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Bhowmik S, Ghosh A, Chandni U. Emergent phases in graphene flat bands. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:096401. [PMID: 39059412 DOI: 10.1088/1361-6633/ad67ed] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Accepted: 07/26/2024] [Indexed: 07/28/2024]
Abstract
Electronic correlations in two-dimensional materials play a crucial role in stabilising emergent phases of matter. The realisation of correlation-driven phenomena in graphene has remained a longstanding goal, primarily due to the absence of strong electron-electron interactions within its low-energy bands. In this context, magic-angle twisted bilayer graphene has recently emerged as a novel platform featuring correlated phases favoured by the low-energy flat bands of the underlying moiré superlattice. Notably, the observation of correlated insulators and superconductivity, and the interplay between these phases have garnered significant attention. A wealth of correlated phases with unprecedented tunability was discovered subsequently, including orbital ferromagnetism, Chern insulators, strange metallicity, density waves, and nematicity. However, a comprehensive understanding of these closely competing phases remains elusive. The ability to controllably twist and stack multiple graphene layers has enabled the creation of a whole new family of moiré superlattices with myriad properties. Here, we review the progress and development achieved so far, encompassing the rich phase diagrams offered by these graphene-based moiré systems. Additionally, we discuss multiple phases recently observed in non-moiré multilayer graphene systems. Finally, we outline future opportunities and challenges for the exploration of hidden phases in this new generation of moiré materials.
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Affiliation(s)
- Saisab Bhowmik
- Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore 560012, India
| | - Arindam Ghosh
- Department of Physics, Indian Institute of Science, Bangalore 560012, India
- Centre for Nano Science and Engineering, Indian Institute of Science, Bangalore 560012, India
| | - U Chandni
- Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore 560012, India
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Hoke JC, Li Y, May-Mann J, Watanabe K, Taniguchi T, Bradlyn B, Hughes TL, Feldman BE. Uncovering the spin ordering in magic-angle graphene via edge state equilibration. Nat Commun 2024; 15:4321. [PMID: 38773076 PMCID: PMC11109299 DOI: 10.1038/s41467-024-48385-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2024] [Accepted: 04/30/2024] [Indexed: 05/23/2024] Open
Abstract
The flat bands in magic-angle twisted bilayer graphene (MATBG) provide an especially rich arena to investigate interaction-driven ground states. While progress has been made in identifying the correlated insulators and their excitations at commensurate moiré filling factors, the spin-valley polarizations of the topological states that emerge at high magnetic field remain unknown. Here we introduce a technique based on twist-decoupled van der Waals layers that enables measurement of their electronic band structure and-by studying the backscattering between counter-propagating edge states-the determination of the relative spin polarization of their edge modes. We find that the symmetry-broken quantum Hall states that extend from the charge neutrality point in MATBG are spin unpolarized at even integer filling factors. The measurements also indicate that the correlated Chern insulator emerging from half filling of the flat valence band is spin unpolarized and suggest that its conduction band counterpart may be spin polarized.
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Affiliation(s)
- Jesse C Hoke
- Department of Physics, Stanford University, Stanford, CA, 94305, USA
- Geballe Laboratory for Advanced Materials, Stanford, CA, 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA
| | - Yifan Li
- Department of Physics, Stanford University, Stanford, CA, 94305, USA
- Geballe Laboratory for Advanced Materials, Stanford, CA, 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA
| | - Julian May-Mann
- Department of Physics, Stanford University, Stanford, CA, 94305, USA
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
| | - 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
| | - Barry Bradlyn
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
| | - Taylor L Hughes
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
| | - Benjamin E Feldman
- Department of Physics, Stanford University, Stanford, CA, 94305, USA.
- Geballe Laboratory for Advanced Materials, Stanford, CA, 94305, USA.
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, 94025, USA.
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Lv H, Yao Y, Yuan M, Chen G, Wang Y, Rao L, Li S, Kara UI, Dupont RL, Zhang C, Chen B, Liu B, Zhou X, Wu R, Adera S, Che R, Zhang X, Wang X. Functional nanoporous graphene superlattice. Nat Commun 2024; 15:1295. [PMID: 38346953 PMCID: PMC10861524 DOI: 10.1038/s41467-024-45503-9] [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: 07/19/2023] [Accepted: 01/26/2024] [Indexed: 02/15/2024] Open
Abstract
Two-dimensional (2D) superlattices, formed by stacking sublattices of 2D materials, have emerged as a powerful platform for tailoring and enhancing material properties beyond their intrinsic characteristics. However, conventional synthesis methods are limited to pristine 2D material sublattices, posing a significant practical challenge when it comes to stacking chemically modified sublattices. Here we report a chemical synthesis method that overcomes this challenge by creating a unique 2D graphene superlattice, stacking graphene sublattices with monodisperse, nanometer-sized, square-shaped pores and strategically doped elements at the pore edges. The resulting graphene superlattice exhibits remarkable correlations between quantum phases at both the electron and phonon levels, leading to diverse functionalities, such as electromagnetic shielding, energy harvesting, optoelectronics, and thermoelectrics. Overall, our findings not only provide chemical design principles for synthesizing and understanding functional 2D superlattices but also expand their enhanced functionality and extensive application potential compared to their pristine counterparts.
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Affiliation(s)
- Hualiang Lv
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, OH, 43210, USA
- Institution of Optoelectronic, Laboratory of Advanced Materials, Academy for Engineering & Technology, Department of Materials Science, Fudan University, Shanghai, 200438, P. R. China
| | - Yuxing Yao
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, 02138, USA
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA
| | - Mingyue Yuan
- Institution of Optoelectronic, Laboratory of Advanced Materials, Academy for Engineering & Technology, Department of Materials Science, Fudan University, Shanghai, 200438, P. R. China
| | - Guanyu Chen
- Institution of Optoelectronic, Laboratory of Advanced Materials, Academy for Engineering & Technology, Department of Materials Science, Fudan University, Shanghai, 200438, P. R. China
| | - Yuchao Wang
- Institution of Optoelectronic, Laboratory of Advanced Materials, Academy for Engineering & Technology, Department of Materials Science, Fudan University, Shanghai, 200438, P. R. China
- Key Laboratory of Materials for High-Power Laser, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, 201800, P. R. China
| | - Longjun Rao
- Institution of Optoelectronic, Laboratory of Advanced Materials, Academy for Engineering & Technology, Department of Materials Science, Fudan University, Shanghai, 200438, P. R. China
| | - Shucong Li
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, 02138, USA
- School of Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Ufuoma I Kara
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, OH, 43210, USA
| | - Robert L Dupont
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, OH, 43210, USA
| | - Cheng Zhang
- Key Laboratory of Materials for High-Power Laser, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, 201800, P. R. China.
| | - Boyuan Chen
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, OH, 43210, USA
| | - Bo Liu
- College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, P. R. China
| | - Xiaodi Zhou
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, OH, 43210, USA
| | - Renbing Wu
- Institution of Optoelectronic, Laboratory of Advanced Materials, Academy for Engineering & Technology, Department of Materials Science, Fudan University, Shanghai, 200438, P. R. China.
| | - Solomon Adera
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, 48109, USA
| | - Renchao Che
- Institution of Optoelectronic, Laboratory of Advanced Materials, Academy for Engineering & Technology, Department of Materials Science, Fudan University, Shanghai, 200438, P. R. China.
| | - Xingcai Zhang
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA.
| | - Xiaoguang Wang
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, OH, 43210, USA.
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA.
- Sustainability Institute, The Ohio State University, Columbus, OH, 43210, USA.
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Li Y, Wan Q, Xu N. Recent Advances in Moiré Superlattice Systems by Angle-Resolved Photoemission Spectroscopy. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023:e2305175. [PMID: 37689836 DOI: 10.1002/adma.202305175] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Revised: 08/16/2023] [Indexed: 09/11/2023]
Abstract
The last decade has witnessed a flourish in 2D materials including graphene and transition metal dichalcogenides (TMDs) as atomic-scale Legos. Artificial moiré superlattices via stacking 2D materials with a twist angle and/or a lattice mismatch have recently become a fertile playground exhibiting a plethora of emergent properties beyond their building blocks. These rich quantum phenomena stem from their nontrivial electronic structures that are effectively tuned by the moiré periodicity. Modern angle-resolved photoemission spectroscopy (ARPES) can directly visualize electronic structures with decent momentum, energy, and spatial resolution, thus can provide enlightening insights into fundamental physics in moiré superlattice systems and guides for designing novel devices. In this review, first, a brief introduction is given on advanced ARPES techniques and basic ideas of band structures in a moiré superlattice system. Then ARPES research results of various moiré superlattice systems are highlighted, including graphene on substrates with small lattice mismatches, twisted graphene/TMD moiré systems, and high-order moiré superlattice systems. Finally, it discusses important questions that remain open, challenges in current experimental investigations, and presents an outlook on this field of research.
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Affiliation(s)
- Yiwei Li
- Institute for Advanced Studies (IAS), Wuhan University, Wuhan, 430072, China
| | - Qiang Wan
- Institute for Advanced Studies (IAS), Wuhan University, Wuhan, 430072, China
| | - Nan Xu
- Institute for Advanced Studies (IAS), Wuhan University, Wuhan, 430072, China
- Wuhan Institute of Quantum Technology, Wuhan, 430206, China
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Mao D, Zhang K, Kim EA. Fractionalization in Fractional Correlated Insulating States at n±1/3 Filled Twisted Bilayer Graphene. PHYSICAL REVIEW LETTERS 2023; 131:106801. [PMID: 37739384 DOI: 10.1103/physrevlett.131.106801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2022] [Revised: 07/13/2023] [Accepted: 08/17/2023] [Indexed: 09/24/2023]
Abstract
Fractionalization without time-reversal symmetry breaking is a long-sought-after goal in the study of correlated phenomena. The earlier proposal of correlated insulating states at n±1/3 filling in twisted bilayer graphene and recent experimental observations of insulating states at those fillings strongly suggest that moiré graphene systems provide a new platform to realize time-reversal symmetric fractionalized states. However, the nature of fractional excitations and the effect of quantum fluctuation on the fractional correlated insulating states are unknown. We show that excitations of the fractional correlated insulator phases in the strong coupling limit carry fractional charges and exhibit fractonic restricted mobility. Upon introduction of quantum fluctuations, the resonance of "lemniscate" structured operators drives the system into quantum lemniscate liquid (QLL) or quantum lemniscate solid (QLS). We find an emergent U(1)×U(1) 1-form symmetry unifies distinct motions of the fractionally charged excitations in the strong coupling limit and in the QLL phase, while providing a new mechanism for fractional excitations in two dimensions. We predict emergent Luttinger liquid behavior upon dilute doping in the strong coupling limit due to restricted mobility and discuss implications at a general n±1/3 filling.
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Affiliation(s)
- Dan Mao
- Laboratory of Atomic and Solid State Physics, Cornell University, 142 Sciences Drive, Ithaca, New York 14853-2501, USA
| | - Kevin Zhang
- Laboratory of Atomic and Solid State Physics, Cornell University, 142 Sciences Drive, Ithaca, New York 14853-2501, USA
| | - Eun-Ah Kim
- Laboratory of Atomic and Solid State Physics, Cornell University, 142 Sciences Drive, Ithaca, New York 14853-2501, USA
- Radcliffe Institute for Advanced Study at Harvard, Harvard University, 10 Garden Street, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA
- Department of Physics, Ewha Womans University, Seoul 03760, Republic of Korea
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Kim S, Kim D, Watanabe K, Taniguchi T, Smet JH, Kim Y. Orbitally Controlled Quantum Hall States in Decoupled Two-Bilayer Graphene Sheets. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2023; 10:e2300574. [PMID: 37259684 PMCID: PMC10427396 DOI: 10.1002/advs.202300574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2023] [Revised: 04/29/2023] [Indexed: 06/02/2023]
Abstract
The authors report on integer and fractional quantum Hall states in a stack of two twisted Bernal bilayer graphene sheets. By exploiting the momentum mismatch in reciprocal space, the single-particle tunneling between both bilayers is suppressed. Since the bilayers are spatially separated by only 0.34 nm, the stack benefits from strong interlayer Coulombic interactions. These interactions can cause the formation of a Bose-Einstein condensate. Indeed, such a condensate is observed for half-filling in each bilayer sheet. However, only when the partially filled levels have orbital index 1. It is absent for partially filled levels with orbital index 0. This discrepancy is tentatively attributed to the role of skyrmion/anti-skyrmion pair excitations and the dependence of the energy of these excitations on the orbital index. The application of asymmetric top and bottom gate voltages enables to influence the orbital nature of the electronic states of the graphene bilayers at the chemical potential and to navigate in orbital mixed space. The latter hosts an even denominator fractional quantum Hall state at total filling of -3/2. These observations suggest a unique edge reconstruction involving both electrons and chiral p-wave composite fermions.
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Affiliation(s)
- Soyun Kim
- Department of Physics and ChemistryDaegu Gyeongbuk Institute of Science and Technology (DGIST)Daegu42988Republic of Korea
| | - Dohun Kim
- Department of Physics and ChemistryDaegu Gyeongbuk Institute of Science and Technology (DGIST)Daegu42988Republic of Korea
| | - Kenji Watanabe
- Research Center for Functional MaterialsNational Institute for Materials ScienceTsukuba305‐0044Japan
| | - Takashi Taniguchi
- International Center for Materials NanoarchitectonicsNational Institute for Materials ScienceTsukuba305‐0044Japan
| | - Jurgen H. Smet
- Max Planck Institute for Solid State Research70569StuttgartGermany
| | - Youngwook Kim
- Department of Physics and ChemistryDaegu Gyeongbuk Institute of Science and Technology (DGIST)Daegu42988Republic of Korea
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Yu D, Li G, Wang L, Leykam D, Yuan L, Chen X. Moiré Lattice in One-Dimensional Synthetic Frequency Dimension. PHYSICAL REVIEW LETTERS 2023; 130:143801. [PMID: 37084429 DOI: 10.1103/physrevlett.130.143801] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2022] [Accepted: 03/13/2023] [Indexed: 05/03/2023]
Abstract
The moiré lattice has recently attracted broad interest in both solid-state physics and photonics where exotic phenomena in manipulating the quantum states are explored. In this work, we study the one-dimensional (1D) analogs of "moiré" lattices in a synthetic frequency dimension constructed by coupling two resonantly modulated ring resonators with different lengths. Unique features associated with the flatband manipulation as well as the flexible control of localization position inside each unit cell in the frequency dimension have been found, which can be controlled via the choice of flatband. Our work therefore provides insight into simulating moiré physics in 1D synthetic frequency space, which holds important promise for potential applications toward optical information processing.
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Affiliation(s)
- Danying Yu
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Guangzhen Li
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Luojia Wang
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Daniel Leykam
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
| | - Luqi Yuan
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
| | - Xianfeng Chen
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China
- Shanghai Research Center for Quantum Sciences, Shanghai, 201315, China
- Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, Jinan, 250358, China
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Yankowitz M. Unravelling the magic of twisted trilayer graphene. NATURE MATERIALS 2023; 22:286-287. [PMID: 36631679 DOI: 10.1038/s41563-022-01462-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Affiliation(s)
- Matthew Yankowitz
- Department of Physics, University of Washington, Seattle, WA, USA.
- Department of Materials Science and Engineering, University of Washington, Seattle, WA, USA.
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