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We show that the entire continuous model of twisted bilayer graphene (TBG) (and not just the two active bands) with particle-hole symmetry is anomalous and hence incompatible with a lattice model.
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Liang Fu and C. L. Kane, “Time reversal polarization and a Z 2 {Z}_{2} adiabatic spin pump,” Phys. Rev. B 74
2006
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Takahiro Fukui and Yasuhiro Hatsugai, “Quantum spin hall effect in three dimensional materials: Lattice computation of z2 topological invariants and its application to bi and sb,” Journal of the Physical Society of Japan 76
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2010
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Rafi Bistritzer and Allan H. MacDonald, “Moiré bands in twisted double-layer graphene,” Proceedings of the National Academy of Sciences 108
2011
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Rui Yu, Xiao Liang Qi, Andrei Bernevig, Zhong Fang, and Xi Dai, “Equivalent expression of $\mathbbZ_2$ topological invariant for band insulators using the non-Abelian Berry connection,” Phys. Rev. B 84
2011
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Taylor L. Hughes, Emil Prodan, and B. Andrei Bernevig, “Inversion-symmetric topological insulators,” Phys. Rev. B 83
2011
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Samuel V Gallego, Emre S Tasci, G Flor, J Manuel Perez-Mato, and Mois I Aroyo, “Magnetic symmetry in the bilbao crystallographic server: a computer program to provide systematic absences of magnetic neutron diffraction,” Journal of Applied Crystallography 45
2012
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Chen Fang, Matthew J. Gilbert, and B. Andrei Bernevig, “Bulk topological invariants in noninteracting point group symmetric insulators,” Phys. Rev. B 86
2012
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Ari M. Turner, Yi Zhang, Roger S. K. Mong, and Ashvin Vishwanath, “Quantized response and topology of magnetic insulators with inversion symmetry,” Phys. Rev. B 85
2012
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B. Andrei Bernevig and Taylor L. Hughes, Topological Insulators and Topological Superconductors (Princeton University Press, 2013)
2013
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Kazuyuki Uchida, Shinnosuke Furuya, Jun-Ichi Iwata, and Atsushi Oshiyama, “Atomic corrugation and electron localization due to moiré patterns in twisted bilayer graphenes,” Phys. Rev. B 90
2014
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A. Alexandradinata, Xi Dai, and B. Andrei Bernevig, “Wilson-loop characterization of inversion-symmetric topological insulators,” Phys. Rev. B 89
2014
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M M van Wijk, A Schuring, M I Katsnelson, and A Fasolino, “Relaxation of moiré patterns for slightly misaligned identical lattices: graphene on graphite,” 2D Materials 2
2015
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Shuyang Dai, Yang Xiang, and David J Srolovitz, “Twisted bilayer graphene: Moiré with a twist,” Nano letters 16
2016
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Sandeep K Jain, Vladimir Juričić, and Gerard T Barkema, “Structure of twisted and buckled bilayer graphene,” 2D Materials 4
2016
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A Alexandradinata, Zhijun Wang, and B Andrei Bernevig, “Topological insulators from group cohomology,” Physical Review X 6
2016
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Junyeong Ahn, Sungjoon Park, and Bohm-Jung Yang, “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,” Physical Review X 9
2019
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Hoi Chun Po, Liujun Zou, T. Senthil, and Ashvin Vishwanath, “Faithful tight-binding models and fragile topology of magic-angle bilayer graphene,” Physical Review B 99
2019
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Zhida Song, Zhijun Wang, Wujun Shi, Gang Li, Chen Fang, and B. Andrei Bernevig, “All Magic Angles in Twisted Bilayer Graphene are Topological,” Physical Review Letters 123
2019
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Grigory Tarnopolsky, Alex Jura Kruchkov, and Ashvin Vishwanath, “Origin of Magic Angles in Twisted Bilayer Graphene,” Physical Review Letters 122
2019
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Zhijun Wang, Aris Alexandradinata, Robert J Cava, and B Andrei Bernevig, “Hourglass fermions,” Nature 532
2016
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Nguyen N. T. Nam and Mikito Koshino, “Lattice relaxation and energy band modulation in twisted bilayer graphene,” Phys. Rev. B 96
2017
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Dmitry K. Efimkin and Allan H. MacDonald, “Helical network model for twisted bilayer graphene,” Phys. Rev. B 98
2018
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John F Dodaro, Steven A Kivelson, Yoni Schattner, Xiao-Qi Sun, and Chao Wang, “Phases of a phenomenological model of twisted bilayer graphene,” Physical Review B 98
2018
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Noah FQ Yuan and Liang Fu, “Model for the metal-insulator transition in graphene superlattices and beyond,” Physical Review B 98
2018
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Masayuki Ochi, Mikito Koshino, and Kazuhiko Kuroki, “Possible correlated insulating states in magic-angle twisted bilayer graphene under strongly competing interactions,” Phys. Rev. B 98
2018
Cited alongside, same era.
Xiao Yan Xu, K. T. Law, and Patrick A. Lee, “Kekulé valence bond order in an extended hubbard model on the honeycomb lattice with possible applications to twisted bilayer graphene,” Phys. Rev. B 98
2018
Cited alongside, same era.
Ya-Hui Zhang, Dan Mao, Yuan Cao, Pablo Jarillo-Herrero, and T Senthil, “Nearly flat chern bands in moiré superlattices,” Physical Review B 99
2019
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Alexander Kerelsky, Leo J. McGilly, Dante M. Kennes, Lede Xian, Matthew Yankowitz, Shaowen Chen, K. Watanabe, T. Taniguchi, James Hone, Cory Dean, and et al., “Maximized electron interactions at the magic angle in twisted bilayer graphene,” Nature 572
2019
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G. William Burg, Jihang Zhu, Takashi Taniguchi, Kenji Watanabe, Allan H. MacDonald, and Emanuel Tutuc, “Correlated insulating states in twisted double bilayer graphene,” Phys. Rev. Lett. 123
2019
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Adrien Bouhon, Annica M. Black-Schaffer, and Robert-Jan Slager, “Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time-reversal symmetry,” Phys. Rev. B 100
2019
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Kangjun Seo, Valeri N. Kotov, and Bruno Uchoa, “Ferromagnetic mott state in twisted graphene bilayers at the magic angle,” Phys. Rev. Lett. 122
2019
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Xiang Hu, Timo Hyart, Dmitry I. Pikulin, and Enrico Rossi, “Geometric and conventional contribution to the superfluid weight in twisted bilayer graphene,” Phys. Rev. Lett. 123
2019
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Yuan Da Liao, Zi Yang Meng, and Xiao Yan Xu, “Valence bond orders at charge neutrality in a possible two-orbital extended hubbard model for twisted bilayer graphene,” Phys. Rev. Lett. 123
2019
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Laura Classen, Carsten Honerkamp, and Michael M Scherer, “Competing phases of interacting electrons on triangular lattices in moiré heterostructures,” Physical Review B 99
2019
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Tongyun Huang, Lufeng Zhang, and Tianxing Ma, “Antiferromagnetically ordered mott insulator and d+ id superconductivity in twisted bilayer graphene: A quantum monte carlo study,” Science Bulletin 64
2019
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Dominic V. Else, Hoi Chun Po, and Haruki Watanabe, “Fragile topological phases in interacting systems,” Phys. Rev. B 99
2019
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Christophe Mora, Nicolas Regnault, and B. Andrei Bernevig, “Flatbands and perfect metal in trilayer moiré graphene,” Phys. Rev. Lett. 123
2019
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2019
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2020
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2020
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