Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene
Abstract
We analyze density wave and Pomeranchuk orders in twisted bilayer graphene. This complements our earlier analysis of the pairing instabilities. We assume that near half filling of either conduction or valence band, the Fermi level is close to Van Hove points, where the density of states diverges, and study potential instabilities in the particle-hole channel within a patch model with two valley degrees of freedom. The hexagonal symmetry of twisted bilayer graphene allows for either six or twelve Van Hove points. We consider both cases and find the same two leading candidates for particle-hole order. One is an SU(2)-breaking spin state with ferromagnetism within a valley. A subleading intervalley hopping induces antiferromagnetism between the valleys. The same state has also been obtained in strong-coupling approaches, indicating that this order is robust. The other is a mixed state with 120° complex spin order and orthogonal complex charge order. In addition, we find a weaker but still attractive interaction in nematic channels, and discuss the type of a nematic order.
- Authors:
-
[2];
[1]
- Univ. of Minnesota, Minneapolis, MN (United States)
- Univ. of Minnesota, Minneapolis, MN (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
- Publication Date:
- Research Org.:
- Brookhaven National Lab. (BNL), Upton, NY (United States); Univ. of Minnesota, Minneapolis, MN (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); Humboldt Foundation
- OSTI Identifier:
- 1670668
- Alternate Identifier(s):
- OSTI ID: 1660737; OSTI ID: 1804111
- Report Number(s):
- BNL-219920-2020-JAAM
Journal ID: ISSN 2469-9950; TRN: US2203868
- Grant/Contract Number:
- SC0012704; SC0014402
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 102; Journal Issue: 12; 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; magnetism; twisted bilayer graphene; exotic phases of matter; order parameters; phase diagrams; 36 MATERIALS SCIENCE
Citation Formats
Chichinadze, Dmitry V., Classen, Laura, and Chubukov, Andrey V. Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene. United States: N. p., 2020.
Web. doi:10.1103/physrevb.102.125120.
Chichinadze, Dmitry V., Classen, Laura, & Chubukov, Andrey V. Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene. United States. https://doi.org/10.1103/physrevb.102.125120
Chichinadze, Dmitry V., Classen, Laura, and Chubukov, Andrey V. Mon .
"Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene". United States. https://doi.org/10.1103/physrevb.102.125120. https://www.osti.gov/servlets/purl/1670668.
@article{osti_1670668,
title = {Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene},
author = {Chichinadze, Dmitry V. and Classen, Laura and Chubukov, Andrey V.},
abstractNote = {We analyze density wave and Pomeranchuk orders in twisted bilayer graphene. This complements our earlier analysis of the pairing instabilities. We assume that near half filling of either conduction or valence band, the Fermi level is close to Van Hove points, where the density of states diverges, and study potential instabilities in the particle-hole channel within a patch model with two valley degrees of freedom. The hexagonal symmetry of twisted bilayer graphene allows for either six or twelve Van Hove points. We consider both cases and find the same two leading candidates for particle-hole order. One is an SU(2)-breaking spin state with ferromagnetism within a valley. A subleading intervalley hopping induces antiferromagnetism between the valleys. The same state has also been obtained in strong-coupling approaches, indicating that this order is robust. The other is a mixed state with 120° complex spin order and orthogonal complex charge order. In addition, we find a weaker but still attractive interaction in nematic channels, and discuss the type of a nematic order.},
doi = {10.1103/physrevb.102.125120},
journal = {Physical Review B},
number = 12,
volume = 102,
place = {United States},
year = {2020},
month = {9}
}
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Works referenced in this record:
Symmetry breaking and skyrmionic transport in twisted bilayer graphene
journal, April 2020
- Chatterjee, Shubhayu; Bultinck, Nick; Zaletel, Michael P.
- Physical Review B, Vol. 101, Issue 16
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
Topological Superconductivity in Twisted Multilayer Graphene
journal, August 2018
- Xu, Cenke; Balents, Leon
- Physical Review Letters, Vol. 121, Issue 8
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
Unconventional superconductivity in magic-angle graphene superlattices
journal, March 2018
- Cao, Yuan; Fatemi, Valla; Fang, Shiang
- Nature, Vol. 556, Issue 7699
Intrinsic quantized anomalous Hall effect in a moiré heterostructure
journal, December 2019
- Serlin, M.; Tschirhart, C. L.; Polshyn, H.
- Science, Vol. 367, Issue 6480
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
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
Competing instabilities, orbital ordering, and splitting of band degeneracies from a parquet renormalization group analysis of a four-pocket model for iron-based superconductors: Application to FeSe
journal, February 2017
- Xing, Rui-Qi; Classen, Laura; Khodas, Maxim
- Physical Review B, Vol. 95, Issue 8
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
Large linear-in-temperature resistivity in twisted bilayer graphene
journal, August 2019
- Polshyn, Hryhoriy; Yankowitz, Matthew; Chen, Shaowen
- Nature Physics, Vol. 15, Issue 10
Electrically Tunable Flat Bands and Magnetism in Twisted Bilayer Graphene
journal, August 2019
- Wolf, T. M. R.; Lado, J. L.; Blatter, G.
- Physical Review Letters, Vol. 123, Issue 9
SU(4) Heisenberg model on the honeycomb lattice with exchange-frustrated perturbations: Implications for twistronics and Mott insulators
journal, November 2019
- Natori, W. M. H.; Nutakki, R.; Pereira, R. G.
- Physical Review B, Vol. 100, Issue 20
Superconductivity and strong correlations in moiré flat bands
journal, May 2020
- Balents, Leon; Dean, Cory R.; Efetov, Dmitri K.
- Nature Physics, Vol. 16, Issue 7
Itinerant Half-Metal Spin-Density-Wave State on the Hexagonal Lattice
journal, May 2012
- Nandkishore, Rahul; Chern, Gia-Wei; Chubukov, Andrey V.
- Physical Review Letters, Vol. 108, Issue 22
Tunable correlated states and spin-polarized phases in twisted bilayer–bilayer graphene
journal, May 2020
- Cao, Yuan; Rodan-Legrain, Daniel; Rubies-Bigorda, Oriol
- Nature
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
Correlated states in twisted double bilayer graphene
journal, March 2020
- Shen, Cheng; Chu, Yanbang; Wu, QuanSheng
- Nature Physics, Vol. 16, Issue 5
The Occurrence of Singularities in the Elastic Frequency Distribution of a Crystal
journal, March 1953
- Van Hove, Léon
- Physical Review, Vol. 89, Issue 6
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
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
Emergence and stability of spin-valley entangled quantum liquids in moiré heterostructures
journal, March 2020
- Kiese, Dominik; Buessen, Finn Lasse; Hickey, Ciarán
- Physical Review Research, Vol. 2, Issue 1
Ferromagnetism in Narrow Bands of Moiré Superlattices
journal, May 2020
- Repellin, Cécile; Dong, Zhihuan; Zhang, Ya-Hui
- Physical Review Letters, Vol. 124, Issue 18
Interacting fermions on the honeycomb bilayer: From weak to strong coupling
journal, November 2010
- Vafek, Oskar
- Physical Review B, Vol. 82, Issue 20
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
Nearly flat Chern bands in moiré superlattices
journal, February 2019
- Zhang, Ya-Hui; Mao, Dan; Cao, Yuan
- Physical Review B, Vol. 99, Issue 7
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
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
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
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
Tunable spin-polarized correlated states in twisted double bilayer graphene
journal, July 2020
- Liu, Xiaomeng; Hao, Zeyu; Khalaf, Eslam
- Nature, Vol. 583, Issue 7815
Unconventional topological superconductivity and phase diagram for an effective two-orbital model as applied to twisted bilayer graphene
journal, August 2018
- Fidrysiak, M.; Zegrodnik, M.; Spałek, J.
- Physical Review B, Vol. 98, Issue 8
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
Chiral twist on the high- phase diagram in moiré heterostructures
journal, August 2019
- Lin, Yu-Ping; Nandkishore, Rahul M.
- Physical Review B, Vol. 100, Issue 8
Charge smoothening and band flattening due to Hartree corrections in twisted bilayer graphene
journal, November 2019
- Rademaker, Louk; Abanin, Dmitry A.; Mellado, Paula
- Physical Review B, Vol. 100, 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
Electronic band structure and pinning of Fermi energy to Van Hove singularities in twisted bilayer graphene: A self-consistent approach
journal, November 2019
- Cea, Tommaso; Walet, Niels R.; Guinea, Francisco
- Physical Review B, Vol. 100, Issue 20
Externally Controlled Magnetism and Band Gap in Twisted Bilayer Graphene
journal, June 2018
- Sboychakov, A. O.; Rozhkov, A. V.; Rakhmanov, A. L.
- Physical Review Letters, Vol. 120, Issue 26
Magic of high-order van Hove singularity
journal, December 2019
- Yuan, Noah F. Q.; Isobe, Hiroki; Fu, Liang
- Nature Communications, Vol. 10, Issue 1
Tuning superconductivity in twisted bilayer graphene
journal, January 2019
- Yankowitz, Matthew; Chen, Shaowen; Polshyn, Hryhoriy
- Science, Vol. 363, Issue 6431
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
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
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
Kohn-Luttinger superconductivity on two orbital honeycomb lattice
journal, December 2018
- Lin, Yu-Ping; Nandkishore, Rahul M.
- Physical Review B, Vol. 98, Issue 21
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
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
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
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
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
Nematic superconductivity in twisted bilayer graphene
journal, June 2020
- Chichinadze, Dmitry V.; Classen, Laura; Chubukov, Andrey V.
- Physical Review B, Vol. 101, Issue 22
Observation of Van Hove singularities in twisted graphene layers
journal, November 2009
- Li, Guohong; Luican, A.; Lopes dos Santos, J. M. B.
- Nature Physics, Vol. 6, Issue 2
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