1
|
Chakraborti H, Gorini C, Knothe A, Liu MH, Makk P, Parmentier FD, Perconte D, Richter K, Roulleau P, Sacépé B, Schönenberger C, Yang W. Electron wave and quantum optics in graphene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:393001. [PMID: 38697131 DOI: 10.1088/1361-648x/ad46bc] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2023] [Accepted: 05/01/2024] [Indexed: 05/04/2024]
Abstract
In the last decade, graphene has become an exciting platform for electron optical experiments, in some aspects superior to conventional two-dimensional electron gases (2DEGs). A major advantage, besides the ultra-large mobilities, is the fine control over the electrostatics, which gives the possibility of realising gap-less and compact p-n interfaces with high precision. The latter host non-trivial states,e.g., snake states in moderate magnetic fields, and serve as building blocks of complex electron interferometers. Thanks to the Dirac spectrum and its non-trivial Berry phase, the internal (valley and sublattice) degrees of freedom, and the possibility to tailor the band structure using proximity effects, such interferometers open up a completely new playground based on novel device architectures. In this review, we introduce the theoretical background of graphene electron optics, fabrication methods used to realise electron-optical devices, and techniques for corresponding numerical simulations. Based on this, we give a comprehensive review of ballistic transport experiments and simple building blocks of electron optical devices both in single and bilayer graphene, highlighting the novel physics that is brought in compared to conventional 2DEGs. After describing the different magnetic field regimes in graphene p-n junctions and nanostructures, we conclude by discussing the state of the art in graphene-based Mach-Zender and Fabry-Perot interferometers.
Collapse
Affiliation(s)
| | - Cosimo Gorini
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette, France
| | - Angelika Knothe
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Ming-Hao Liu
- Department of Physics and Center for Quantum Frontiers of Research and Technology (QFort), National Cheng Kung University, Tainan 70101, Taiwan
| | - Péter Makk
- Department of Physics, Institute of Physics, Budapest University of Technology and Economics, Műegyetem rkp. 3., Budapest H-1111, Hungary
- MTA-BME Correlated van der Waals Structures Momentum Research Group, Műegyetem rkp. 3., Budapest H-1111, Hungary
| | | | - David Perconte
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | - Klaus Richter
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Preden Roulleau
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette, France
| | - Benjamin Sacépé
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | | | - Wenmin Yang
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| |
Collapse
|
2
|
Li Q, Chen Y, Wei L, Chen H, Huang Y, Zhu Y, Zhu W, An D, Song J, Gan Q, Zhang Q, Watanabe K, Taniguchi T, Shi X, Novoselov KS, Wang R, Yu G, Wang L. Strongly coupled magneto-exciton condensates in large-angle twisted double bilayer graphene. Nat Commun 2024; 15:5065. [PMID: 38871728 DOI: 10.1038/s41467-024-49406-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2023] [Accepted: 05/31/2024] [Indexed: 06/15/2024] Open
Abstract
Excitons, pairs of electrons and holes, undergo a Bose-Einstein condensation at low temperatures. An important platform to study excitons is double-layer two-dimensional electron gases, with two parallel planes of electrons and holes separated by a thin insulating layer. Lowering this separation (d) strengthens the exciton binding energy, however, leads to the undesired interlayer tunneling, resulting in annihilation of excitons. Here, we report the observation of a sequences of robust exciton condensates (ECs) in double bilayer graphene twisted to ~ 10° with no insulating mid-layer. The large momentum mismatch between two graphene layers suppresses interlayer tunneling, reaching a d ~ 0.334 nm. Measuring the bulk and edge transport, we find incompressible states corresponding to ECs when both layers are in half-filled N = 0, 1 Landau levels (LLs). Theoretical calculations suggest that the low-energy charged excitation of ECs can be meron-antimeron or particle-hole pair, which relies on both LL index and carrier type. Our results establish a novel platform with extreme coupling strength for studying quantum bosonic phase.
Collapse
Affiliation(s)
- Qingxin Li
- National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Yiwei Chen
- National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - LingNan Wei
- National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Hong Chen
- National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Yan Huang
- National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Yujian Zhu
- National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Wang Zhu
- National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Dongdong An
- National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Junwei Song
- National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Qikang Gan
- National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - Qi Zhang
- National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China
| | - 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
| | - Xiaoyang Shi
- Environmental and Sustainable Engineering, College of Engineering and Applied Science, University at Albany, Albany, NY, 12222, USA.
| | - Kostya S Novoselov
- Institute for Functional Intelligent Materials, National University of Singapore, Building S9, 4 Science Drive 2, Singapore, 117544, Singapore
| | - Rui Wang
- National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China.
| | - Geliang Yu
- National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China.
| | - Lei Wang
- National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China.
| |
Collapse
|
3
|
Kuang X, Pantaleón Peralta PA, Angel Silva-Guillén J, Yuan S, Guinea F, Zhan Z. Optical properties and plasmons in moiré structures. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:173001. [PMID: 38232397 DOI: 10.1088/1361-648x/ad1f8c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2023] [Accepted: 01/17/2024] [Indexed: 01/19/2024]
Abstract
The discoveries of numerous exciting phenomena in twisted bilayer graphene (TBG) are stimulating significant investigations on moiré structures that possess a tunable moiré potential. Optical response can provide insights into the electronic structures and transport phenomena of non-twisted and twisted moiré structures. In this article, we review both experimental and theoretical studies of optical properties such as optical conductivity, dielectric function, non-linear optical response, and plasmons in moiré structures composed of graphene, hexagonal boron nitride (hBN), and/or transition metal dichalcogenides. Firstly, a comprehensive introduction to the widely employed methodology on optical properties is presented. After, moiré potential induced optical conductivity and plasmons in non-twisted structures are reviewed, such as single layer graphene-hBN, bilayer graphene-hBN and graphene-metal moiré heterostructures. Next, recent investigations of twist-angle dependent optical response and plasmons are addressed in twisted moiré structures. Additionally, we discuss how optical properties and plasmons could contribute to the understanding of the many-body effects and superconductivity observed in moiré structures.
Collapse
Affiliation(s)
- Xueheng Kuang
- Yangtze Delta Industrial Innovation Center of Quantum Science and Technology, Suzhou 215000, People's Republic of China
| | | | - Jose Angel Silva-Guillén
- Instituto Madrileño de Estudios Avanzados, IMDEA Nanociencia, Calle Faraday 9, 28049 Madrid, Spain
| | - Shengjun Yuan
- Key Laboratory of Artificial Micro- and Nano-structures of the Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, People's Republic of China
- Wuhan Institute of Quantum Technology, Wuhan 430206, People's Republic of China
| | - Francisco Guinea
- Instituto Madrileño de Estudios Avanzados, IMDEA Nanociencia, Calle Faraday 9, 28049 Madrid, Spain
- Donostia International Physics Center, Paseo Manuel de Lardizábal 4, 20018 San Sebastián, Spain
| | - Zhen Zhan
- Instituto Madrileño de Estudios Avanzados, IMDEA Nanociencia, Calle Faraday 9, 28049 Madrid, Spain
| |
Collapse
|
4
|
Arrighi E, Nguyen VH, Di Luca M, Maffione G, Hong Y, Farrar L, Watanabe K, Taniguchi T, Mailly D, Charlier JC, Ribeiro-Palau R. Non-identical moiré twins in bilayer graphene. Nat Commun 2023; 14:8178. [PMID: 38081818 PMCID: PMC10713781 DOI: 10.1038/s41467-023-43965-x] [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: 08/06/2022] [Accepted: 11/24/2023] [Indexed: 02/09/2024] Open
Abstract
The superlattice obtained by aligning a monolayer graphene and boron nitride (BN) inherits from the hexagonal lattice a sixty degrees periodicity with the layer alignment. It implies that, in principle, the properties of the heterostructure must be identical for 0° and 60° of layer alignment. Here, we demonstrate, using dynamically rotatable van der Waals heterostructures, that the moiré superlattice formed in a bilayer graphene/BN has different electronic properties at 0° and 60° of alignment. Although the existence of these non-identical moiré twins is explained by different relaxation of the atomic structures for each alignment, the origin of the observed valley Hall effect remains to be explained. A simple Berry curvature argument is not sufficient to explain the 120° periodicity of this observation. Our results highlight the complexity of the interplay between mechanical and electronic properties in moiré structures and the importance of taking into account atomic structure relaxation to understand their electronic properties.
Collapse
Affiliation(s)
- Everton Arrighi
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies (C2N), 91120, Palaiseau, France
| | - Viet-Hung Nguyen
- Institute of Condensed Matter and Nanosciences, Université catholique de Louvain (UCLouvain), 1348, Louvain-la-Neuve, Belgium
| | - Mario Di Luca
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies (C2N), 91120, Palaiseau, France
| | - Gaia Maffione
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies (C2N), 91120, Palaiseau, France
| | - Yuanzhuo Hong
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies (C2N), 91120, Palaiseau, France
| | - Liam Farrar
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies (C2N), 91120, Palaiseau, France
| | - Kenji Watanabe
- National Institute for Materials Science, 1-1 Namiki, Tsukuba, Japan
| | - Takashi Taniguchi
- National Institute for Materials Science, 1-1 Namiki, Tsukuba, Japan
| | - Dominique Mailly
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies (C2N), 91120, Palaiseau, France
| | - Jean-Christophe Charlier
- Institute of Condensed Matter and Nanosciences, Université catholique de Louvain (UCLouvain), 1348, Louvain-la-Neuve, Belgium
| | - Rebeca Ribeiro-Palau
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies (C2N), 91120, Palaiseau, France.
| |
Collapse
|
5
|
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.
Collapse
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
| |
Collapse
|
6
|
Zhang S, Xie B, Wu Q, Liu J, Yazyev OV. Chiral Decomposition of Twisted Graphene Multilayers with Arbitrary Stacking. NANO LETTERS 2023; 23:2921-2926. [PMID: 36940241 DOI: 10.1021/acs.nanolett.3c00275] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
We formulate the chiral decomposition rules that govern the electronic structure of a broad family of twisted N + M multilayer graphene configurations that combine arbitrary stacking order and a mutual twist. We show that at the magic angle in the chiral limit the low-energy bands of such systems are composed of chiral pseudospin doublets that are energetically entangled with two flat bands per valley induced by the moiré superlattice potential. The analytic construction is supported by explicit numerical calculations based on realistic parametrization. We further show that vertical displacement fields can open energy gaps between the pseudospin doublets and the two flat bands, such that the flat bands may carry nonzero valley Chern numbers. These results provide guidelines for the rational design of topological and correlated states in generic twisted graphene multilayers.
Collapse
Affiliation(s)
- ShengNan Zhang
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials MARVEL, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Bo Xie
- School of Physical Sciences and Technology, ShanghaiTech University, Shanghai 200031, China and
| | - QuanSheng Wu
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials MARVEL, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Jianpeng Liu
- School of Physical Sciences and Technology, ShanghaiTech University, Shanghai 200031, China and
- ShanghaiTech laboratory for Topological Physics, ShanghaiTech University, Shanghai 200031, China
| | - Oleg V Yazyev
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials MARVEL, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| |
Collapse
|
7
|
Szentpéteri B, Rickhaus P, de Vries FK, Márffy A, Fülöp B, Tóvári E, Watanabe K, Taniguchi T, Kormányos A, Csonka S, Makk P. Tailoring the Band Structure of Twisted Double Bilayer Graphene with Pressure. NANO LETTERS 2021; 21:8777-8784. [PMID: 34662136 PMCID: PMC8554798 DOI: 10.1021/acs.nanolett.1c03066] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2021] [Revised: 10/11/2021] [Indexed: 05/21/2023]
Abstract
Twisted two-dimensional structures open new possibilities in band structure engineering. At magic twist angles, flat bands emerge, which gave a new drive to the field of strongly correlated physics. In twisted double bilayer graphene dual gating allows changing of the Fermi level and hence the electron density and also allows tuning of the interlayer potential, giving further control over band gaps. Here, we demonstrate that by application of hydrostatic pressure, an additional control of the band structure becomes possible due to the change of tunnel couplings between the layers. We find that the flat bands and the gaps separating them can be drastically changed by pressures up to 2 GPa, in good agreement with our theoretical simulations. Furthermore, our measurements suggest that in finite magnetic field due to pressure a topologically nontrivial band gap opens at the charge neutrality point at zero displacement field.
Collapse
Affiliation(s)
- Bálint Szentpéteri
- Department
of Physics, Budapest University of Technology
and Economics and Nanoelectronics Momentum Research Group of the Hungarian
Academy of Sciences, Budafoki ut 8, 1111 Budapest, Hungary
| | - Peter Rickhaus
- Solid
State Physics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | | | - Albin Márffy
- Department
of Physics, Budapest University of Technology
and Economics and Correlated van der Waals Structures Momentum Research
Group of the Hungarian Academy of Sciences, Budafoki ut 8, 1111 Budapest, Hungary
| | - Bálint Fülöp
- Department
of Physics, Budapest University of Technology
and Economics and Nanoelectronics Momentum Research Group of the Hungarian
Academy of Sciences, Budafoki ut 8, 1111 Budapest, Hungary
| | - Endre Tóvári
- Department
of Physics, Budapest University of Technology
and Economics and Nanoelectronics Momentum Research Group of the Hungarian
Academy of Sciences, Budafoki ut 8, 1111 Budapest, Hungary
| | - 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
| | - Andor Kormányos
- Department
of Physics of Complex Systems, Eötvös
Loránd University, Pázmány P. s. 1/A, 1117 Budapest, Hungary
| | - Szabolcs Csonka
- Department
of Physics, Budapest University of Technology
and Economics and Nanoelectronics Momentum Research Group of the Hungarian
Academy of Sciences, Budafoki ut 8, 1111 Budapest, Hungary
| | - Péter Makk
- Department
of Physics, Budapest University of Technology
and Economics and Correlated van der Waals Structures Momentum Research
Group of the Hungarian Academy of Sciences, Budafoki ut 8, 1111 Budapest, Hungary
| |
Collapse
|
8
|
Rickhaus P, de Vries FK, Zhu J, Portoles E, Zheng G, Masseroni M, Kurzmann A, Taniguchi T, Watanabe K, MacDonald AH, Ihn T, Ensslin K. Correlated electron-hole state in twisted double-bilayer graphene. Science 2021; 373:1257-1260. [PMID: 34516786 DOI: 10.1126/science.abc3534] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
[Figure: see text].
Collapse
Affiliation(s)
- Peter Rickhaus
- Solid State Physics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | | | - Jihang Zhu
- Department of Physics, University of Texas at Austin, Austin, TX 78712, USA
| | - Elías Portoles
- Solid State Physics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Giulia Zheng
- Solid State Physics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Michele Masseroni
- Solid State Physics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Annika Kurzmann
- Solid State Physics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Takashi Taniguchi
- National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Kenji Watanabe
- National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Allan H MacDonald
- Department of Physics, University of Texas at Austin, Austin, TX 78712, USA
| | - Thomas Ihn
- Solid State Physics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland.,Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | - Klaus Ensslin
- Solid State Physics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland.,Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| |
Collapse
|
9
|
Souza ACR, Matos MJS, Mazzoni MSC. Interplay between structural deformations and flat band phenomenology in twisted bilayer antimonene. RSC Adv 2021; 11:27855-27859. [PMID: 35480738 PMCID: PMC9038057 DOI: 10.1039/d1ra05301a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2021] [Accepted: 08/10/2021] [Indexed: 11/21/2022] Open
Abstract
In this work we apply first principles calculations to investigate the flat band phenomenology in twisted antimonene bilayer. We show that the relatively strong interlayer interactions which characterize this compound have profound effects in the emergence and properties of the flat bands. Specifically, when the moiré length becomes large enough to create well defined stacking patterns along the structure, out-of-plane displacements take place and are stabilized in the regions dominated by the AB stacking, leading to the emergence of flat bands. The interplay between structural and electronic properties allows for detection of flat bands in higher twist angles comparable to other two-dimensional materials. We also show that their energy position may be modulated by noncovalent functionalization with electron acceptor molecules. Strong interlayer interactions allows for electron localization and emergence of flat bands in relatively higher twist angles in Sb bilayer. Noncovalent functionalization with electron acceptor molecules may modulate their energy position.![]()
Collapse
Affiliation(s)
- Alan C R Souza
- Departamento de Física, Universidade Federal de Minas Gerais Belo Horizonte MG Brazil 31270-901
| | - Matheus J S Matos
- Departamento de Física, Universidade Federal de Ouro Preto Ouro Preto MG Brazil 35400-000
| | - Mario S C Mazzoni
- Departamento de Física, Universidade Federal de Minas Gerais Belo Horizonte MG Brazil 31270-901
| |
Collapse
|
10
|
Tepliakov NV, Wu Q, Yazyev OV. Crystal Field Effect and Electric Field Screening in Multilayer Graphene with and without Twist. NANO LETTERS 2021; 21:4636-4642. [PMID: 34033719 DOI: 10.1021/acs.nanolett.1c00678] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We address the intrinsic polarization and screening of an external electric field in a broad range of ordered and twisted configurations of multilayer graphene, using an ab initio approach combining density functional theory and the Wannier function formalism. We show that multilayer graphene is intrinsically polarized due to the crystal field effect, an effect that is often neglected in tight-binding models of twisted bilayer graphene and similar systems. This intrinsic polarization of the order of up to a few tens of millielectronvolts has different out-of-plane alignments in ordered and twisted graphene multilayers, while the in-plane potential modulation is found to be much stronger in twisted systems. We further investigate the dielectric permittivity ε in same multilayer graphene configurations at different electric field strengths. Our findings establish a deep insight into intrinsic and extrinsic polarization in graphene multilayers and provide parameters necessary for building accurate models of these systems.
Collapse
Affiliation(s)
- Nikita V Tepliakov
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- Information Optical Technologies Center, ITMO University, Saint Petersburg 197101, Russia
| | - QuanSheng Wu
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Oleg V Yazyev
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| |
Collapse
|
11
|
Cai L, Yu G. Fabrication Strategies of Twisted Bilayer Graphenes and Their Unique Properties. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2021; 33:e2004974. [PMID: 33615593 DOI: 10.1002/adma.202004974] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2020] [Revised: 10/09/2020] [Indexed: 06/12/2023]
Abstract
Twisted bilayer graphene (tBLG) exhibits a host of innovative physical phenomena owing to the formation of moiré superlattice. Especially, the discovery of superconducting behavior has generated new interest in graphene. The growing studies of tBLG mainly focus on its physical properties, while the fabrication of high-quality tBLG is a prerequisite for achieving the desired properties due to the great dependence on the twist angle and the interfacial contact. Here, the cutting-edge preparation strategies and challenges of tBLG fabrication are reviewed. The advantages and disadvantages of chemical vapor deposition, epitaxial growth on silicon carbide, stacking monolayer graphene, and folding monolayer graphene methods for the fabrication of tBLG are analyzed in detail, providing a reference for further development of preparation methods. Moreover, the characterization methods of twist angle for the tBLG are presented. Then, the unique physicochemical properties and corresponding applications of tBLG, containing correlated insulating and superconducting states, ferromagnetic state, soliton, enhanced optical absorption, tunable bandgap, and lithium intercalation and diffusion, are described. Finally, the opportunities and challenges for fabricating high-quality and large-area tBLG are discussed, unique physical properties are displayed, and new applications inferred from its angle-dependent features are explored, thereby impelling the commercialization of tBLG from laboratory to market.
Collapse
Affiliation(s)
- Le Cai
- Beijing National Laboratory for Molecular Sciences, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing, 100190, P. R. China
- School of Chemical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, P. R. China
| | - Gui Yu
- Beijing National Laboratory for Molecular Sciences, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing, 100190, P. R. China
- School of Chemical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, P. R. China
| |
Collapse
|
12
|
Wu Q, Liu J, Guan Y, Yazyev OV. Landau Levels as a Probe for Band Topology in Graphene Moiré Superlattices. PHYSICAL REVIEW LETTERS 2021; 126:056401. [PMID: 33605745 DOI: 10.1103/physrevlett.126.056401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2020] [Accepted: 01/05/2021] [Indexed: 06/12/2023]
Abstract
We propose Landau levels as a probe for the topological character of electronic bands in two-dimensional moiré superlattices. We consider two configurations of twisted double bilayer graphene (TDBG) that have very similar band structures, but show different valley Chern numbers of the flat bands. These differences between the AB-AB and AB-BA configurations of TDBG clearly manifest as different Landau level sequences in the Hofstadter butterfly spectra calculated using the tight-binding model. The Landau level sequences are explained from the point of view of the distribution of orbital magnetization in momentum space that is governed by the rotational C_{2} and time-reversal T symmetries. Our results can be readily extended to other twisted graphene multilayers and h-BN/graphene heterostructures thus establishing the Hofstadter butterfly spectra as a powerful tool for detecting the nontrivial valley band topology.
Collapse
Affiliation(s)
- QuanSheng Wu
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials MARVEL, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Jianpeng Liu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 200031, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 200031, China
| | - Yifei Guan
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Oleg V Yazyev
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials MARVEL, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| |
Collapse
|
13
|
de Vries FK, Zhu J, Portolés E, Zheng G, Masseroni M, Kurzmann A, Taniguchi T, Watanabe K, MacDonald AH, Ensslin K, Ihn T, Rickhaus P. Combined Minivalley and Layer Control in Twisted Double Bilayer Graphene. PHYSICAL REVIEW LETTERS 2020; 125:176801. [PMID: 33156662 DOI: 10.1103/physrevlett.125.176801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2020] [Accepted: 09/03/2020] [Indexed: 06/11/2023]
Abstract
Control over minivalley polarization and interlayer coupling is demonstrated in double bilayer graphene twisted with an angle of 2.37°. This intermediate angle is small enough for the minibands to form and large enough such that the charge carrier gases in the layers can be tuned independently. Using a dual-gated geometry we identify and control all possible combinations of minivalley polarization via the population of the two bilayers. An applied displacement field opens a band gap in either of the two bilayers, allowing us to even obtain full minivalley polarization. In addition, the carriers, formerly separated by their minivalley character, are mixed by tuning through a Lifshitz transition, where the Fermi surface topology changes. The high degree of control over the minivalley character of the bulk charge transport in twisted double bilayer graphene offers new opportunities for realizing valleytronics devices such as valley valves, filters, and logic gates.
Collapse
Affiliation(s)
- Folkert K de Vries
- Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Jihang Zhu
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Elías Portolés
- Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Giulia Zheng
- Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Michele Masseroni
- Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Annika Kurzmann
- Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Takashi Taniguchi
- National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Kenji Watanabe
- National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Allan H MacDonald
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Klaus Ensslin
- Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Thomas Ihn
- Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Peter Rickhaus
- Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| |
Collapse
|
14
|
Haddadi F, Wu Q, Kruchkov AJ, Yazyev OV. Moiré Flat Bands in Twisted Double Bilayer Graphene. NANO LETTERS 2020; 20:2410-2415. [PMID: 32097013 DOI: 10.1021/acs.nanolett.9b05117] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We investigate twisted double bilayer graphene (TDBG), a four-layer system composed of two AB-stacked graphene bilayers rotated with respect to each other by a small angle. Our ab initio band structure calculations reveal a considerable energy gap at the charge-neutrality point that we assign to the intrinsic symmetric polarization (ISP). We then introduce the ISP effect into the tight-binding parametrization and perform calculations on TDBG models that include lattice relaxation effects down to very small twist angles. We identify a narrow region around the magic angle characterized by a manifold of remarkably flat bands gapped out from other states even without external electric fields. To understand the fundamental origin of the magic angle in TDBG, we construct a continuum model that points to a hidden mathematical link to the twisted bilayer graphene model, thus indicating that the band flattening is a fundamental feature of TDBG and is not a result of external fields.
Collapse
Affiliation(s)
- Fatemeh Haddadi
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - QuanSheng Wu
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials MARVEL, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Alex J Kruchkov
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Oleg V Yazyev
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials MARVEL, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| |
Collapse
|