Twisted bilayer graphene. IV. Exact insulator ground states and phase diagram
Abstract
Here, we derive the exact insulator ground states of the projected Hamiltonian of magic-angle twisted bilayer graphene (TBG) flat bands with Coulomb interactions in various limits, and study the perturbations away from these limits. We define the (first) chiral limit where the AA stacking hopping is zero, and a flat limit with exactly flat bands. In the chiral-flat limit, the TBG Hamiltonian has a U(4) × U(4) symmetry, and we find that the exact ground states at integer filling – 4 ≤ $$\textit{ν}$$ ≤ 4 relative to charge neutrality are Chern insulators of Chern numbers $$ν_C$$ = 4 – |$$\textit{ν}$$ |, 2 – |$$\textit{ν}$$ |, $$\cdots$$, |$$\textit{ν}$$ | – 4, all of which are degenerate. This confirms recent experiments where Chern insulators are found to be competitive low-energy states of TBG. When the chiral-flat limit is reduced to the nonchiral-flat limit which has a U(4) symmetry, we find $$\textit{ν}$$ = 0 , ± 2 has exact ground states of Chern number 0, while $$\textit{ν}$$ = ±1, ± 3 has perturbative ground states of Chern number $$ν_C$$ = ± 1, which are U(4) ferromagnetic. In the chiral-nonflat limit with a different U(4) symmetry, different Chern number states are degenerate up to second-order perturbations. In the realistic nonchiral-nonflat case, we find that the perturbative insulator states with Chern number $$ν_C$$ = 0 (0 < |$$ν_C$$| < 4 – |$$\textit{ν}$$ |) at integer fillings $$\textit{ν}$$ are fully (partially) intervalley coherent, while the insulator states with Chern number |$$ν_C$$| = 4 – |$$\textit{ν}$$ | are valley polarized. However, for 0 < |$$ν_C$$| ≤ 4 – |$$\textit{ν}$$ |, the fully intervalley coherent states are highly competitive (0.005 meV/electron higher). At nonzero magnetic field |$$\textit{B}$$ | > 0, a first-order phase transition for $$\textit{ν}$$ = ± 1, ± 2 from Chern number $$ν_C$$ = sgn ($$\textit{νB}$$)(2 – |$$\textit{ν}$$ |) to $$ν_C$$ = sgn ($$\textit{νB}$$)(4 – |$$\textit{ν}$$ |) is expected, which agrees with recent experimental observations. Lastly, the TBG Hamiltonian reduces into an extended Hubbard model in the stabilizer code limit.
- Authors:
-
- Princeton Univ., NJ (United States)
- Princeton Univ., NJ (United States); Laboratoire de Physique de l’Ecole normale supérieure (LPENS), Paris (France); École Normale Supérieure (ENS), Paris (France); Université PSL, Paris (France); Centre National de la Recherche Scientifique (CNRS) (France); Sorbonne Univ., Paris (France); University Paris-Diderot (France); Paris Cité, Paris (France)
- Barcelona Institute of Science and Technology (BIST) (Spain)
- Publication Date:
- Research Org.:
- Princeton Univ., NJ (United States)
- Sponsoring Org.:
- Schmidt Fund for Innovative Research; Packard Foundation; Gordon and Betty Moore Foundation; John Simon Guggenheim Memorial Foundation; National Science Foundation (NSF); US Department of the Navy, Office of Naval Research (ONR); United States-Israel Binational Science Foundation (BSF) ; Ministry of Economic Affairs and Digital Transformation of Spain (MINECO); Fundació Privada Cellex; Fundació Privada Mir-Puig; Generalitat de Catalunya; European Research Council (ERC); La Caixa Foundation; USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1849769
- Grant/Contract Number:
- FG02-07ER46419; SC0016239; 404513; GBMF8685; DMR 1643312; DMR-1420541; DMR-2011750; N00014-20-1-2303; 2018226; SE5-0522; 852927; GBMF9469; NSF-DMR-1420541; NSF-DMR-1904442
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 103; Journal Issue: 20; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Materials Science; Physics
Citation Formats
Lian, Biao, Song, Zhi-Da, Regnault, Nicolas, Efetov, Dmitri K., Yazdani, Ali, and Bernevig, B. Andrei. Twisted bilayer graphene. IV. Exact insulator ground states and phase diagram. United States: N. p., 2021.
Web. doi:10.1103/physrevb.103.205414.
Lian, Biao, Song, Zhi-Da, Regnault, Nicolas, Efetov, Dmitri K., Yazdani, Ali, & Bernevig, B. Andrei. Twisted bilayer graphene. IV. Exact insulator ground states and phase diagram. United States. https://doi.org/10.1103/physrevb.103.205414
Lian, Biao, Song, Zhi-Da, Regnault, Nicolas, Efetov, Dmitri K., Yazdani, Ali, and Bernevig, B. Andrei. Tue .
"Twisted bilayer graphene. IV. Exact insulator ground states and phase diagram". United States. https://doi.org/10.1103/physrevb.103.205414. https://www.osti.gov/servlets/purl/1849769.
@article{osti_1849769,
title = {Twisted bilayer graphene. IV. Exact insulator ground states and phase diagram},
author = {Lian, Biao and Song, Zhi-Da and Regnault, Nicolas and Efetov, Dmitri K. and Yazdani, Ali and Bernevig, B. Andrei},
abstractNote = {Here, we derive the exact insulator ground states of the projected Hamiltonian of magic-angle twisted bilayer graphene (TBG) flat bands with Coulomb interactions in various limits, and study the perturbations away from these limits. We define the (first) chiral limit where the AA stacking hopping is zero, and a flat limit with exactly flat bands. In the chiral-flat limit, the TBG Hamiltonian has a U(4) × U(4) symmetry, and we find that the exact ground states at integer filling – 4 ≤ $\textit{ν}$ ≤ 4 relative to charge neutrality are Chern insulators of Chern numbers $ν_C$ = 4 – |$\textit{ν}$ |, 2 – |$\textit{ν}$ |, $\cdots$, |$\textit{ν}$ | – 4, all of which are degenerate. This confirms recent experiments where Chern insulators are found to be competitive low-energy states of TBG. When the chiral-flat limit is reduced to the nonchiral-flat limit which has a U(4) symmetry, we find $\textit{ν}$ = 0 , ± 2 has exact ground states of Chern number 0, while $\textit{ν}$ = ±1, ± 3 has perturbative ground states of Chern number $ν_C$ = ± 1, which are U(4) ferromagnetic. In the chiral-nonflat limit with a different U(4) symmetry, different Chern number states are degenerate up to second-order perturbations. In the realistic nonchiral-nonflat case, we find that the perturbative insulator states with Chern number $ν_C$ = 0 (0 < |$ν_C$| < 4 – |$\textit{ν}$ |) at integer fillings $\textit{ν}$ are fully (partially) intervalley coherent, while the insulator states with Chern number |$ν_C$| = 4 – |$\textit{ν}$ | are valley polarized. However, for 0 < |$ν_C$| ≤ 4 – |$\textit{ν}$ |, the fully intervalley coherent states are highly competitive (0.005 meV/electron higher). At nonzero magnetic field |$\textit{B}$ | > 0, a first-order phase transition for $\textit{ν}$ = ± 1, ± 2 from Chern number $ν_C$ = sgn ($\textit{νB}$)(2 – |$\textit{ν}$ |) to $ν_C$ = sgn ($\textit{νB}$)(4 – |$\textit{ν}$ |) is expected, which agrees with recent experimental observations. Lastly, the TBG Hamiltonian reduces into an extended Hubbard model in the stabilizer code limit.},
doi = {10.1103/physrevb.103.205414},
journal = {Physical Review. B},
number = 20,
volume = 103,
place = {United States},
year = {Tue May 11 00:00:00 EDT 2021},
month = {Tue May 11 00:00:00 EDT 2021}
}
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Works referenced in this record:
Topology-Bounded Superfluid Weight in Twisted Bilayer Graphene
journal, April 2020
- Xie, Fang; Song, Zhida; Lian, Biao
- Physical Review Letters, Vol. 124, Issue 16
Origin of Magic Angles in Twisted Bilayer Graphene
journal, March 2019
- Tarnopolsky, Grigory; Kruchkov, Alex Jura; Vishwanath, Ashvin
- Physical Review Letters, Vol. 122, Issue 10
Ground State and Hidden Symmetry of Magic-Angle Graphene at Even Integer Filling
journal, August 2020
- Bultinck, Nick; Khalaf, Eslam; Liu, Shang
- Physical Review X, Vol. 10, Issue 3
Renormalization Group Study of Hidden Symmetry in Twisted Bilayer Graphene with Coulomb Interactions
journal, December 2020
- Vafek, Oskar; Kang, Jian
- Physical Review Letters, Vol. 125, Issue 25
Topological Superconductivity in Twisted Multilayer Graphene
journal, August 2018
- Xu, Cenke; Balents, Leon
- Physical Review Letters, Vol. 121, Issue 8
Non-Abelian Dirac node braiding and near-degeneracy of correlated phases at odd integer filling in magic-angle twisted bilayer graphene
journal, July 2020
- Kang, Jian; Vafek, Oskar
- Physical Review B, Vol. 102, Issue 3
Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene
journal, October 2019
- Lu, Xiaobo; Stepanov, Petr; Yang, Wei
- Nature, Vol. 574, Issue 7780
Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice with possible applications to twisted bilayer graphene
journal, September 2018
- Xu, Xiao Yan; Law, K. T.; Lee, Patrick A.
- Physical Review B, Vol. 98, Issue 12
Kohn-Luttinger Superconductivity in Twisted Bilayer Graphene
journal, January 2019
- González, J.; Stauber, T.
- Physical Review Letters, Vol. 122, Issue 2
Intrinsic quantized anomalous Hall effect in a moiré heterostructure
journal, December 2019
- Serlin, M.; Tschirhart, C. L.; Polshyn, H.
- Science, Vol. 367, Issue 6480
Particle-Hole Duality, Emergent Fermi Liquids, and Fractional Chern Insulators in Moiré Flatbands
journal, March 2020
- Abouelkomsan, Ahmed; Liu, Zhao; Bergholtz, Emil J.
- Physical Review Letters, Vol. 124, Issue 10
Helical network model for twisted bilayer graphene
journal, July 2018
- Efimkin, Dmitry K.; MacDonald, Allan H.
- Physical Review B, Vol. 98, Issue 3
Pseudo Landau level representation of twisted bilayer graphene: Band topology and implications on the correlated insulating phase
journal, April 2019
- Liu, Jianpeng; Liu, Junwei; Dai, Xi
- Physical Review B, Vol. 99, Issue 15
DMRG study of strongly interacting $\mathbb{Z}_2$ flatbands: a toy model inspired by twisted bilayer graphene
journal, January 2020
- Eugenio, Paul; Dag, Ceren
- SciPost Physics Core, Vol. 3, Issue 2
Twisted Bilayer Graphene: Moiré with a Twist
journal, August 2016
- Dai, Shuyang; Xiang, Yang; Srolovitz, David J.
- Nano Letters, Vol. 16, Issue 9
Large linear-in-temperature resistivity in twisted bilayer graphene
journal, August 2019
- Polshyn, Hryhoriy; Yankowitz, Matthew; Chen, Shaowen
- Nature Physics, Vol. 15, Issue 10
Maximized electron interactions at the magic angle in twisted bilayer graphene
journal, July 2019
- Kerelsky, Alexander; McGilly, Leo J.; Kennes, Dante M.
- Nature, Vol. 572, Issue 7767
Electrostatic effects, band distortions, and superconductivity in twisted graphene bilayers
journal, December 2018
- Guinea, Francisco; Walet, Niels R.
- Proceedings of the National Academy of Sciences, Vol. 115, Issue 52
Fragile Topology and Wannier Obstructions
journal, September 2018
- Po, Hoi Chun; Watanabe, Haruki; Vishwanath, Ashvin
- Physical Review Letters, Vol. 121, Issue 12
Collective Excitations of Quantum Anomalous Hall Ferromagnets in Twisted Bilayer Graphene
journal, January 2020
- Wu, Fengcheng; Das Sarma, Sankar
- Physical Review Letters, Vol. 124, Issue 4
Valence Bond Orders at Charge Neutrality in a Possible Two-Orbital Extended Hubbard Model for Twisted Bilayer Graphene
journal, October 2019
- Da Liao, Yuan; Meng, Zi Yang; Xu, Xiao Yan
- Physical Review Letters, Vol. 123, Issue 15
Tunable correlated states and spin-polarized phases in twisted bilayer–bilayer graphene
journal, May 2020
- Cao, Yuan; Rodan-Legrain, Daniel; Rubies-Bigorda, Oriol
- Nature
Disorder in twisted bilayer graphene
journal, June 2020
- Wilson, Justin H.; Fu, Yixing; Das Sarma, S.
- Physical Review Research, Vol. 2, Issue 2
Correlated states in twisted double bilayer graphene
journal, March 2020
- Shen, Cheng; Chu, Yanbang; Wu, QuanSheng
- Nature Physics, Vol. 16, Issue 5
Mechanism for Anomalous Hall Ferromagnetism in Twisted Bilayer Graphene
journal, April 2020
- Bultinck, Nick; Chatterjee, Shubhayu; Zaletel, Michael P.
- Physical Review Letters, Vol. 124, Issue 16
Correlations and electronic order in a two-orbital honeycomb lattice model for twisted bilayer graphene
journal, December 2018
- Venderbos, Jörn W. F.; Fernandes, Rafael M.
- Physical Review B, Vol. 98, Issue 24
Superconductivity from valley fluctuations and approximate SO(4) symmetry in a weak coupling theory of twisted bilayer graphene
journal, April 2019
- You, Yi-Zhuang; Vishwanath, Ashvin
- npj Quantum Materials, Vol. 4, Issue 1
Relaxation of moiré patterns for slightly misaligned identical lattices: graphene on graphite
journal, July 2015
- Wijk, M. M. van; Schuring, A.; Katsnelson, M. I.
- 2D Materials, Vol. 2, Issue 3
Flavour Hund’s coupling, Chern gaps and charge diffusivity in moiré graphene
journal, March 2021
- Park, Jeong Min; Cao, Yuan; Watanabe, Kenji
- Nature, Vol. 592, Issue 7852
Superfluid weight and Berezinskii-Kosterlitz-Thouless transition temperature of twisted bilayer graphene
journal, February 2020
- Julku, A.; Peltonen, T. J.; Liang, L.
- Physical Review B, Vol. 101, Issue 6
Chiral Spin Density Wave and Superconductivity in the Magic-Angle-Twisted Bilayer Graphene
journal, November 2018
- Liu, Cheng-Cheng; Zhang, Li-Da; Chen, Wei-Qiang
- Physical Review Letters, Vol. 121, Issue 21
Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice
journal, March 2020
- Chen, Guorui; Sharpe, Aaron L.; Fox, Eli J.
- Nature, Vol. 579, Issue 7797
Phases of a phenomenological model of twisted bilayer graphene
journal, August 2018
- Dodaro, J. F.; Kivelson, S. A.; Schattner, Y.
- Physical Review B, Vol. 98, Issue 7
Theories for the correlated insulating states and quantum anomalous Hall effect phenomena in twisted bilayer graphene
journal, January 2021
- Liu, Jianpeng; Dai, Xi
- Physical Review B, Vol. 103, Issue 3
Antiferromagnetically ordered Mott insulator and superconductivity in twisted bilayer graphene: a quantum Monte Carlo study
journal, March 2019
- Huang, Tongyun; Zhang, Lufeng; Ma, Tianxing
- Science Bulletin, Vol. 64, Issue 5
Magic-angle semimetals
journal, October 2020
- Fu, Yixing; König, Elio J.; Wilson, Justin H.
- npj Quantum Materials, Vol. 5, Issue 1
Twisted bilayer graphene. VI. An exact diagonalization study at nonzero integer filling
journal, May 2021
- Xie, Fang; Cowsik, Aditya; Song, Zhi-Da
- Physical Review B, Vol. 103, Issue 20
Tunable spin-polarized correlated states in twisted double bilayer graphene
journal, July 2020
- Liu, Xiaomeng; Hao, Zeyu; Khalaf, Eslam
- Nature, Vol. 583, Issue 7815
Twisted bilayer graphene. V. Exact analytic many-body excitations in Coulomb Hamiltonians: Charge gap, Goldstone modes, and absence of Cooper pairing
journal, May 2021
- Bernevig, B. Andrei; Lian, Biao; Cowsik, Aditya
- Physical Review B, Vol. 103, Issue 20
Twisted bilayer graphene. III. Interacting Hamiltonian and exact symmetries
journal, May 2021
- Bernevig, B. Andrei; Song, Zhi-Da; Regnault, Nicolas
- Physical Review B, Vol. 103, Issue 20
Twisted bilayer graphene. II. Stable symmetry anomaly
journal, May 2021
- Song, Zhi-Da; Lian, Biao; Regnault, Nicolas
- Physical Review B, Vol. 103, Issue 20
Twisted bilayer graphene. I. Matrix elements, approximations, perturbation theory, and a two-band model
journal, May 2021
- Bernevig, B. Andrei; Song, Zhi-Da; Regnault, Nicolas
- Physical Review B, Vol. 103, Issue 20
Superconductivity in metallic twisted bilayer graphene stabilized by WSe2
journal, July 2020
- Arora, Harpreet Singh; Polski, Robert; Zhang, Yiran
- Nature, Vol. 583, Issue 7816
Efficient simulation of moiré materials using the density matrix renormalization group
journal, November 2020
- Soejima, Tomohiro; Parker, Daniel E.; Bultinck, Nick
- Physical Review B, Vol. 102, Issue 20
Independent superconductors and correlated insulators in twisted bilayer graphene
journal, June 2020
- Saito, Yu; Ge, Jingyuan; Watanabe, Kenji
- Nature Physics, Vol. 16, Issue 9
Strongly correlated Chern insulators in magic-angle twisted bilayer graphene
journal, December 2020
- Nuckolls, Kevin P.; Oh, Myungchul; Wong, Dillon
- Nature, Vol. 588, Issue 7839
Multiple topological transitions in twisted bilayer graphene near the first magic angle
journal, January 2019
- Hejazi, Kasra; Liu, Chunxiao; Shapourian, Hassan
- Physical Review B, Vol. 99, Issue 3
Entropic evidence for a Pomeranchuk effect in magic-angle graphene
journal, April 2021
- Rozen, Asaf; Park, Jeong Min; Zondiner, Uri
- Nature, Vol. 592, Issue 7853
Strong correlations and superconductivity in twisted bilayer graphene
journal, December 2018
- Kennes, Dante M.; Lischner, Johannes; Karrasch, Christoph
- Physical Review B, Vol. 98, Issue 24
Chern insulators, van Hove singularities and topological flat bands in magic-angle twisted bilayer graphene
journal, February 2021
- Wu, Shuang; Zhang, Zhenyuan; Watanabe, K.
- Nature Materials, Vol. 20, Issue 4
Strong Coupling Phases of Partially Filled Twisted Bilayer Graphene Narrow Bands
journal, June 2019
- Kang, Jian; Vafek, Oskar
- Physical Review Letters, Vol. 122, Issue 24
Ferromagnetic Mott state in Twisted Graphene Bilayers at the Magic Angle
journal, June 2019
- Seo, Kangjun; Kotov, Valeri N.; Uchoa, Bruno
- Physical Review Letters, Vol. 122, Issue 24
Ferromagnetism in magic-angle graphene
journal, August 2019
- Pixley, Jed H.; Andrei, Eva Y.
- Science, Vol. 365, Issue 6453
Possible correlated insulating states in magic-angle twisted bilayer graphene under strongly competing interactions
journal, August 2018
- Ochi, Masayuki; Koshino, Mikito; Kuroki, Kazuhiko
- Physical Review B, Vol. 98, Issue 8
Unconventional superconductivity in magic-angle graphene superlattices
journal, March 2018
- Cao, Yuan; Fatemi, Valla; Fang, Shiang
- Nature, Vol. 556, Issue 7699
Landau level of fragile topology
journal, July 2020
- Lian, Biao; Xie, Fang; Bernevig, B. Andrei
- Physical Review B, Vol. 102, Issue 4
Pairing symmetry of interacting fermions on a twisted bilayer graphene superlattice
journal, June 2018
- Guo, Huaiming; Zhu, Xingchuan; Feng, Shiping
- Physical Review B, Vol. 97, Issue 23
Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
journal, July 2019
- Sharpe, Aaron L.; Fox, Eli J.; Barnard, Arthur W.
- Science, Vol. 365, Issue 6453
Isospin Pomeranchuk effect in twisted bilayer graphene
journal, April 2021
- Saito, Yu; Yang, Fangyuan; Ge, Jingyuan
- Nature, Vol. 592, Issue 7853
Tuning electron correlation in magic-angle twisted bilayer graphene using Coulomb screening
journal, March 2021
- Liu, Xiaoxue; Wang, Zhi; Watanabe, K.
- Science, Vol. 371, Issue 6535
Fractional Chern insulator states in twisted bilayer graphene: An analytical approach
journal, May 2020
- Ledwith, Patrick J.; Tarnopolsky, Grigory; Khalaf, Eslam
- Physical Review Research, Vol. 2, Issue 2
Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice
journal, January 2019
- Chen, Guorui; Jiang, Lili; Wu, Shuang
- Nature Physics, Vol. 15, Issue 3
Chern bands of twisted bilayer graphene: Fractional Chern insulators and spin phase transition
journal, May 2020
- Repellin, Cécile; Senthil, T.
- Physical Review Research, Vol. 2, Issue 2
Structure of twisted and buckled bilayer graphene
journal, November 2016
- Jain, Sandeep K.; Juričić, Vladimir; Barkema, Gerard T.
- 2D Materials, Vol. 4, Issue 1
Superconductivity, correlated insulators, and Wess–Zumino–Witten terms in twisted bilayer graphene
journal, November 2020
- Christos, Maine; Sachdev, Subir; Scheurer, Mathias S.
- Proceedings of the National Academy of Sciences, Vol. 117, Issue 47
Twisted Bilayer Graphene: A Phonon-Driven Superconductor
journal, June 2019
- Lian, Biao; Wang, Zhijun; Bernevig, B. Andrei
- Physical Review Letters, Vol. 122, Issue 25
Theory of Phonon-Mediated Superconductivity in Twisted Bilayer Graphene
journal, December 2018
- Wu, Fengcheng; MacDonald, A. H.; Martin, Ivar
- Physical Review Letters, Vol. 121, Issue 25
Untying the insulating and superconducting orders in magic-angle graphene
journal, July 2020
- Stepanov, Petr; Das, Ipsita; Lu, Xiaobo
- Nature, Vol. 583, Issue 7816
Failure of Nielsen-Ninomiya Theorem and Fragile Topology in Two-Dimensional Systems with Space-Time Inversion Symmetry: Application to Twisted Bilayer Graphene at Magic Angle
journal, April 2019
- Ahn, Junyeong; Park, Sungjoon; Yang, Bohm-Jung
- Physical Review X, Vol. 9, Issue 2
Quasi-flat-band physics in a two-leg ladder model and its relation to magic-angle twisted bilayer graphene
journal, October 2020
- Huang, Yixuan; Hosur, Pavan; Pal, Hridis K.
- Physical Review B, Vol. 102, Issue 15
Cascade of phase transitions and Dirac revivals in magic-angle graphene
journal, June 2020
- Zondiner, U.; Rozen, A.; Rodan-Legrain, D.
- Nature, Vol. 582, Issue 7811
Spin magnetometry as a probe of stripe superconductivity in twisted bilayer graphene
journal, September 2020
- König, E. J.; Coleman, Piers; Tsvelik, A. M.
- Physical Review B, Vol. 102, Issue 10
Correlated Insulating States in Twisted Double Bilayer Graphene
journal, November 2019
- Burg, G. William; Zhu, Jihang; Taniguchi, Takashi
- Physical Review Letters, Vol. 123, Issue 19
Triangular antiferromagnetism on the honeycomb lattice of twisted bilayer graphene
journal, August 2018
- Thomson, Alex; Chatterjee, Shubhayu; Sachdev, Subir
- Physical Review B, Vol. 98, Issue 7
Competing phases of interacting electrons on triangular lattices in moiré heterostructures
journal, May 2019
- Classen, Laura; Honerkamp, Carsten; Scherer, Michael M.
- Physical Review B, Vol. 99, Issue 19
Nematicity with a twist: Rotational symmetry breaking in a moiré superlattice
journal, August 2020
- Fernandes, Rafael M.; Venderbos, Jörn W. F.
- Science Advances, Vol. 6, Issue 32
Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene
journal, July 2019
- Xie, Yonglong; Lian, Biao; Jäck, Berthold
- Nature, Vol. 572, Issue 7767
Ferromagnetism in Narrow Bands of Moiré Superlattices
journal, May 2020
- Repellin, Cécile; Dong, Zhihuan; Zhang, Ya-Hui
- Physical Review Letters, Vol. 124, Issue 18
Correlated insulating phases of twisted bilayer graphene at commensurate filling fractions: A Hartree-Fock study
journal, July 2020
- Zhang, Yi; Jiang, Kun; Wang, Ziqiang
- Physical Review B, Vol. 102, Issue 3
Nematic topological semimetal and insulator in magic-angle bilayer graphene at charge neutrality
journal, January 2021
- Liu, Shang; Khalaf, Eslam; Lee, Jong Yeon
- Physical Review Research, Vol. 3, Issue 1
Quantum Theory of Orbital Magnetization and Its Generalization to Interacting Systems
journal, November 2007
- Shi, Junren; Vignale, G.; Xiao, Di
- Physical Review Letters, Vol. 99, Issue 19
Hofstadter subband ferromagnetism and symmetry-broken Chern insulators in twisted bilayer graphene
journal, January 2021
- Saito, Yu; Ge, Jingyuan; Rademaker, Louk
- Nature Physics, Vol. 17, Issue 4
Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time-reversal symmetry
journal, November 2019
- Bouhon, Adrien; Black-Schaffer, Annica M.; Slager, Robert-Jan
- Physical Review B, Vol. 100, Issue 19
Nearly flat Chern bands in moiré superlattices
journal, February 2019
- Zhang, Ya-Hui; Mao, Dan; Cao, Yuan
- Physical Review B, Vol. 99, Issue 7
Band structure and insulating states driven by Coulomb interaction in twisted bilayer graphene
journal, July 2020
- Cea, Tommaso; Guinea, Francisco
- Physical Review B, Vol. 102, Issue 4
Coupled-wire description of the correlated physics in twisted bilayer graphene
journal, April 2019
- Wu, Xiao-Chuan; Jian, Chao-Ming; Xu, Cenke
- Physical Review B, Vol. 99, Issue 16
Model for the metal-insulator transition in graphene superlattices and beyond
journal, July 2018
- Yuan, Noah F. Q.; Fu, Liang
- Physical Review B, Vol. 98, Issue 4
Cascade of electronic transitions in magic-angle twisted bilayer graphene
journal, June 2020
- Wong, Dillon; Nuckolls, Kevin P.; Oh, Myungchul
- Nature, Vol. 582, Issue 7811
Electronic correlations in twisted bilayer graphene near the magic angle
journal, August 2019
- Choi, Youngjoon; Kemmer, Jeannette; Peng, Yang
- Nature Physics, Vol. 15, Issue 11
Faithful tight-binding models and fragile topology of magic-angle bilayer graphene
journal, May 2019
- Po, Hoi Chun; Zou, Liujun; Senthil, T.
- Physical Review B, Vol. 99, Issue 19
Transport across twist angle domains in moiré graphene
journal, September 2020
- Padhi, Bikash; Tiwari, Apoorv; Neupert, Titus
- Physical Review Research, Vol. 2, Issue 3
Correlation-Induced Insulating Topological Phases at Charge Neutrality in Twisted Bilayer Graphene
journal, January 2021
- Da Liao, Yuan; Kang, Jian; Breiø, Clara N.
- Physical Review X, Vol. 11, Issue 1
Hybrid Wannier Chern bands in magic angle twisted bilayer graphene and the quantized anomalous Hall effect
journal, March 2021
- Hejazi, Kasra; Chen, Xiao; Balents, Leon
- Physical Review Research, Vol. 3, Issue 1
Moire bands in twisted double-layer graphene
journal, July 2011
- Bistritzer, R.; MacDonald, A. H.
- Proceedings of the National Academy of Sciences, Vol. 108, Issue 30
Correlated insulator behaviour at half-filling in magic-angle graphene superlattices
journal, March 2018
- Cao, Yuan; Fatemi, Valla; Demir, Ahmet
- Nature, Vol. 556, Issue 7699
Unconventional Superconductivity and Density Waves in Twisted Bilayer Graphene
journal, December 2018
- Isobe, Hiroki; Yuan, Noah F. Q.; Fu, Liang
- Physical Review X, Vol. 8, Issue 4
Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions
journal, August 2018
- Zou, Liujun; Po, Hoi Chun; Vishwanath, Ashvin
- Physical Review B, Vol. 98, Issue 8
Topology of Disconnected Elementary Band Representations
journal, June 2018
- Cano, Jennifer; Bradlyn, Barry; Wang, Zhijun
- Physical Review Letters, Vol. 120, Issue 26
Tuning superconductivity in twisted bilayer graphene
journal, January 2019
- Yankowitz, Matthew; Chen, Shaowen; Polshyn, Hryhoriy
- Science, Vol. 363, Issue 6431
Theory of quantised Hall conductivity in two dimensions
journal, August 1982
- Streda, P.
- Journal of Physics C: Solid State Physics, Vol. 15, Issue 22
Signatures of tunable superconductivity in a trilayer graphene moiré superlattice
journal, July 2019
- Chen, Guorui; Sharpe, Aaron L.; Gallagher, Patrick
- Nature, Vol. 572, Issue 7768
Symmetry-broken Chern insulators and Rashba-like Landau-level crossings in magic-angle bilayer graphene
journal, March 2021
- Das, Ipsita; Lu, Xiaobo; Herzog-Arbeitman, Jonah
- Nature Physics, Vol. 17, Issue 6
Spectral Flow and Global Topology of the Hofstadter Butterfly
journal, May 2017
- Asbóth, János K.; Alberti, Andrea
- Physical Review Letters, Vol. 118, Issue 21
Geometric and Conventional Contribution to the Superfluid Weight in Twisted Bilayer Graphene
journal, December 2019
- Hu, Xiang; Hyart, Timo; Pikulin, Dmitry I.
- Physical Review Letters, Vol. 123, Issue 23
Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene
journal, September 2018
- Po, Hoi Chun; Zou, Liujun; Vishwanath, Ashvin
- Physical Review X, Vol. 8, Issue 3
Symmetry, Maximally Localized Wannier States, and a Low-Energy Model for Twisted Bilayer Graphene Narrow Bands
journal, September 2018
- Kang, Jian; Vafek, Oskar
- Physical Review X, Vol. 8, Issue 3
Maximally Localized Wannier Orbitals and the Extended Hubbard Model for Twisted Bilayer Graphene
journal, September 2018
- Koshino, Mikito; Yuan, Noah F. Q.; Koretsune, Takashi
- Physical Review X, Vol. 8, Issue 3
Quantum Valley Hall Effect, Orbital Magnetism, and Anomalous Hall Effect in Twisted Multilayer Graphene Systems
journal, August 2019
- Liu, Jianpeng; Ma, Zhen; Gao, Jinhua
- Physical Review X, Vol. 9, Issue 3
Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene
journal, July 2019
- Jiang, Yuhang; Lai, Xinyuan; Watanabe, Kenji
- Nature, Vol. 573, Issue 7772
All Magic Angles in Twisted Bilayer Graphene are Topological
journal, July 2019
- Song, Zhida; Wang, Zhijun; Shi, Wujun
- Physical Review Letters, Vol. 123, Issue 3
Nature of the Correlated Insulator States in Twisted Bilayer Graphene
journal, March 2020
- Xie, Ming; MacDonald, A. H.
- Physical Review Letters, Vol. 124, Issue 9
Strange Metal in Magic-Angle Graphene with near Planckian Dissipation
journal, February 2020
- Cao, Yuan; Chowdhury, Debanjan; Rodan-Legrain, Daniel
- Physical Review Letters, Vol. 124, Issue 7
Landau levels in twisted bilayer graphene and semiclassical orbits
journal, July 2019
- Hejazi, Kasra; Liu, Chunxiao; Balents, Leon
- Physical Review B, Vol. 100, Issue 3