Flatbands and Perfect Metal in Trilayer Moiré Graphene

Mora, Christophe; Regnault, Nicolas; Bernevig, B. Andrei

doi:10.1103/physrevlett.123.026402

Flatbands and Perfect Metal in Trilayer Moiré Graphene

Journal Article · Thu Jul 11 00:00:00 EDT 2019 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.123.026402· OSTI ID:1612434

Mora, Christophe ^[1]; Regnault, Nicolas ^[2]; Bernevig, B. Andrei ^[3]

Univ. Paris-Diderot, Paris (France); DOE/OSTI
Univ. Paris-Diderot, Paris (France)
Princeton Univ., NJ (United States)

We investigate the electronic structure of a twisted multilayer graphene system forming a moiré pattern. We consider small twist angles separating the graphene sheets and develop a low-energy theory to describe the coupling of Dirac Bloch states close to the K point in each individual plane. Extending beyond the bilayer case, we show that, when the ratio of the consecutive twist angles is rational, a periodicity emerges in quasimomentum space with moiré Bloch bands even when the system does not exhibit a crystalline lattice structure in real space. For a trilayer geometry, we find flatbands in the spectrum at certain rotation angles. Performing a symmetry analysis of the band model for the trilayer, we prove that the system is a perfect metal in the sense that it is gapless at all energies. Furthermore, this striking result originates from the three Dirac cones which can only gap in pairs and produce bands with an infinite connectivity. It also holds quite generally for multilayer graphene with an odd number of planes under the condition of C_2zT symmetry.

View Accepted Manuscript (DOE)

Research Organization:: Princeton Univ., NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0016239

OSTI ID:: 1612434

Alternate ID(s):: OSTI ID: 1546386

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 2 Vol. 123; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (72)

Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization, Not Mott Insulation Padhi, Bikash; Setty, Chandan; Phillips, Philip W. Nano Letters, Vol. 18, Issue 10 https://doi.org/10.1021/acs.nanolett.8b02033	journal	September 2018
Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene Kim, Kyounghwan; DaSilva, Ashley; Huang, Shengqiang Proceedings of the National Academy of Sciences, Vol. 114, Issue 13 https://doi.org/10.1073/pnas.1620140114	journal	March 2017
A review and outlook for an anomaly of scanning tunnelling microscopy (STM): superlattices on graphite Pong, Wing-Tat; Durkan, Colm Journal of Physics D: Applied Physics, Vol. 38, Issue 21 https://doi.org/10.1088/0022-3727/38/21/r01	journal	October 2005
Transport between twisted graphene layers Bistritzer, R.; MacDonald, A. H. Physical Review B, Vol. 81, Issue 24 https://doi.org/10.1103/physrevb.81.245412	journal	June 2010
Theory of Phonon-Mediated Superconductivity in Twisted Bilayer Graphene Wu, Fengcheng; MacDonald, A. H.; Martin, Ivar Physical Review Letters, Vol. 121, Issue 25 https://doi.org/10.1103/physrevlett.121.257001	journal	December 2018
Symmetry, Maximally Localized Wannier States, and a Low-Energy Model for Twisted Bilayer Graphene Narrow Bands Kang, Jian; Vafek, Oskar Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/physrevx.8.031088	journal	September 2018
Topological quantum chemistry Bradlyn, Barry; Elcoro, L.; Cano, Jennifer arXiv https://doi.org/10.48550/arxiv.1703.02050	text	January 2017
Topological Superconductivity in Twisted Multilayer Graphene Xu, Cenke; Balents, Leon arXiv https://doi.org/10.48550/arxiv.1803.08057	text	January 2018
Unconventional superconductivity in nearly flat bands in twisted bilayer graphene Roy, Bitan; Juricic, Vladimir arXiv https://doi.org/10.48550/arxiv.1803.11190	text	January 2018
Phases of a phenomenological model of twisted bilayer graphene Dodaro, John F.; Kivelson, Steven A.; Schattner, Yoni arXiv https://doi.org/10.48550/arxiv.1804.03162	text	January 2018
Antiferromagnetically ordered Mott insulator and d + i d superconductivity in twisted bilayer graphene: a quantum Monte Carlo study Huang, Tongyun; Zhang, Lufeng; Ma, Tianxing Science Bulletin, Vol. 64, Issue 5 https://doi.org/10.1016/j.scib.2019.01.026	journal	March 2019
Localization of Dirac Electrons in Rotated Graphene Bilayers Trambly de Laissardière, G.; Mayou, D.; Magaud, L. Nano Letters, Vol. 10, Issue 3 https://doi.org/10.1021/nl902948m	journal	March 2010
Topological quantum chemistry Bradlyn, Barry; Elcoro, L.; Cano, Jennifer Nature, Vol. 547, Issue 7663 https://doi.org/10.1038/nature23268	journal	July 2017
Correlated insulator behaviour at half-filling in magic-angle graphene superlattices Cao, Yuan; Fatemi, Valla; Demir, Ahmet Nature, Vol. 556, Issue 7699 https://doi.org/10.1038/nature26154	journal	March 2018
Unconventional superconductivity in magic-angle graphene superlattices Cao, Yuan; Fatemi, Valla; Fang, Shiang Nature, Vol. 556, Issue 7699 https://doi.org/10.1038/nature26160	journal	March 2018
Correlated electronic phases in twisted bilayer transition metal dichalcogenides Wang, Lei; Shih, En-Min; Ghiotto, Augusto Nature Materials, Vol. 19, Issue 8 https://doi.org/10.1038/s41563-020-0708-6	journal	June 2020
Comprehensive search for topological materials using symmetry indicators Tang, Feng; Po, Hoi Chun; Vishwanath, Ashvin Nature, Vol. 566, Issue 7745 https://doi.org/10.1038/s41586-019-0937-5	journal	February 2019
Catalogue of topological electronic materials Zhang, Tiantian; Jiang, Yi; Song, Zhida Nature, Vol. 566, Issue 7745 https://doi.org/10.1038/s41586-019-0944-6	journal	February 2019
A complete catalogue of high-quality topological materials Vergniory, M. G.; Elcoro, L.; Felser, Claudia Nature, Vol. 566, Issue 7745 https://doi.org/10.1038/s41586-019-0954-4	journal	February 2019
Strongly correlated Chern insulators in magic-angle twisted bilayer graphene Nuckolls, Kevin P.; Oh, Myungchul; Wong, Dillon Nature, Vol. 588, Issue 7839 https://doi.org/10.1038/s41586-020-3028-8	journal	December 2020
Moire bands in twisted double-layer graphene Bistritzer, R.; MacDonald, A. H. Proceedings of the National Academy of Sciences, Vol. 108, Issue 30 https://doi.org/10.1073/pnas.1108174108	journal	July 2011
Electrostatic effects, band distortions, and superconductivity in twisted graphene bilayers Guinea, Francisco; Walet, Niels R. Proceedings of the National Academy of Sciences, Vol. 115, Issue 52 https://doi.org/10.1073/pnas.1810947115	journal	December 2018
A review and outlook for an anomaly of scanning tunnelling microscopy (STM): superlattices on graphite Pong, Wing-Tat; Durkan, Colm Journal of Physics D: Applied Physics, Vol. 38, Issue 21 https://doi.org/10.1088/0022-3727/38/21/R01	journal	October 2005
Transport between twisted graphene layers Bistritzer, R.; MacDonald, A. H. Physical Review B, Vol. 81, Issue 24 https://doi.org/10.1103/PhysRevB.81.245412	journal	June 2010
Topologically protected zero modes in twisted bilayer graphene de Gail, R.; Goerbig, M. O.; Guinea, F. Physical Review B, Vol. 84, Issue 4 https://doi.org/10.1103/PhysRevB.84.045436	journal	July 2011
Continuum model of the twisted graphene bilayer Lopes dos Santos, J. M. B.; Peres, N. M. R.; Castro Neto, A. H. Physical Review B, Vol. 86, Issue 15 https://doi.org/10.1103/PhysRevB.86.155449	journal	October 2012
Helical networks in twisted bilayer graphene under interlayer bias San-Jose, Pablo; Prada, Elsa Physical Review B, Vol. 88, Issue 12 https://doi.org/10.1103/PhysRevB.88.121408	journal	September 2013
Electronic structure theory of weakly interacting bilayers Fang, Shiang; Kaxiras, Efthimios Physical Review B, Vol. 93, Issue 23 https://doi.org/10.1103/PhysRevB.93.235153	journal	June 2016
Model for the metal-insulator transition in graphene superlattices and beyond Yuan, Noah F. Q.; Fu, Liang Physical Review B, Vol. 98, Issue 4 https://doi.org/10.1103/PhysRevB.98.045103	journal	July 2018
Phases of a phenomenological model of twisted bilayer graphene Dodaro, J. F.; Kivelson, S. A.; Schattner, Y. Physical Review B, Vol. 98, Issue 7 https://doi.org/10.1103/PhysRevB.98.075154	journal	August 2018
Pressure dependence of the magic twist angle in graphene superlattices Carr, Stephen; Fang, Shiang; Jarillo-Herrero, Pablo Physical Review B, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevB.98.085144	journal	August 2018
Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions Zou, Liujun; Po, Hoi Chun; Vishwanath, Ashvin Physical Review B, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevB.98.085435	journal	August 2018
Electronic phases in twisted bilayer graphene at magic angles as a result of Van Hove singularities and interactions Sherkunov, Yury; Betouras, Joseph J. Physical Review B, Vol. 98, Issue 20 https://doi.org/10.1103/PhysRevB.98.205151	journal	November 2018
Strong correlations and d + id superconductivity in twisted bilayer graphene Kennes, Dante M.; Lischner, Johannes; Karrasch, Christoph Physical Review B, Vol. 98, Issue 24 https://doi.org/10.1103/PhysRevB.98.241407	journal	December 2018
Multiple topological transitions in twisted bilayer graphene near the first magic angle Hejazi, Kasra; Liu, Chunxiao; Shapourian, Hassan Physical Review B, Vol. 99, Issue 3 https://doi.org/10.1103/PhysRevB.99.035111	journal	January 2019
Nearly flat Chern bands in moiré superlattices Zhang, Ya-Hui; Mao, Dan; Cao, Yuan Physical Review B, Vol. 99, Issue 7 https://doi.org/10.1103/PhysRevB.99.075127	journal	February 2019
Unconventional superconductivity in nearly flat bands in twisted bilayer graphene Roy, Bitan; Juričić, Vladimir Physical Review B, Vol. 99, Issue 12 https://doi.org/10.1103/PhysRevB.99.121407	journal	March 2019
Wannier pairs in superconducting twisted bilayer graphene and related systems Ray, Sujay; Jung, Jeil; Das, Tanmoy Physical Review B, Vol. 99, Issue 13 https://doi.org/10.1103/PhysRevB.99.134515	journal	April 2019
Pseudo Landau level representation of twisted bilayer graphene: Band topology and implications on the correlated insulating phase Liu, Jianpeng; Liu, Junwei; Dai, Xi Physical Review B, Vol. 99, Issue 15 https://doi.org/10.1103/PhysRevB.99.155415	journal	April 2019
Faithful tight-binding models and fragile topology of magic-angle bilayer graphene Po, Hoi Chun; Zou, Liujun; Senthil, T. Physical Review B, Vol. 99, Issue 19 https://doi.org/10.1103/PhysRevB.99.195455	journal	May 2019
Graph theory data for topological quantum chemistry Vergniory, M. G.; Elcoro, L.; Wang, Zhijun Physical Review E, Vol. 96, Issue 2 https://doi.org/10.1103/PhysRevE.96.023310	journal	August 2017
Non-Abelian Gauge Potentials in Graphene Bilayers San-Jose, P.; González, J.; Guinea, F. Physical Review Letters, Vol. 108, Issue 21 https://doi.org/10.1103/PhysRevLett.108.216802	journal	May 2012
Superlattice-Induced Insulating States and Valley-Protected Orbits in Twisted Bilayer Graphene Cao, Y.; Luo, J. Y.; Fatemi, V. Physical Review Letters, Vol. 117, Issue 11 https://doi.org/10.1103/PhysRevLett.117.116804	journal	September 2016
Topological Superconductivity in Twisted Multilayer Graphene Xu, Cenke; Balents, Leon Physical Review Letters, Vol. 121, Issue 8 https://doi.org/10.1103/PhysRevLett.121.087001	journal	August 2018
Electrically Tunable Gauge Fields in Tiny-Angle Twisted Bilayer Graphene Ramires, Aline; Lado, Jose L. Physical Review Letters, Vol. 121, Issue 14 https://doi.org/10.1103/PhysRevLett.121.146801	journal	October 2018
Theory of Phonon-Mediated Superconductivity in Twisted Bilayer Graphene Wu, Fengcheng; MacDonald, A. H.; Martin, Ivar Physical Review Letters, Vol. 121, Issue 25 https://doi.org/10.1103/PhysRevLett.121.257001	journal	December 2018
Kohn-Luttinger Superconductivity in Twisted Bilayer Graphene González, J.; Stauber, T. Physical Review Letters, Vol. 122, Issue 2 https://doi.org/10.1103/PhysRevLett.122.026801	journal	January 2019
Origin of Magic Angles in Twisted Bilayer Graphene Tarnopolsky, Grigory; Kruchkov, Alex Jura; Vishwanath, Ashvin Physical Review Letters, Vol. 122, Issue 10 https://doi.org/10.1103/PhysRevLett.122.106405	journal	March 2019
Graphene Bilayer with a Twist: Electronic Structure Lopes dos Santos, J. M. B.; Peres, N. M. R.; Castro Neto, A. H. Physical Review Letters, Vol. 99, Issue 25 https://doi.org/10.1103/PhysRevLett.99.256802	journal	December 2007
Maximally Localized Wannier Orbitals and the Extended Hubbard Model for Twisted Bilayer Graphene Koshino, Mikito; Yuan, Noah F. Q.; Koretsune, Takashi Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031087	journal	September 2018
Symmetry, Maximally Localized Wannier States, and a Low-Energy Model for Twisted Bilayer Graphene Narrow Bands Kang, Jian; Vafek, Oskar Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031088	journal	September 2018
Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene Po, Hoi Chun; Zou, Liujun; Vishwanath, Ashvin Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/PhysRevX.8.031089	journal	September 2018
Unconventional Superconductivity and Density Waves in Twisted Bilayer Graphene Isobe, Hiroki; Yuan, Noah F. Q.; Fu, Liang Physical Review X, Vol. 8, Issue 4 https://doi.org/10.1103/PhysRevX.8.041041	journal	December 2018
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 Ahn, Junyeong; Park, Sungjoon; Yang, Bohm-Jung Physical Review X, Vol. 9, Issue 2 https://doi.org/10.1103/PhysRevX.9.021013	journal	April 2019
Magnetic symmetry in the Bilbao Crystallographic Server: a computer program to provide systematic absences of magnetic neutron diffraction Gallego, Samuel V.; Tasci, Emre S.; de la Flor, Gemma Journal of Applied Crystallography, Vol. 45, Issue 6 https://doi.org/10.1107/S0021889812042185	journal	November 2012
Tuning superconductivity in twisted bilayer graphene Yankowitz, Matthew; Chen, Shaowen; Polshyn, Hryhoriy Science, Vol. 363, Issue 6431 https://doi.org/10.1126/science.aav1910	journal	January 2019
Transport Between Twisted Graphene Layers Bistritzer, Rafi; MacDonald, Allan H. arXiv https://doi.org/10.48550/arxiv.1002.2983	text	January 2010
Moire bands in twisted double-layer graphene Bistritzer, R.; MacDonald, A. H. arXiv https://doi.org/10.48550/arxiv.1009.4203	text	January 2010
Topologically Protected Zero Modes in Twisted Bilayer Graphene de Gail, R.; Goerbig, M. O.; Guinea, F. arXiv https://doi.org/10.48550/arxiv.1103.3172	text	January 2011
Non-Abelian gauge potentials in graphene bilayers San-Jose, Pablo; Gonzalez, Jose; Guinea, Francisco arXiv https://doi.org/10.48550/arxiv.1110.2883	text	January 2011
Electronic Structure Theory of Weakly Interacting Bilayers Fang, Shiang; Kaxiras, Efthimios arXiv https://doi.org/10.48550/arxiv.1604.05371	text	January 2016
Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene Cao, Y.; Luo, J. Y.; Fatemi, V. arXiv https://doi.org/10.48550/arxiv.1607.05147	text	January 2016
Electrically tunable gauge fields in tiny-angle twisted bilayer graphene Ramires, A.; Lado, J. L. arXiv https://doi.org/10.48550/arxiv.1803.04400	text	January 2018
Model for Metal-Insulator Transition in Graphene Superlattices and Beyond Yuan, Noah F. Q.; Fu, Liang arXiv https://doi.org/10.48550/arxiv.1803.09699	text	January 2018
Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene Po, Hoi Chun; Zou, Liujun; Vishwanath, Ashvin arXiv https://doi.org/10.48550/arxiv.1803.09742	text	January 2018
Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization not Mott Insulation Padhi, Bikash; Setty, Chandan; Phillips, Philip W. arXiv https://doi.org/10.48550/arxiv.1804.01101	text	January 2018
Antiferromagnetically ordered Mott insulator and $d+id$ superconductivity in twisted bilayer graphene: A quantum Monte carlo study Huang, Tongyun; Zhang, Lufeng; Ma, Tianxing arXiv https://doi.org/10.48550/arxiv.1804.06096	text	January 2018
Theory of phonon-mediated superconductivity in twisted bilayer graphene Wu, Fengcheng; MacDonald, A. H.; Martin, Ivar arXiv https://doi.org/10.48550/arxiv.1805.08735	text	January 2018
Kohn-Luttinger Superconductivity in Twisted Bilayer Graphene González, J.; Stauber, T. arXiv https://doi.org/10.48550/arxiv.1807.01275	text	January 2018
Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene Po, Hoi Chun; Zou, Liujun; Senthil, T. arXiv https://doi.org/10.48550/arxiv.1808.02482	text	January 2018
Tuning superconductivity in twisted bilayer graphene Yankowitz, Matthew; Chen, Shaowen; Polshyn, Hryhoriy arXiv https://doi.org/10.48550/arxiv.1808.07865	text	January 2018
The pseudo-Landau-level representation of twisted bilayer graphene: band topology and the implications on the correlated insulating phase Liu, Jianpeng; Liu, Junwei; Dai, Xi arXiv https://doi.org/10.48550/arxiv.1810.03103	text	January 2018

Cited By (4)

Twisted bilayer graphene. II. Stable symmetry anomaly Song, Zhi-Da; Lian, Biao; Regnault, Nicolas Physical Review B, Vol. 103, Issue 20 https://doi.org/10.1103/physrevb.103.205412	journal	May 2021
Electronic band structure and pinning of Fermi energy to Van Hove singularities in twisted bilayer graphene: A self-consistent approach Cea, Tommaso; Walet, Niels R.; Guinea, Francisco Physical Review B, Vol. 100, Issue 20 https://doi.org/10.1103/physrevb.100.205113	journal	November 2019
Ground state superconducting pair correlations in twisted bilayer graphene Zhang, Lufeng; Huang, Tongyun; Liang, Ying Modern Physics Letters B, Vol. 34, Issue 01 https://doi.org/10.1142/s0217984920500165	journal	December 2019
Electronic band structure and pinning of Fermi energy to van Hove singularities in twisted bilayer graphene: a self consistent approach Cea, Tommaso; Walet, Niels R.; Guinea, Francisco arXiv https://doi.org/10.48550/arxiv.1906.10570	text	January 2019

Similar Records

Twisted symmetric trilayer graphene: Single-particle and many-body Hamiltonians and hidden nonlocal symmetries of trilayer moiré systems with and without displacement field

Journal Article · Mon May 10 00:00:00 EDT 2021 · Physical Review. B · OSTI ID:1852142

Magic-angle twisted symmetric trilayer graphene as a topological heavy-fermion problem

Journal Article · Mon Jul 17 00:00:00 EDT 2023 · Physical Review. B · OSTI ID:2420479

Local atomic stacking and symmetry in twisted graphene trilayers

Journal Article · Sun Jan 07 23:00:00 EST 2024 · Nature Materials · OSTI ID:2323399

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Electronic structure
Graphene
Local density of states
Physics
Symmetry protected topological states
Topological materials

Flatbands and Perfect Metal in Trilayer Moiré Graphene

Citation Formats

References (72)

Cited By (4)

Similar Records

Related Subjects