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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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Liu L, Chu Y, Yang G, Yuan Y, Wu F, Ji Y, Tian J, Yang R, Watanabe K, Taniguchi T, Long G, Shi D, Liu J, Shen J, Lu L, Yang W, Zhang G. Quantum oscillations in field-induced correlated insulators of a moiré superlattice. Sci Bull (Beijing) 2023; 68:1127-1133. [PMID: 37210331 DOI: 10.1016/j.scib.2023.05.006] [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: 01/05/2023] [Revised: 04/03/2023] [Accepted: 04/26/2023] [Indexed: 05/22/2023]
Abstract
We report an observation of quantum oscillations (QOs) in the correlated insulators with valley anisotropy of twisted double bilayer graphene (TDBG). The anomalous QOs are best captured in the magneto resistivity oscillations of the insulators at v = -2, with a period of 1/B and an oscillation amplitude as high as 150 kΩ. The QOs can survive up to ∼10 K, and above 12 K, the insulating behaviors are dominant. The QOs of the insulator are strongly D dependent: the carrier density extracted from the 1/B periodicity decreases almost linearly with D from -0.7 to -1.1 V/nm, suggesting a reduced Fermi surface; the effective mass from Lifshitz-Kosevich analysis depends nonlinearly on D, reaching a minimal value of 0.1 me at D = ∼ -1.0 V/nm. Similar observations of QOs are also found at v = 2, as well as in other devices without graphite gate. We interpret the D sensitive QOs of the correlated insulators in the picture of band inversion. By reconstructing an inverted band model with the measured effective mass and Fermi surface, the density of state at the gap, calculated from thermal broadened Landau levels, agrees qualitatively with the observed QOs in the insulators. While more theoretical understandings are needed in the future to fully account for the anomalous QOs in this moiré system, our study suggests that TDBG is an excellent platform to discover exotic phases where correlation and topology are at play.
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Affiliation(s)
- Le Liu
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Yanbang Chu
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Guang Yang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Yalong Yuan
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Fanfan Wu
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Yiru Ji
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Jinpeng Tian
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Rong Yang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; Songshan Lake Materials Laboratory, Dongguan 523808, China
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba 305-0044, Japan
| | - Gen Long
- Songshan Lake Materials Laboratory, Dongguan 523808, China
| | - Dongxia Shi
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China; Songshan Lake Materials Laboratory, Dongguan 523808, China
| | - Jianpeng Liu
- School of Physical Sciences and Technology, ShanghaiTech University, Shanghai 200031, China; ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 200031, China
| | - Jie Shen
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China; Songshan Lake Materials Laboratory, Dongguan 523808, China
| | - Li Lu
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China; Songshan Lake Materials Laboratory, Dongguan 523808, China
| | - Wei Yang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China; Songshan Lake Materials Laboratory, Dongguan 523808, China.
| | - Guangyu Zhang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China; Songshan Lake Materials Laboratory, Dongguan 523808, China.
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Herzog-Arbeitman J, Song ZD, Elcoro L, Bernevig BA. Hofstadter Topology with Real Space Invariants and Reentrant Projective Symmetries. PHYSICAL REVIEW LETTERS 2023; 130:236601. [PMID: 37354423 DOI: 10.1103/physrevlett.130.236601] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2022] [Revised: 04/15/2023] [Accepted: 05/04/2023] [Indexed: 06/26/2023]
Abstract
Adding magnetic flux to a band structure breaks Bloch's theorem by realizing a projective representation of the translation group. The resulting Hofstadter spectrum encodes the nonperturbative response of the bands to flux. Depending on their topology, adding flux can enforce a bulk gap closing (a Hofstadter semimetal) or boundary state pumping (a Hofstadter topological insulator). In this Letter, we present a real space classification of these Hofstadter phases. We give topological indices in terms of symmetry-protected real space invariants, which reveal the bulk and boundary responses of fragile topological states to flux. In fact, we find that the flux periodicity in tight-binding models causes the symmetries which are broken by the magnetic field to reenter at strong flux where they form projective point group representations. We completely classify the reentrant projective point groups and find that the Schur multipliers which define them are Arahanov-Bohm phases calculated along the bonds of the crystal. We find that a nontrivial Schur multiplier is enough to predict and protect the Hofstadter response with only zero-flux topology.
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Affiliation(s)
| | - Zhi-Da Song
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Luis Elcoro
- Department of Physics, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
| | - B Andrei Bernevig
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastian, Spain
- IKERBASQUE, Basque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Spain
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Isospin competitions and valley polarized correlated insulators in twisted double bilayer graphene. Nat Commun 2022; 13:3292. [PMID: 35672329 PMCID: PMC9174269 DOI: 10.1038/s41467-022-30998-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2021] [Accepted: 05/20/2022] [Indexed: 12/02/2022] Open
Abstract
New phase of matter usually emerges when a given symmetry breaks spontaneously, which can involve charge, spin, and valley degree of freedoms. Here, we report an observation of new correlated insulators evolved from spin-polarized states to valley-polarized states in twisted double bilayer graphene (TDBG) driven by the displacement field (D). At a high field |D | > 0.7 V/nm, we observe valley polarized correlated insulators with a big Zeeman g factor of ~10, both at v = 2 in the moiré conduction band and more surprisingly at v = −2 in the moiré valence band. Moreover, we observe a valley polarized Chern insulator with C = 2 emanating at v = 2 in the electron side and a valley polarized Fermi surface around v = −2 in the hole side. Our results demonstrate a feasible way to realize isospin control and to obtain new phases of matter in TDBG by the displacement field, and might benefit other twisted or non-twisted multilayer systems. Previous studies of twisted double bilayer graphene have been limited to AB-AB stacking, featuring spin-polarized correlated insulators. Here, the authors fabricate AB-BA devices and report a competition between spin and valley polarization, along with the emergence of valley-polarized correlated insulators tuned by electric field.
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Zhang S, Dai X, Liu J. Spin-Polarized Nematic Order, Quantum Valley Hall States, and Field-Tunable Topological Transitions in Twisted Multilayer Graphene Systems. PHYSICAL REVIEW LETTERS 2022; 128:026403. [PMID: 35089764 DOI: 10.1103/physrevlett.128.026403] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2021] [Revised: 07/17/2021] [Accepted: 12/22/2021] [Indexed: 06/14/2023]
Abstract
We theoretically study the correlated insulator states, quantum anomalous Hall (QAH) states, and field-induced topological transitions between different correlated states in twisted multilayer graphene systems. Taking twisted bilayer-monolayer graphene and twisted double-bilayer graphene as examples, we show that both systems stay in spin-polarized, C_{3z}-broken insulator states with zero Chern number at 1/2 filling of the flat bands under finite displacement fields. In some cases these spin-polarized, nematic insulator states are in the quantum valley Hall (QVH) phase by virtue of the nontrivial band topology of the systems. The spin-polarized insulator state is quasidegenerate with the valley polarized state if only the dominant intravalley Coulomb interaction is included. Such quasidegeneracy can be split by atomic on-site interactions such that the spin-polarized, nematic state become the unique ground state. Such a scenario applies to various twisted multilayer graphene systems at 1/2 filling, thus can be considered as a universal mechanism. Moreover, under vertical magnetic fields, the orbital Zeeman splittings and the field-induced change of charge density in twisted multilayer graphene systems would compete with the atomic Hubbard interactions, which can drive transitions from spin-polarized zero-Chern-number states to valley-polarized QAH states with small onset magnetic fields.
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Affiliation(s)
- Shihao Zhang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 200031, China
| | - Xi Dai
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
| | - Jianpeng Liu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 200031, China
- ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai 200031, China
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