell, we observe atomic-scale reconstruction of the graphene lattice that accompanies a correlated gap in the tunnelling spectrum. This short-scale restructuring appears as a Kekulé supercell-implying spontaneous inter-valley coherence between electrons-and persists in a wide range of magnetic fields and temperatures that coincide with the development of the gap. Large-scale maps covering several moiré unit cells further reveal a slow evolution of the Kekulé pattern, indicating that atomic-scale reconstruction coexists with translation symmetry breaking at a much longer moiré scale. We use auto-correlation and Fourier analyses to extract the intrinsic periodicity of these phases and find that they are consistent with the theoretically proposed incommensurate Kekulé spiral order3,4. Moreover, we find that the wavelength characterizing moiré-scale modulations monotonically decreases with hole doping away from half-filling of the bands and depends weakly on the magnetic field. Our results provide essential insights into the nature of the correlated phases of MATTG in the presence of strain and indicate that superconductivity can emerge from an inter-valley coherent parent state.
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Affiliation(s)
- Hyunjin Kim
- Thomas J. Watson, Sr, Laboratories of Applied Physics, California Institute of Technology, Pasadena, CA, USA.
- Department of Physics, California Institute of Technology, Pasadena, CA, USA.
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA.
| | - Youngjoon Choi
- Department of Physics, University of California, Santa Barbara, Santa Barbara, CA, USA
| | - Étienne Lantagne-Hurtubise
- Department of Physics, California Institute of Technology, Pasadena, CA, USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA
| | - Cyprian Lewandowski
- Department of Physics, California Institute of Technology, Pasadena, CA, USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA
- National High Magnetic Field Laboratory, Tallahassee, FL, USA
- Department of Physics, Florida State University, Tallahassee, FL, USA
| | - Alex Thomson
- Department of Physics, California Institute of Technology, Pasadena, CA, USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA, USA
- Department of Physics, University of California, Davis, Davis, CA, USA
| | - Lingyuan Kong
- Thomas J. Watson, Sr, Laboratories of Applied Physics, California Institute of Technology, Pasadena, CA, USA
- Department of Physics, California Institute of Technology, Pasadena, CA, USA
| | - Haoxin Zhou
- Thomas J. Watson, Sr, Laboratories of Applied Physics, California Institute of Technology, Pasadena, CA, USA
- Department of Physics, California Institute of Technology, Pasadena, CA, USA
| | - Eli Baum
- Thomas J. Watson, Sr, Laboratories of Applied Physics, California Institute of Technology, Pasadena, CA, USA
- Department of Physics, California Institute of Technology, Pasadena, CA, USA
| | - Yiran Zhang
- Thomas J. Watson, Sr, Laboratories of Applied Physics, California Institute of Technology, Pasadena, CA, USA
- Department of Physics, California Institute of Technology, Pasadena, CA, USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA
| | - Ludwig Holleis
- Department of Physics, University of California, Santa Barbara, Santa Barbara, CA, USA
| | - Kenji Watanabe
- Department of Physics, University of California, Davis, Davis, CA, USA
| | | | - Andrea F Young
- National Institute for Materials Science, Tsukuba, Ibaraki, Japan
| | - Jason Alicea
- Department of Physics, California Institute of Technology, Pasadena, CA, USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA, USA
| | - Stevan Nadj-Perge
- Thomas J. Watson, Sr, Laboratories of Applied Physics, California Institute of Technology, Pasadena, CA, USA.
- Department of Physics, California Institute of Technology, Pasadena, CA, USA.
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21
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Wang S, Song J, Sun M, Cao S. Emerging Characteristics and Properties of Moiré Materials. NANOMATERIALS (BASEL, SWITZERLAND) 2023; 13:2881. [PMID: 37947726 PMCID: PMC10649551 DOI: 10.3390/nano13212881] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2023] [Revised: 10/26/2023] [Accepted: 10/29/2023] [Indexed: 11/12/2023]
Abstract
In recent years, scientists have conducted extensive research on Moiré materials and have discovered some compelling properties. The Moiré superlattice allows superconductivity through flat-band and strong correlation effects. The presence of flat bands causes the Moiré material to exhibit topological properties as well. Modulating electronic interactions with magnetic fields in Moiré materials enables the fractional quantum Hall effect. In addition, Moiré materials have ferromagnetic and antiferromagnetic properties. By tuning the interlayer coupling and spin interactions of the Moiré superlattice, different magnetic properties can be achieved. Finally, this review also discusses the applications of Moiré materials in the fields of photocurrent, superconductivity, and thermoelectricity. Overall, Moiré superlattices provide a new dimension in the development of two-dimensional materials.
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Affiliation(s)
- Shaofeng Wang
- School of Physics, Liaoning University, Shenyang 110036, China
| | - Jizhe Song
- School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;
| | - Mengtao Sun
- School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;
| | - Shuo Cao
- School of Physics, Liaoning University, Shenyang 110036, China
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22
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Hu H, Rai G, Crippa L, Herzog-Arbeitman J, Călugăru D, Wehling T, Sangiovanni G, Valentí R, Tsvelik AM, Bernevig BA. Symmetric Kondo Lattice States in Doped Strained Twisted Bilayer Graphene. PHYSICAL REVIEW LETTERS 2023; 131:166501. [PMID: 37925696 DOI: 10.1103/physrevlett.131.166501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2023] [Accepted: 09/11/2023] [Indexed: 11/07/2023]
Abstract
We use the topological heavy fermion (THF) model and its Kondo lattice (KL) formulation to study the possibility of a symmetric Kondo (SK) state in twisted bilayer graphene. Via a large-N approximation, we find a SK state in the KL model at fillings ν=0,±1,±2 where a KL model can be constructed. In the SK state, all symmetries are preserved and the local moments are Kondo screened by the conduction electrons. At the mean-field level of the THF model at ν=0,±1,±2,±3 we also find a similar symmetric state that is adiabatically connected to the symmetric Kondo state. We study the stability of the symmetric state by comparing its energy with the ordered (symmetry-breaking) states found in [H. Hu et al., Phys. Rev. Lett. 131, 026502 (2023).PRLTAO0031-900710.1103/PhysRevLett.131.026502, Z.-D. Song and B. A. Bernevig, Phys. Rev. Lett. 129, 047601 (2022).PRLTAO0031-900710.1103/PhysRevLett.129.047601] and find the ordered states to have lower energy at ν=0,±1,±2. However, moving away from integer fillings by doping the light bands, our mean-field calculations find the energy difference between the ordered state and the symmetric state to be reduced, which suggests the loss of ordering and a tendency toward Kondo screening. In order to include many-body effects beyond the mean-field approximation, we also performed dynamical mean-field theory calculations on the THF model in the nonordered phase. The spin susceptibility follows a Curie behavior at ν=0,±1,±2 down to ∼2 K where the onset of screening of the local moment becomes visible. This hints to very low Kondo temperatures at these fillings, in agreement with the outcome of our mean-field calculations. At noninteger filling ν=±0.5,±0.8,±1.2 dynamical mean-field theory shows deviations from a 1/T susceptibility at much higher temperatures, suggesting a more effective screening of local moments with doping. Finally, we study the effect of a C_{3z}-rotational-symmetry-breaking strain via mean-field approaches and find that a symmetric phase (that only breaks C_{3z} symmetry) can be stabilized at sufficiently large strain at ν=0,±1,±2. Our results suggest that a symmetric Kondo phase is strongly suppressed at integer fillings, but could be stabilized either at noninteger fillings or by applying strain.
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Affiliation(s)
- Haoyu Hu
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastian, Spain
| | - Gautam Rai
- I. Institute of Theoretical Physics, University of Hamburg, Notkestrasse 9, 22607 Hamburg, Germany
| | - Lorenzo Crippa
- Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, 97074 Würzburg, Germany
| | | | - Dumitru Călugăru
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Tim Wehling
- I. Institute of Theoretical Physics, University of Hamburg, Notkestrasse 9, 22607 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, 22761 Hamburg, Germany
| | - Giorgio Sangiovanni
- Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, 97074 Würzburg, Germany
| | - Roser Valentí
- Institut für Theoretische Physik, Goethe Universität Frankfurt, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
| | - Alexei M Tsvelik
- Division of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
| | - B Andrei Bernevig
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastian, Spain
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- IKERBASQUE, Basque Foundation for Science, Bilbao 48009, Spain
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23
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Kim D, Pandey J, Jeong J, Cho W, Lee S, Cho S, Yang H. Phase Engineering of 2D Materials. Chem Rev 2023; 123:11230-11268. [PMID: 37589590 DOI: 10.1021/acs.chemrev.3c00132] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/18/2023]
Abstract
Polymorphic 2D materials allow structural and electronic phase engineering, which can be used to realize energy-efficient, cost-effective, and scalable device applications. The phase engineering covers not only conventional structural and metal-insulator transitions but also magnetic states, strongly correlated band structures, and topological phases in rich 2D materials. The methods used for the local phase engineering of 2D materials include various optical, geometrical, and chemical processes as well as traditional thermodynamic approaches. In this Review, we survey the precise manipulation of local phases and phase patterning of 2D materials, particularly with ideal and versatile phase interfaces for electronic and energy device applications. Polymorphic 2D materials and diverse quantum materials with their layered, vertical, and lateral geometries are discussed with an emphasis on the role and use of their phase interfaces. Various phase interfaces have demonstrated superior and unique performance in electronic and energy devices. The phase patterning leads to novel homo- and heterojunction structures of 2D materials with low-dimensional phase boundaries, which highlights their potential for technological breakthroughs in future electronic, quantum, and energy devices. Accordingly, we encourage researchers to investigate and exploit phase patterning in emerging 2D materials.
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Affiliation(s)
- Dohyun Kim
- Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
| | - Juhi Pandey
- Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
| | - Juyeong Jeong
- Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
| | - Woohyun Cho
- Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
| | - Seungyeon Lee
- Division of Chemical Engineering and Materials Science, Graduate Program in System Health Science and Engineering, Ewha Womans University, Seoul 03760, Korea
| | - Suyeon Cho
- Division of Chemical Engineering and Materials Science, Graduate Program in System Health Science and Engineering, Ewha Womans University, Seoul 03760, Korea
| | - Heejun Yang
- Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
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24
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Melchakova IA, Oyeniyi GT, Polyutov SP, Avramov PV. Spin Polarization and Flat Bands in Eu-Doped Nanoporous and Twisted Bilayer Graphenes. MICROMACHINES 2023; 14:1889. [PMID: 37893326 PMCID: PMC10609095 DOI: 10.3390/mi14101889] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2023] [Revised: 09/25/2023] [Accepted: 09/28/2023] [Indexed: 10/29/2023]
Abstract
Advanced two-dimensional spin-polarized heterostructures based on twisted (TBG) and nanoporous (NPBG) bilayer graphenes doped with Eu ions were theoretically proposed and studied using Periodic Boundary Conditions Density Functional theory electronic structure calculations. The significant polarization of the electronic states at the Fermi level was discovered for both Eu/NPBG(AA) and Eu/TBG lattices. Eu ions' chemi- and physisorption to both graphenes may lead to structural deformations, drop of symmetry of low-dimensional lattices, interlayer fusion, and mutual slides of TBG graphene fragments. The frontier bands in the valence region at the vicinity of the Fermi level of both spin-polarized 2D Eu/NPBG(AA) and Eu/TBG lattices clearly demonstrate flat dispersion laws caused by localized electronic states formed by TBG Moiré patterns, which could lead to strong electron correlations and the formation of exotic quantum phases.
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Affiliation(s)
- Iu. A. Melchakova
- School of Physics and Engineering, ITMO University, 197101 St. Petersburg, Russia;
| | - G. T. Oyeniyi
- Department of Chemistry, Kyungpook National University, Daegu 41566, Republic of Korea;
| | - S. P. Polyutov
- International Research Center of Spectroscopy and Quantum Chemistry (IRC SQC), Siberian Federal University, Svobodniy pr. 79/10, 600041 Krasnoyarsk, Russia;
| | - P. V. Avramov
- Department of Chemistry, Kyungpook National University, Daegu 41566, Republic of Korea;
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25
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Yin R, Wang Z, Tan S, Ma C, Wang B. On-Surface Synthesis of Graphene Nanoribbons with Atomically Precise Structural Heterogeneities and On-Site Characterizations. ACS NANO 2023; 17:17610-17623. [PMID: 37666005 DOI: 10.1021/acsnano.3c06128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/06/2023]
Abstract
Graphene nanoribbons (GNRs) are strips of graphene, with widths of a few nanometers, that are promising candidates for future applications in nanodevices and quantum information processing due to their highly tunable structure-dependent electronic, spintronic, topological, and optical properties. Implantation of periodic structural heterogeneities, such as heteroatoms, nanopores, and non-hexagonal rings, has become a powerful manner for tailoring the designer properties of GNRs. The bottom-up synthesis approach, by combining on-surface chemical reactions based on rationally designed molecular precursors and in situ tip-based microscopic and spectroscopic techniques, promotes the construction of atomically precise GNRs with periodic structural modulations. However, there are still obstacles and challenges lying on the way toward the understanding of the intrinsic structure-property relations, such as the strong screening and Fermi level pinning effect of the normally used transition metal substrates and the lack of collective tip-based techniques that can cover multi-internal degrees of freedom of the GNRs. In this Perspective, we briefly review the recent progress in the on-surface synthesis of GNRs with diverse structural heterogeneities and highlight the structure-property relations as characterized by the noncontact atomic force microscopy and scanning tunneling microscopy/spectroscopy. We furthermore motivate to deliver the need for developing strategies to achieve quasi-freestanding GNRs and for exploiting multifunctional tip-based techniques to collectively probe the intrinsic properties.
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Affiliation(s)
- Ruoting Yin
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information & Quantum Physics, New Cornerstone Science Laboratory, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zhengya Wang
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information & Quantum Physics, New Cornerstone Science Laboratory, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Shijing Tan
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information & Quantum Physics, New Cornerstone Science Laboratory, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Chuanxu Ma
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information & Quantum Physics, New Cornerstone Science Laboratory, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Bing Wang
- Hefei National Research Center for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information & Quantum Physics, New Cornerstone Science Laboratory, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
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26
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Liu M, Senga R, Koshino M, Lin YC, Suenaga K. Direct Observation of Locally Modified Excitonic Effects within a Moiré Unit Cell in Twisted Bilayer Graphene. ACS NANO 2023; 17:18433-18440. [PMID: 37682623 DOI: 10.1021/acsnano.3c06021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/10/2023]
Abstract
Bilayer graphene, which forms moiré superlattices, possesses distinct electronic and optical properties owing to its hybridized energy band and the emergence of van Hove singularities depending on its twist angle. Extensive research has been conducted on the global characteristics of moiré superlattices induced by their long-range periodicity. However, the local properties, which differ owing to the variations in the three-dimensional atomic arrangement, within a moiré unit cell have been rarely explored. In this study, we demonstrate the highly localized excitation of carbon 1s electrons to unoccupied van Hove singularities in twisted bilayer graphene by electron energy loss spectroscopy using a monochromated transmission electron microscope. The core-level excitations associated with the van Hove singularities exhibit a systematic twist-angle dependence analogous to optical excitations. Furthermore, local variations in the core-level van Hove singularity peaks, which can originate from the core-exciton lifetimes and band modifications corresponding to the local stacking geometry within a moiré unit cell, are unambiguously corroborated.
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Affiliation(s)
- Ming Liu
- The Institute of Scientific and Industrial Research (SANKEN), Osaka University, Mihogaoka 8-1, Ibaraki, Osaka 567-0047, Japan
| | - Ryosuke Senga
- Nanomaterials Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Higashi 1-1-1, Tsukuba 305-8565, Japan
| | - Masanori Koshino
- Nanomaterials Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Higashi 1-1-1, Tsukuba 305-8565, Japan
| | - Yung-Chang Lin
- Nanomaterials Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Higashi 1-1-1, Tsukuba 305-8565, Japan
| | - Kazu Suenaga
- The Institute of Scientific and Industrial Research (SANKEN), Osaka University, Mihogaoka 8-1, Ibaraki, Osaka 567-0047, Japan
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27
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Datta A, Calderón MJ, Camjayi A, Bascones E. Heavy quasiparticles and cascades without symmetry breaking in twisted bilayer graphene. Nat Commun 2023; 14:5036. [PMID: 37596252 PMCID: PMC10439139 DOI: 10.1038/s41467-023-40754-4] [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: 02/21/2023] [Accepted: 08/07/2023] [Indexed: 08/20/2023] Open
Abstract
Among the variety of correlated states exhibited by twisted bilayer graphene, cascades in the spectroscopic properties and in the electronic compressibility occur over larger ranges of energy, twist angle and temperature compared to other effects. This suggests a hierarchy of phenomena. Using a combined dynamical mean-field theory and Hartree calculation, we show that the spectral weight reorganisation associated with the formation of local moments and heavy quasiparticles can explain the cascade of electronic resets without invoking symmetry breaking orders. The phenomena reproduced here include the cascade flow of spectral weight, the oscillations of remote band energies, and the asymmetric jumps of the inverse compressibility. We also predict a strong momentum differentiation in the incoherent spectral weight associated with the fragile topology of twisted bilayer graphene.
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Affiliation(s)
- Anushree Datta
- Instituto de Ciencia de Materiales de Madrid (ICMM). Consejo Superior de Investigaciones Científicas (CSIC), Sor Juana Inés de la Cruz 3, 28049, Madrid, Spain
- Université Paris-Cité, CNRS, Laboratoire Matériaux et Phénomenes Quantiques, 75013, Paris, France
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France
| | - M J Calderón
- Instituto de Ciencia de Materiales de Madrid (ICMM). Consejo Superior de Investigaciones Científicas (CSIC), Sor Juana Inés de la Cruz 3, 28049, Madrid, Spain
| | - A Camjayi
- Universidad de Buenos Aires, Ciclo Básico Común, Buenos Aires, Argentina
- CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina
| | - E Bascones
- Instituto de Ciencia de Materiales de Madrid (ICMM). Consejo Superior de Investigaciones Científicas (CSIC), Sor Juana Inés de la Cruz 3, 28049, Madrid, Spain.
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28
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Sobral JA, Obernauer S, Turkel S, Pasupathy AN, Scheurer MS. Machine learning the microscopic form of nematic order in twisted double-bilayer graphene. Nat Commun 2023; 14:5012. [PMID: 37591848 PMCID: PMC10435506 DOI: 10.1038/s41467-023-40684-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Accepted: 08/01/2023] [Indexed: 08/19/2023] Open
Abstract
Modern scanning probe techniques, such as scanning tunneling microscopy, provide access to a large amount of data encoding the underlying physics of quantum matter. In this work, we show how convolutional neural networks can be used to learn effective theoretical models from scanning tunneling microscopy data on correlated moiré superlattices. Moiré systems are particularly well suited for this task as their increased lattice constant provides access to intra-unit-cell physics, while their tunability allows for the collection of high-dimensional data sets from a single sample. Using electronic nematic order in twisted double-bilayer graphene as an example, we show that incorporating correlations between the local density of states at different energies allows convolutional neural networks not only to learn the microscopic nematic order parameter, but also to distinguish it from heterostrain. These results demonstrate that neural networks are a powerful method for investigating the microscopic details of correlated phenomena in moiré systems and beyond.
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Affiliation(s)
- João Augusto Sobral
- Institute for Theoretical Physics III, University of Stuttgart, 70550, Stuttgart, Germany.
- Institute for Theoretical Physics, University of Innsbruck, A-6020, Innsbruck, Austria.
| | - Stefan Obernauer
- Institute for Theoretical Physics, University of Innsbruck, A-6020, Innsbruck, Austria
| | - Simon Turkel
- Department of Physics, Columbia University, 10027, New York, NY, USA
| | - Abhay N Pasupathy
- Department of Physics, Columbia University, 10027, New York, NY, USA
- Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, 11973, Upton, NY, USA
| | - Mathias S Scheurer
- Institute for Theoretical Physics III, University of Stuttgart, 70550, Stuttgart, Germany
- Institute for Theoretical Physics, University of Innsbruck, A-6020, Innsbruck, Austria
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29
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Han X, Liu Q, Wang Y, Niu R, Qu Z, Wang Z, Li Z, Han C, Watanabe K, Taniguchi T, Song Z, Mao J, Han ZV, Gan Z, Lu J. Chemical Potential Characterization of Symmetry-Breaking Phases in a Rhombohedral Trilayer Graphene. NANO LETTERS 2023; 23:6875-6882. [PMID: 37466217 DOI: 10.1021/acs.nanolett.3c01262] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/20/2023]
Abstract
Rhombohedral trilayer graphene has recently emerged as a natural flat-band platform for studying interaction-driven symmetry-breaking phases. The displacement field (D) can further flatten the band to enhance the density of states, thereby controlling the electronic correlation that tips the energy balance between spin and valley degrees of freedom. To characterize the energy competition, chemical potential measurement─a direct thermodynamic probe of Fermi surfaces─is highly demanding to be conducted under a constant D. In this work, we characterize D-dependent isospin flavor polarization, where electronic states with isospin degeneracies of one and two can be identified. We also developed a method to measure the chemical potential at a fixed D, allowing for the extraction of energy variation during phase transitions. Furthermore, symmetry breaking could also be invoked in Landau levels, manifesting as quantum Hall ferromagnetism. Our work opens more opportunities for the thermodynamic characterization of displacement-field tuned van der Waals heterostructures.
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Affiliation(s)
- Xiangyan Han
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Qianling Liu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Yijie Wang
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Ruirui Niu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Zhuangzhuang Qu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Zhiyu Wang
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Zhuoxian Li
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Chunrui Han
- Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - 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
| | - Zhida Song
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Jinhai Mao
- School of Physical Sciences and CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Zheng Vitto Han
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Optoelectronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Zizhao Gan
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Jianming Lu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
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30
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Liu X, Wang X, Yu S, Wang G, Li B, Cui T, Lou Z, Ge H. Polarizability characteristics of twisted bilayer graphene quantum dots in the absence of periodic moiré potential. RSC Adv 2023; 13:23590-23600. [PMID: 37555100 PMCID: PMC10404935 DOI: 10.1039/d3ra03444e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Accepted: 08/01/2023] [Indexed: 08/10/2023] Open
Abstract
Recent studies have documented a rich phenomenology in twisted bilayer graphene (TBG), which is significantly relevant to interlayer electronic coupling, in particular to the cases under an applied electric field. While polarizability measures the response of electrons against applied fields, this work adopts a unique strategy of decomposing global polarizability into distributional contributions to access the interlayer polarization in TBG, as a function of varying twisting angles (θ). Through the construction of a model of twisted graphene quantum dots, we assess distributional polarizability at the first-principles level. Our findings demonstrate that the polarizability perpendicular to the graphene plates can be decomposed into intralayer dipoles and interlayer charge-transfer (CT) components, the latter of which provides an explicit measurement of the interlayer coupling strength and charge transfer potential. Our analysis further reveals that interlayer polarizability dominates the polarizability variation during twisting. Intriguingly, the largest interlayer polarizability and CT driven by an external field occur in the misaligned structures with a size-dependent small angle corresponding to the first appearance of AB stacking, rather than the well-recognized Bernal structures. A derived equation is then employed to address the size dependence on the angle corresponding to the largest values in interlayer polarizability and CT. Our investigation not only characterizes the CT features in the interlayer polarizability of TBG quantum dots, but also sheds light on the existence of the strongest interlayer coupling and charge transfer at small twist angles in the presence of an external electric field, thereby providing a comprehensive understanding of the novel properties of graphene-based nanomaterials.
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Affiliation(s)
- Xiangyue Liu
- The Affiliated Cancer Hospital of Zhengzhou University, Henan Cancer Hospital Zhengzhou 450008 China
| | - Xian Wang
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics of Ministry of Education, Sichuan University Chengdu 610065 China
| | - Shengping Yu
- School of Chemistry and Environment, Southwest Minzu University Chengdu 610041 China
| | - Guangzhao Wang
- School of Electronic Information Engineering, Key Laboratory of Extraordinary Bond Engineering and Advanced Materials Technology of Chongqing, Yangtze Normal University Chongqing 408100 China
| | - Bing Li
- The Affiliated Cancer Hospital of Zhengzhou University, Henan Cancer Hospital Zhengzhou 450008 China
| | - Tiantian Cui
- The Affiliated Cancer Hospital of Zhengzhou University, Henan Cancer Hospital Zhengzhou 450008 China
| | - Zhaoyang Lou
- The Affiliated Cancer Hospital of Zhengzhou University, Henan Cancer Hospital Zhengzhou 450008 China
| | - Hong Ge
- The Affiliated Cancer Hospital of Zhengzhou University, Henan Cancer Hospital Zhengzhou 450008 China
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31
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Nuckolls KP, Lee RL, Oh M, Wong D, Soejima T, Hong JP, Călugăru D, Herzog-Arbeitman J, Bernevig BA, Watanabe K, Taniguchi T, Regnault N, Zaletel MP, Yazdani A. Quantum textures of the many-body wavefunctions in magic-angle graphene. Nature 2023; 620:525-532. [PMID: 37587297 DOI: 10.1038/s41586-023-06226-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Accepted: 05/16/2023] [Indexed: 08/18/2023]
Abstract
Interactions among electrons create novel many-body quantum phases of matter with wavefunctions that reflect electronic correlation effects, broken symmetries and collective excitations. Many quantum phases have been discovered in magic-angle twisted bilayer graphene (MATBG), including correlated insulating1, unconventional superconducting2-5 and magnetic topological6-9 phases. The lack of microscopic information10,11 of possible broken symmetries has hampered our understanding of these phases12-17. Here we use high-resolution scanning tunnelling microscopy to study the wavefunctions of the correlated phases in MATBG. The squares of the wavefunctions of gapped phases, including those of the correlated insulating, pseudogap and superconducting phases, show distinct broken-symmetry patterns with a √3 × √3 super-periodicity on the graphene atomic lattice that has a complex spatial dependence on the moiré scale. We introduce a symmetry-based analysis using a set of complex-valued local order parameters, which show intricate textures that distinguish the various correlated phases. We compare the observed quantum textures of the correlated insulators at fillings of ±2 electrons per moiré unit cell to those expected for proposed theoretical ground states. In typical MATBG devices, these textures closely match those of the proposed incommensurate Kekulé spiral order15, whereas in ultralow-strain samples, our data have local symmetries like those of a time-reversal symmetric intervalley coherent phase12. Moreover, the superconducting state of MATBG shows strong signatures of intervalley coherence, only distinguishable from those of the insulator with our phase-sensitive measurements.
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Affiliation(s)
- Kevin P Nuckolls
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
| | - Ryan L Lee
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
| | - Myungchul Oh
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
| | - Dillon Wong
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
| | - Tomohiro Soejima
- Department of Physics, University of California, Berkeley, CA, USA
| | - Jung Pyo Hong
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
| | - Dumitru Călugăru
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
| | - Jonah Herzog-Arbeitman
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
| | - B Andrei Bernevig
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA
- Donostia International Physics Center, Donostia-San Sebastian, Spain
- IKERBASQUE, Basque Foundation for Science, Bilbao, Spain
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Nicolas Regnault
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France
| | - Michael P Zaletel
- Department of Physics, University of California, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Ali Yazdani
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ, USA.
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32
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Wang H, Wang S, Zhang S, Zhu M, Ouyang W, Li Q. Deducing the internal interfaces of twisted multilayer graphene via moiré-regulated surface conductivity. Natl Sci Rev 2023; 10:nwad175. [PMID: 37484999 PMCID: PMC10361741 DOI: 10.1093/nsr/nwad175] [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: 01/29/2023] [Revised: 04/19/2023] [Accepted: 06/15/2023] [Indexed: 07/25/2023] Open
Abstract
The stacking state of atomic layers critically determines the physical properties of twisted van der Waals materials. Unfortunately, precise characterization of the stacked interfaces remains a great challenge as they are buried internally. With conductive atomic force microscopy, we show that the moiré superlattice structure formed at the embedded interfaces of small-angle twisted multilayer graphene (tMLG) can noticeably regulate surface conductivity even when the twisted interfaces are 10 atomic layers beneath the surface. Assisted by molecular dynamics (MD) simulations, a theoretical model is proposed to correlate surface conductivity with the sequential stacking state of the graphene layers of tMLG. The theoretical model is then employed to extract the complex structure of a tMLG sample with crystalline defects. Probing and visualizing the internal stacking structures of twisted layered materials is essential for understanding their unique physical properties, and our work offers a powerful tool for this via simple surface conductivity mapping.
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Affiliation(s)
| | | | | | - Mengzhen Zhu
- Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
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33
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Hu H, Bernevig BA, Tsvelik AM. Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund's Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory. PHYSICAL REVIEW LETTERS 2023; 131:026502. [PMID: 37505959 DOI: 10.1103/physrevlett.131.026502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/25/2022] [Accepted: 06/13/2023] [Indexed: 07/30/2023]
Abstract
We apply a generalized Schrieffer-Wolff transformation to the extended Anderson-like topological heavy fermion (THF) model for the magic-angle (θ=1.05°) twisted bilayer graphene (MATBLG) [Phys. Rev. Lett. 129, 047601 (2022)PRLTAO0031-900710.1103/PhysRevLett.129.047601], to obtain its Kondo lattice limit. In this limit localized f electrons on a triangular lattice interact with topological conduction c electrons. By solving the exact limit of the THF model, we show that the integer fillings ν=0,±1,±2 are controlled by the heavy f electrons, while ν=±3 is at the border of a phase transition between two f-electron fillings. For ν=0,±1,±2, we then calculate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between the f moments in the full model and analytically prove the SU(4) Hund's rule for the ground state which maintains that two f electrons fill the same valley-spin flavor. Our (ferromagnetic interactions in the) spin model dramatically differ from the usual Heisenberg antiferromagnetic interactions expected at strong coupling. We show the ground state in some limits can be found exactly by employing a positive semidefinite "bond-operators" method. We then compute the excitation spectrum of the f moments in the ordered ground state, prove the stability of the ground state favored by RKKY interactions, and discuss the properties of the Goldstone modes, the (reason for the accidental) degeneracy of (some of) the excitation modes, and the physics of their phase stiffness. We develop a low-energy effective theory for the f moments and obtain analytic expressions for the dispersion of the collective modes. We discuss the relevance of our results to the spin-entropy experiments in TBG.
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Affiliation(s)
- Haoyu Hu
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastian, Spain
| | - B Andrei Bernevig
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastian, Spain
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- IKERBASQUE, Basque Foundation for Science, Bilbao, Spain
| | - Alexei M Tsvelik
- Division of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
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34
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Chou YZ, Das Sarma S. Kondo Lattice Model in Magic-Angle Twisted Bilayer Graphene. PHYSICAL REVIEW LETTERS 2023; 131:026501. [PMID: 37505969 DOI: 10.1103/physrevlett.131.026501] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/25/2022] [Accepted: 06/02/2023] [Indexed: 07/30/2023]
Abstract
We systematically study emergent Kondo lattice models from magic-angle twisted bilayer graphene using the topological heavy fermion representation. At the commensurate fillings, we demonstrate a series of symmetric strongly correlated metallic states driven by the hybridization between a triangular lattice of SU(8) local moments and delocalized fermions. In particular, a (fragile) topological Dirac Kondo semimetal can be realized, providing a potential explanation for the symmetry-preserving correlated state at ν=0. We further investigate the stability of the Dirac Kondo semimetal by constructing a quantum phase diagram showing the interplay between Kondo hybridization and magnetic correlation. The destruction of Kondo hybridization suggests that the magic-angle twisted bilayer graphene may be on the verge of a solid-state quantum simulator for novel magnetic orders on a triangular lattice. Experimental implications are also discussed.
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Affiliation(s)
- Yang-Zhi Chou
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Sankar Das Sarma
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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35
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van Loon EGCP, Schüler M, Springer D, Sangiovanni G, Tomczak JM, Wehling TO. Coulomb engineering of two-dimensional Mott materials. NPJ 2D MATERIALS AND APPLICATIONS 2023; 7:47. [PMID: 38665482 PMCID: PMC11041779 DOI: 10.1038/s41699-023-00408-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/14/2022] [Accepted: 06/15/2023] [Indexed: 04/28/2024]
Abstract
Two-dimensional materials can be strongly influenced by their surroundings. A dielectric environment screens and reduces the Coulomb interaction between electrons in the two-dimensional material. Since in Mott materials the Coulomb interaction is responsible for the insulating state, manipulating the dielectric screening provides direct control over Mottness. Our many-body calculations reveal the spectroscopic fingerprints of such Coulomb engineering: we demonstrate eV-scale changes to the position of the Hubbard bands and show a Coulomb engineered insulator-to-metal transition. Based on our proof-of-principle calculations, we discuss the (feasible) conditions under which our scenario of Coulomb engineering of Mott materials can be realized experimentally.
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Affiliation(s)
- Erik G. C. P. van Loon
- Mathematical Physics Division, Department of Physics, Lund University, Lund, Sweden
- Institut für Theoretische Physik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany
- Bremen Center for Computational Materials Science, Universität Bremen, Am Fallturm 1a, 28359 Bremen, Germany
| | - Malte Schüler
- Institut für Theoretische Physik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany
- Bremen Center for Computational Materials Science, Universität Bremen, Am Fallturm 1a, 28359 Bremen, Germany
| | - Daniel Springer
- Institute of Solid State Physics, TU Wien, A-1040 Vienna, Austria
- Institute of Advanced Research in Artificial Intelligence, IARAI, A-1030 Vienna, Austria
| | - Giorgio Sangiovanni
- Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, 97074 Würzburg, Germany
| | - Jan M. Tomczak
- Institute of Solid State Physics, TU Wien, A-1040 Vienna, Austria
- Department of Physics, King’s College London, Strand, London, WC2R 2LS UK
| | - Tim O. Wehling
- I. Institute of Theoretical Physics, University of Hamburg, D-22607 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, D-22761 Hamburg, Germany
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36
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Li Y, Yuan Q, Guo D, Lou C, Cui X, Mei G, Petek H, Cao L, Ji W, Feng M. 1D Electronic Flat Bands in Untwisted Moiré Superlattices. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023; 35:e2300572. [PMID: 37057612 DOI: 10.1002/adma.202300572] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2023] [Revised: 04/03/2023] [Indexed: 06/16/2023]
Abstract
After the preparation of 2D electronic flat band (EFB) in van der Waals (vdW) superlattices, recent measurements suggest the existence of 1D electronic flat bands (1D-EFBs) in twisted vdW bilayers. However, the realization of 1D-EFBs is experimentally elusive in untwisted 2D layers, which is desired considering their fabrication and scalability. Herein, the discovery of 1D-EFBs is reported in an untwisted in situ-grown two atomic-layer Bi(110) superlattice self-aligned on an SnSe(001) substrate using scanning probe microscopy measurements and density functional theory calculations. While the Bi-Bi dimers of Bi zigzag (ZZ) chains are buckled, the epitaxial lattice mismatch between the Bi and SnSe layers induces two 1D buckling reversal regions (BRRs) extending along the ZZ direction in each Bi(110)-11 × 11 supercell. A series of 1D-EFBs arises spatially following BRRs that isolate electronic states along the armchair (AC) direction and localize electrons in 1D extended states along ZZ due to quantum interference at a topological node. This work provides a generalized strategy for engineering 1D-EFBs in utilizing lattice mismatch between untwisted rectangular vdW layers.
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Affiliation(s)
- Yafei Li
- School of Physics and Technology and Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education, Wuhan University, Wuhan, 430072, P. R. China
| | - Qing Yuan
- School of Physics and Technology and Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education, Wuhan University, Wuhan, 430072, P. R. China
| | - Deping Guo
- Beijing Key Laboratory of Optoelectronic Functional Materials & Micro-Nano Devices, Department of Physics, Renmin University of China, Beijing, 100872, P. R. China
- Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin Universiry of China, Beijing, 100872, P. R. China
| | - Cancan Lou
- School of Physics and Technology and Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education, Wuhan University, Wuhan, 430072, P. R. China
| | - Xingxia Cui
- School of Physics and Technology and Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education, Wuhan University, Wuhan, 430072, P. R. China
| | - Guangqiang Mei
- School of Physics and Technology and Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education, Wuhan University, Wuhan, 430072, P. R. China
| | - Hrvoje Petek
- Department of Physics and Astronomy and the IQ Initiative, University of Pittsburgh, Pittsburgh, 15260, USA
| | - Limin Cao
- School of Physics and Technology and Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education, Wuhan University, Wuhan, 430072, P. R. China
| | - Wei Ji
- Beijing Key Laboratory of Optoelectronic Functional Materials & Micro-Nano Devices, Department of Physics, Renmin University of China, Beijing, 100872, P. R. China
- Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin Universiry of China, Beijing, 100872, P. R. China
| | - Min Feng
- School of Physics and Technology and Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education, Wuhan University, Wuhan, 430072, P. R. China
- Institute for Advanced Study, Wuhan University, Wuhan, 430072, P. R. China
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37
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Wan X, Sarkar S, Lin SZ, Sun K. Topological Exact Flat Bands in Two-Dimensional Materials under Periodic Strain. PHYSICAL REVIEW LETTERS 2023; 130:216401. [PMID: 37295089 DOI: 10.1103/physrevlett.130.216401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2022] [Accepted: 04/26/2023] [Indexed: 06/12/2023]
Abstract
We study flat bands and their topology in 2D materials with quadratic band crossing points under periodic strain. In contrast to Dirac points in graphene, where strain acts as a vector potential, strain for quadratic band crossing points serves as a director potential with angular momentum ℓ=2. We prove that when the strengths of the strain fields hit certain "magic" values, exact flat bands with C=±1 emerge at charge neutrality point in the chiral limit, in strong analogy to magic angle twisted-bilayer graphene. These flat bands have ideal quantum geometry for the realization of fractional Chern insulators, and they are always fragile topological. The number of flat bands can be doubled for certain point group, and the interacting Hamiltonian is exactly solvable at integer fillings. We further demonstrate the stability of these flat bands against deviations from the chiral limit, and discuss possible realization in 2D materials.
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Affiliation(s)
- Xiaohan Wan
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
- Theoretical Division, T-4 and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Siddhartha Sarkar
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Shi-Zeng Lin
- Theoretical Division, T-4 and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Center for Integrated Nanotechnologies (CINT), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Kai Sun
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
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38
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González J, Stauber T. Ising superconductivity induced from spin-selective valley symmetry breaking in twisted trilayer graphene. Nat Commun 2023; 14:2746. [PMID: 37173312 PMCID: PMC10182018 DOI: 10.1038/s41467-023-38250-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Accepted: 04/17/2023] [Indexed: 05/15/2023] Open
Abstract
We show that the e-e interaction induces a strong breakdown of valley symmetry for each spin channel in twisted trilayer graphene, leading to a ground state where the two spin projections have opposite sign of the valley symmetry breaking order parameter. This leads to a spin-valley locking in which the electrons of a Cooper pair are forced to live on different Fermi lines attached to opposite valleys. Furthermore, we find an effective intrinsic spin-orbit coupling explaining the protection of the superconductivity against in-plane magnetic fields. The effect of spin-selective valley symmetry breaking is validated as it reproduces the experimental observation of the reset of the Hall density at 2-hole doping. It also implies a breakdown of the symmetry of the bands from C6 to C3, with an enhancement of the anisotropy of the Fermi lines which is at the origin of a Kohn-Luttinger (pairing) instability. The isotropy of the bands is gradually recovered, however, when the Fermi level approaches the bottom of the second valence band, explaining why the superconductivity fades away in the doping range beyond 3 holes per moiré unit cell in twisted trilayer graphene.
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Affiliation(s)
- J González
- Instituto de Estructura de la Materia, CSIC, E-28006, Madrid, Spain.
| | - T Stauber
- Instituto de Ciencia de Materiales de Madrid, CSIC, E-28049, Madrid, Spain.
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39
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Papaj M, Lewandowski C. Probing correlated states with plasmons. SCIENCE ADVANCES 2023; 9:eadg3262. [PMID: 37126543 DOI: 10.1126/sciadv.adg3262] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Understanding the nature of strongly correlated states in flat-band materials (such as moiré heterostructures) is at the forefront of both experimental and theoretical pursuits. While magnetotransport, scanning probe, and optical techniques are often very successful in investigating the properties of the underlying order, the exact nature of the ground state often remains unknown. Here, we propose to leverage strong light-matter coupling present in the flat-band systems to gain insight through dynamical dielectric response into the structure of the many-body ground state. We argue that because of the enlargement of the effective lattice of the system arising from correlations, conventional long-range plasmon becomes "folded" to yield a multiband plasmon spectrum. We detail several mechanisms through which the structure of the plasmon spectrum and that of the dynamical dielectric response is susceptible to the underlying order, revealing valued insights such as the interaction-driven band gaps, spin-structure, and the order periodicity.
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Affiliation(s)
- Michał Papaj
- Department of Physics, University of California, Berkeley, CA 94720, USA
| | - Cyprian Lewandowski
- National High Magnetic Field Laboratory, Tallahassee, FL, 32310, USA
- Department of Physics, Florida State University, Tallahassee, FL 32306, USA
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40
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Wu YM, Wu Z, Yao H. Pair-Density-Wave and Chiral Superconductivity in Twisted Bilayer Transition Metal Dichalcogenides. PHYSICAL REVIEW LETTERS 2023; 130:126001. [PMID: 37027848 DOI: 10.1103/physrevlett.130.126001] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2022] [Accepted: 02/24/2023] [Indexed: 06/19/2023]
Abstract
We theoretically explore possible orders induced by weak repulsive interactions in twisted bilayer transition metal dichalcogenides (e.g., WSe_{2}) in the presence of an out-of-plane electric field. Using renormalization group analysis, we show that superconductivity survives even with the conventional van Hove singularities. We find that topological chiral superconducting states with Chern number N=1, 2, 4 (namely, p+ip, d+id, and g+ig) appear over a large parameter region with a moiré filling factor around n=1. At some special values of applied electric field and in the presence of a weak out-of-plane Zeeman field, spin-polarized pair-density-wave (PDW) superconductivity can emerge. This spin-polarized PDW state can be probed by experiments such as spin-polarized STM measuring spin-resolved pairing gap and quasiparticle interference. Moreover, the spin-polarized PDW could lead to a spin-polarized superconducting diode effect.
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Affiliation(s)
- Yi-Ming Wu
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
| | - Zhengzhi Wu
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Hong Yao
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
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41
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Twisted bilayer zigzag-graphene nanoribbon junctions with tunable edge states. Nat Commun 2023; 14:1018. [PMID: 36823140 PMCID: PMC9950076 DOI: 10.1038/s41467-023-36613-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2022] [Accepted: 02/08/2023] [Indexed: 02/25/2023] Open
Abstract
Stacking two-dimensional layered materials such as graphene and transitional metal dichalcogenides with nonzero interlayer twist angles has recently become attractive because of the emergence of novel physical properties. Stacking of one-dimensional nanomaterials offers the lateral stacking offset as an additional parameter for modulating the resulting material properties. Here, we report that the edge states of twisted bilayer zigzag graphene nanoribbons (TBZGNRs) can be tuned with both the twist angle and the stacking offset. Strong edge state variations in the stacking region are first revealed by density functional theory (DFT) calculations. We construct and characterize twisted bilayer zigzag graphene nanoribbon (TBZGNR) systems on a Au(111) surface using scanning tunneling microscopy. A detailed analysis of three prototypical orthogonal TBZGNR junctions exhibiting different stacking offsets by means of scanning tunneling spectroscopy reveals emergent near-zero-energy states. From a comparison with DFT calculations, we conclude that the emergent edge states originate from the formation of flat bands whose energy and spin degeneracy are highly tunable with the stacking offset. Our work highlights fundamental differences between 2D and 1D twistronics and spurs further investigation of twisted one-dimensional systems.
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42
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Aggarwal D, Narula R, Ghosh S. A primer on twistronics: a massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:143001. [PMID: 36745922 DOI: 10.1088/1361-648x/acb984] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2022] [Accepted: 02/06/2023] [Indexed: 06/18/2023]
Abstract
The recent discovery of superconductivity in magic-angle twisted bilayer graphene (TBLG) has sparked a renewed interest in the strongly-correlated physics ofsp2carbons, in stark contrast to preliminary investigations which were dominated by the one-body physics of the massless Dirac fermions. We thus provide a self-contained, theoretical perspective of the journey of graphene from its single-particle physics-dominated regime to the strongly-correlated physics of the flat bands. Beginning from the origin of the Dirac points in condensed matter systems, we discuss the effect of the superlattice on the Fermi velocity and Van Hove singularities in graphene and how it leads naturally to investigations of the moiré pattern in van der Waals heterostructures exemplified by graphene-hexagonal boron-nitride and TBLG. Subsequently, we illuminate the origin of flat bands in TBLG at the magic angles by elaborating on a broad range of prominent theoretical works in a pedagogical way while linking them to available experimental support, where appropriate. We conclude by providing a list of topics in the study of the electronic properties of TBLG not covered by this review but may readily be approached with the help of this primer.
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Affiliation(s)
| | - Rohit Narula
- Department of Physics, IIT Delhi, Hauz Khas, New Delhi, India
| | - Sankalpa Ghosh
- Department of Physics, IIT Delhi, Hauz Khas, New Delhi, India
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43
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Scammell HD, Scheurer MS. Tunable Superconductivity and Möbius Fermi Surfaces in an Inversion-Symmetric Twisted van der Waals Heterostructure. PHYSICAL REVIEW LETTERS 2023; 130:066001. [PMID: 36827571 DOI: 10.1103/physrevlett.130.066001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2022] [Accepted: 01/11/2023] [Indexed: 06/18/2023]
Abstract
We theoretically study a moiré superlattice geometry consisting of mirror-symmetric twisted trilayer graphene surrounded by identical transition metal dichalcogenide layers. We show that this setup allows us to switch on or off and control the spin-orbit splitting of the Fermi surfaces via application of a perpendicular displacement field D_{0} and explore two manifestations of this control: first, we compute the evolution of superconducting pairing with D_{0}; this features a complex admixture of singlet and triplet pairing and, depending on the pairing state in the parent trilayer system, phase transitions between competing superconducting phases. Second, we reveal that, with application of D_{0}, the spin-orbit-induced spin textures exhibit vortices which lead to "Möbius fermi surfaces" in the interior of the Brillouin zone: diabatic electron trajectories, which are predicted to dominate quantum oscillation experiments, require encircling the Γ point twice, making their Möbius nature directly observable. Further, we show that the superconducting order parameter inherits the unconventional, Möbius spin textures. Our findings suggest that this system provides a promising experimental avenue for systematically studying the impact of spin-orbit coupling on the multitude of topological and correlated phases in near-magic-angle twisted trilayer graphene.
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Affiliation(s)
- Harley D Scammell
- School of Physics, the University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Mathias S Scheurer
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria
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44
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Tian H, Gao X, Zhang Y, Che S, Xu T, Cheung P, Watanabe K, Taniguchi T, Randeria M, Zhang F, Lau CN, Bockrath MW. Evidence for Dirac flat band superconductivity enabled by quantum geometry. Nature 2023; 614:440-444. [PMID: 36792742 DOI: 10.1038/s41586-022-05576-2] [Citation(s) in RCA: 13] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2021] [Accepted: 11/18/2022] [Indexed: 02/17/2023]
Abstract
In a flat band superconductor, the charge carriers' group velocity vF is extremely slow. Superconductivity therein is particularly intriguing, being related to the long-standing mysteries of high-temperature superconductors1 and heavy-fermion systems2. Yet the emergence of superconductivity in flat bands would appear paradoxical, as a small vF in the conventional Bardeen-Cooper-Schrieffer theory implies vanishing coherence length, superfluid stiffness and critical current. Here, using twisted bilayer graphene3-7, we explore the profound effect of vanishingly small velocity in a superconducting Dirac flat band system8-13. Using Schwinger-limited non-linear transport studies14,15, we demonstrate an extremely slow normal state drift velocity vn ≈ 1,000 m s-1 for filling fraction ν between -1/2 and -3/4 of the moiré superlattice. In the superconducting state, the same velocity limit constitutes a new limiting mechanism for the critical current, analogous to a relativistic superfluid16. Importantly, our measurement of superfluid stiffness, which controls the superconductor's electrodynamic response, shows that it is not dominated by the kinetic energy but instead by the interaction-driven superconducting gap, consistent with recent theories on a quantum geometric contribution8-12. We find evidence for small Cooper pairs, characteristic of the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover17-19, with an unprecedented ratio of the superconducting transition temperature to the Fermi temperature exceeding unity and discuss how this arises for ultra-strong coupling superconductivity in ultra-flat Dirac bands.
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Affiliation(s)
- Haidong Tian
- Department of Physics, The Ohio State University, Columbus, OH, USA
| | - Xueshi Gao
- Department of Physics, The Ohio State University, Columbus, OH, USA
| | - Yuxin Zhang
- Department of Physics, The Ohio State University, Columbus, OH, USA
| | - Shi Che
- Department of Physics, The Ohio State University, Columbus, OH, USA
| | - Tianyi Xu
- Department of Physics, The University of Texas at Dallas, Richardson, TX, USA
| | - Patrick Cheung
- Department of Physics, The University of Texas at Dallas, Richardson, TX, USA
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Mohit Randeria
- Department of Physics, The Ohio State University, Columbus, OH, USA
| | - Fan Zhang
- Department of Physics, The University of Texas at Dallas, Richardson, TX, USA
| | - Chun Ning Lau
- Department of Physics, The Ohio State University, Columbus, OH, USA.
| | - Marc W Bockrath
- Department of Physics, The Ohio State University, Columbus, OH, USA.
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45
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Tilak N, Li G, Taniguchi T, Watanabe K, Andrei EY. Moiré Potential, Lattice Relaxation, and Layer Polarization in Marginally Twisted MoS 2 Bilayers. NANO LETTERS 2023; 23:73-81. [PMID: 36576808 DOI: 10.1021/acs.nanolett.2c03676] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Artificially twisted heterostructures of semiconducting transition-metal dichalcogenides (TMDs) offer unprecedented control over their electronic and optical properties via the spatial modulation of interlayer interactions and structural reconstruction. Here we study twisted MoS2 bilayers in a wide range of twist angles near 0° using scanning tunneling microscopy/spectroscopy. We investigate the twist angle dependence of the moiré pattern, which is dominated by lattice reconstruction for small angles (<2°), leading to large triangular domains with rhombohedral stacking. Local spectroscopy measurements reveal a large moiré-potential strength of 100-200 meV for angles <3°. In reconstructed regions, we see a bias-dependent asymmetry between neighboring triangular domains, which we relate to the vertical polarization that is intrinsic to rhombohedral stacked TMDs. This viewpoint is further supported by spectroscopy maps and ambient piezoresponse measurements. Our results provide a microscopic perspective of this new class of interfacial ferroelectrics and can offer clues for designing novel heterostructures that harness this effect.
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Affiliation(s)
- Nikhil Tilak
- Department of Physics and Astronomy, Rutgers, The State University of New Jersey, 136 Frelinghuysen Rd, Piscataway, New Jersey 08854, United States
| | - Guohong Li
- Department of Physics and Astronomy, Rutgers, The State University of New Jersey, 136 Frelinghuysen Rd, Piscataway, New Jersey 08854, United States
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Eva Y Andrei
- Department of Physics and Astronomy, Rutgers, The State University of New Jersey, 136 Frelinghuysen Rd, Piscataway, New Jersey 08854, United States
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46
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Wang Y, Song Z, Wan J, Betzler S, Xie Y, Ophus C, Bustillo KC, Ercius P, Wang LW, Zheng H. Strong Structural and Electronic Coupling in Metavalent PbS Moiré Superlattices. J Am Chem Soc 2022; 144:23474-23482. [PMID: 36512727 DOI: 10.1021/jacs.2c09947] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Moiré superlattices are twisted bilayer materials in which the tunable interlayer quantum confinement offers access to new physics and novel device functionalities. Previously, moiré superlattices were built exclusively using materials with weak van der Waals interactions, and synthesizing moiré superlattices with strong interlayer chemical bonding was considered to be impractical. Here, using lead sulfide (PbS) as an example, we report a strategy for synthesizing moiré superlattices coupled by strong chemical bonding. We use water-soluble ligands as a removable template to obtain free-standing ultrathin PbS nanosheets and assemble them into direct-contact bilayers with various twist angles. Atomic-resolution imaging shows the moiré periodic structural reconstruction at the superlattice interface due to the strong metavalent coupling. Electron energy loss spectroscopy and theoretical calculations collectively reveal the twist-angle-dependent electronic structure, especially the emergent separation of flat bands at small twist angles. The localized states of flat bands are similar to well-arranged quantum dots, promising an application in devices. This study opens a new door to the exploration of deep energy modulations within moiré superlattices alternative to van der Waals twistronics.
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Affiliation(s)
- Yu Wang
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States.,Center for Electron Microscopy and South China Advanced Institute for Soft Matter Science and Technology, School of Emergent Soft Matter, South China University of Technology, Guangzhou510640, China
| | - Zhigang Song
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts02138, United States
| | - Jiawei Wan
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States.,Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, California94720, United States
| | - Sophia Betzler
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States
| | - Yujun Xie
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States
| | - Colin Ophus
- National Center for Electron Microscopy, The Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States
| | - Karen C Bustillo
- National Center for Electron Microscopy, The Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States
| | - Peter Ercius
- National Center for Electron Microscopy, The Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States
| | - Lin-Wang Wang
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States
| | - Haimei Zheng
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States.,Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, California94720, United States
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47
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Halbertal D, Turkel S, Ciccarino CJ, Profe JB, Finney N, Hsieh V, Watanabe K, Taniguchi T, Hone J, Dean C, Narang P, Pasupathy AN, Kennes DM, Basov DN. Unconventional non-local relaxation dynamics in a twisted trilayer graphene moiré superlattice. Nat Commun 2022; 13:7587. [PMID: 36481831 PMCID: PMC9731949 DOI: 10.1038/s41467-022-35213-5] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2022] [Accepted: 11/18/2022] [Indexed: 12/13/2022] Open
Abstract
The electronic and structural properties of atomically thin materials can be controllably tuned by assembling them with an interlayer twist. During this process, constituent layers spontaneously rearrange themselves in search of a lowest energy configuration. Such relaxation phenomena can lead to unexpected and novel material properties. Here, we study twisted double trilayer graphene (TDTG) using nano-optical and tunneling spectroscopy tools. We reveal a surprising optical and electronic contrast, as well as a stacking energy imbalance emerging between the moiré domains. We attribute this contrast to an unconventional form of lattice relaxation in which an entire graphene layer spontaneously shifts position during assembly, resulting in domains of ABABAB and BCBACA stacking. We analyze the energetics of this transition and demonstrate that it is the result of a non-local relaxation process, in which an energy gain in one domain of the moiré lattice is paid for by a relaxation that occurs in the other.
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Affiliation(s)
- Dorri Halbertal
- Department of Physics, Columbia University, New York, NY, 10027, USA.
| | - Simon Turkel
- Department of Physics, Columbia University, New York, NY, 10027, USA
- Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - Christopher J Ciccarino
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - Jonas B Profe
- Institute for Theory of Statistical Physics, RWTH Aachen University, and JARA Fundamentals of Future Information Technology, 52062, Aachen, Germany
| | - Nathan Finney
- Department of Physics, Columbia University, New York, NY, 10027, USA
| | - Valerie Hsieh
- Department of Physics, Columbia University, New York, NY, 10027, USA
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
| | - James Hone
- Department of Physics, Columbia University, New York, NY, 10027, USA
| | - Cory Dean
- Department of Physics, Columbia University, New York, NY, 10027, USA
| | - Prineha Narang
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - Abhay N Pasupathy
- Department of Physics, Columbia University, New York, NY, 10027, USA
- Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - Dante M Kennes
- Institute for Theory of Statistical Physics, RWTH Aachen University, and JARA Fundamentals of Future Information Technology, 52062, Aachen, Germany
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, Hamburg, Germany
| | - D N Basov
- Department of Physics, Columbia University, New York, NY, 10027, USA
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48
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Li SY, Wang Z, Xue Y, Wang Y, Zhang S, Liu J, Zhu Z, Watanabe K, Taniguchi T, Gao HJ, Jiang Y, Mao J. Imaging topological and correlated insulating states in twisted monolayer-bilayer graphene. Nat Commun 2022; 13:4225. [PMID: 35869069 PMCID: PMC9307793 DOI: 10.1038/s41467-022-31851-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Accepted: 07/05/2022] [Indexed: 11/22/2022] Open
Abstract
Flat bands in Van der Waals heterostructure provide an ideal platform for unveiling emergent quantum electronic phases. One celebrated example is twisted monolayer-bilayer graphene, in which the effects of electronic correlation have been observed. Here, we report the observation via scanning tunnelling microscopy and spectroscopy of correlated insulating states in twisted monolayer-bilayer graphene, leading to the formation of an electron crystal phase. At integer fillings, the strong Coulomb interaction redistributes flat-band electrons within one moiré unit cell, producing an insulating state with vanishing density of states at the Fermi level. Moreover, our approach enables the direct visualization of an ordered lattice of topological torus-shaped states, generated by the interaction between the electron crystal and the non-trivial band topology of twisted monolayer-bilayer graphene. Our results illustrate an efficient strategy for entwining topological physics with strong electron correlation in twisted van der Waals structures. Twisted van der Waals structures represent a versatile platform to investigate topological and correlated electronic states. Here, the authors report the visualization of an electron crystal phase in twisted monolayer-bilayer graphene via scanning tunnelling microscopy, studying the coupling between strong electron correlation and nontrivial band topology.
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49
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Portolés E, Iwakiri S, Zheng G, Rickhaus P, Taniguchi T, Watanabe K, Ihn T, Ensslin K, de Vries FK. A tunable monolithic SQUID in twisted bilayer graphene. NATURE NANOTECHNOLOGY 2022; 17:1159-1164. [PMID: 36280761 DOI: 10.1038/s41565-022-01222-0] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2022] [Accepted: 09/05/2022] [Indexed: 06/16/2023]
Abstract
Magic-angle twisted bilayer graphene (MATBG) hosts a number of correlated states of matter that can be tuned by electrostatic doping1-4. Transport5,6 and scanning-probe7-9 experiments have shown evidence for band, correlated and Chern insulators along with superconductivity. This variety of in situ tunable states has allowed for the realization of tunable Josephson junctions10-12. However, although phase-coherent phenomena have been measured10-12, no control of the phase difference of the superconducting condensates has been demonstrated so far. Here we build on previous gate-defined junction realizations and form a superconducting quantum interference device13 (SQUID) in MATBG, where the superconducting phase difference is controlled through the magnetic field. We observe magneto-oscillations of the critical current, demonstrating long-range coherence of superconducting charge carriers with an effective charge of 2e. We tune to both asymmetric and symmetric SQUID configurations by electrostatically controlling the critical currents through the junctions. This tunability allows us to study the inductances in the device, finding values of up to 2 μH. Furthermore, we directly probe the current-phase relation of one of the junctions of the device. Our results show that complex devices in MATBG can be realized and used to reveal the properties of the material. We envision our findings, together with the established history of applications SQUIDs have14-16, will foster the development of a wide range of devices such as phase-slip junctions17 or high kinetic inductance detectors18.
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Affiliation(s)
- Elías Portolés
- Solid State Physics Laboratory, ETH Zurich, Zurich, Switzerland.
| | - Shuichi Iwakiri
- Solid State Physics Laboratory, ETH Zurich, Zurich, Switzerland
| | - Giulia Zheng
- Solid State Physics Laboratory, ETH Zurich, Zurich, Switzerland
| | - Peter Rickhaus
- Solid State Physics Laboratory, ETH Zurich, Zurich, Switzerland
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan
| | - Thomas Ihn
- Solid State Physics Laboratory, ETH Zurich, Zurich, Switzerland
- Quantum Center, ETH Zurich, Zurich, Switzerland
| | - Klaus Ensslin
- Solid State Physics Laboratory, ETH Zurich, Zurich, Switzerland.
- Quantum Center, ETH Zurich, Zurich, Switzerland.
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50
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Duan J, Jian Y, Gao Y, Peng H, Zhong J, Feng Q, Mao J, Yao Y. Giant Second-Order Nonlinear Hall Effect in Twisted Bilayer Graphene. PHYSICAL REVIEW LETTERS 2022; 129:186801. [PMID: 36374703 DOI: 10.1103/physrevlett.129.186801] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2022] [Revised: 08/08/2022] [Accepted: 09/30/2022] [Indexed: 06/16/2023]
Abstract
In the second-order response regime, the Hall voltage can be nonzero without time-reversal symmetry breaking but inversion symmetry breaking. Multiple mechanisms contribute to the nonlinear Hall effect. The disorder-related contributions can enter the NLHE in the leading role, but experimental investigations are scarce, especially the exploration of the contributions from different disorder sources. Here, we report a giant nonlinear response in twisted bilayer graphene, dominated by disorder-induced skew scattering. The magnitude and direction of the second-order nonlinearity can be effectively tuned by the gate voltage. A peak value of the second-order Hall conductivity reaching 8.76 μm SV^{-1} is observed close to the full filling of the moiré band, four order larger than the intrinsic contribution detected in WTe_{2}. The scaling shows that the giant second-order nonlinear Hall effect in twisted bilayer graphene stems from the collaboration of the static (impurities) and dynamic (phonons) disorders. It is mainly determined by the impurity skew scattering at 1.7 K. The phonon skew scattering, however, has a much larger coupling coefficient, and becomes comparable to the impurity contribution as the temperature rises. Our observations provide a comprehensive experimental understanding of the disorder-related mechanisms in the nonlinear Hall effect.
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Affiliation(s)
- Junxi Duan
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100086, China
| | - Yu Jian
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100086, China
| | - Yang Gao
- Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Huimin Peng
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100086, China
| | - Jinrui Zhong
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100086, China
| | - Qi Feng
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100086, China
| | - Jinhai Mao
- School of Physical Sciences and CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yugui Yao
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100086, China
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