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We study the Hofstadter butterfly and Landau levels of the twisted bilayer graphene (TBG).
J. M. Luttinger, “The effect of a magnetic field on electrons in a periodic potential,” Phys. Rev. 84
1951
Earlier work this paper cites.
Douglas R. Hofstadter, “Energy levels and wave functions of bloch electrons in rational and irrational magnetic fields,” Phys. Rev. B 14
1976
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G. H. Wannier, “A result not dependent on rationality for bloch electrons in a magnetic field,” physica status solidi (b) 88
1978
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P Streda, “Theory of quantised hall conductivity in two dimensions,” Journal of Physics C: Solid State Physics 15
1982
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J. M. B. Lopes dos Santos, N. M. R. Peres, and A. H. Castro Neto, “Graphene bilayer with a twist: Electronic structure,” Phys. Rev. Lett. 99
2007
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E. Suárez Morell, J. D. Correa, P. Vargas, M. Pacheco, and Z. Barticevic, “Flat bands in slightly twisted bilayer graphene: Tight-binding calculations,” Phys. Rev. B 82
2010
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G. Trambly de Laissardiere, D. Mayou, and L. Magaud, “Localization of dirac electrons in rotated graphene bilayers,” Nano Letters 10
2010
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Pilkyung Moon and Mikito Koshino, “Energy spectrum and quantum hall effect in twisted bilayer graphene,” Phys. Rev. B 85
2012
Earlier work this paper cites.
Y. Cao, J. Y. Luo, V. Fatemi, S. Fang, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene,” Phys. Rev. Lett. 117
2016
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János K. Asbóth and Andrea Alberti, “Spectral flow and global topology of the hofstadter butterfly,” Phys. Rev. Lett. 118
2017
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2017
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Shengqiang Huang, Kyounghwan Kim, Dmitry K. Efimkin, Timothy Lovorn, Takashi Taniguchi, Kenji Watanabe, Allan H. MacDonald, Emanuel Tutuc, and Brian J. LeRoy, “Topologically protected helical states in minimally twisted bilayer graphene,” Phys. Rev. Lett. 121
2018
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Noah F. Q. Yuan and Liang Fu, “Model for the metal-insulator transition in graphene superlattices and beyond,” Phys. Rev. B 98
2018
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Cenke Xu and Leon Balents, “Topological superconductivity in twisted multilayer graphene,” Phys. Rev. Lett. 121
2018
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G. E. Volovik, “Graphite, graphene and the flat band superconductivity,” JETP Letters (2018), 10.1134/S0021364018080052
2018
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2018
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J. F. Dodaro, S. A. Kivelson, Y. Schattner, X. Q. Sun, and C. Wang, “Phases of a phenomenological model of twisted bilayer graphene,” Phys. Rev. B 98
2018
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2018
Earlier work this paper cites.
2018
Earlier work this paper cites.
Jian Kang and Oskar Vafek, “Symmetry, maximally localized wannier states, and a low-energy model for twisted bilayer graphene narrow bands,” Phys. Rev. X 8
2018
Earlier work this paper cites.
Mikito Koshino, Noah F. Q. Yuan, Takashi Koretsune, Masayuki Ochi, Kazuhiko Kuroki, and Liang Fu, “Maximally localized wannier orbitals and the extended hubbard model for twisted bilayer graphene,” Phys. Rev. X 8
2018
Cited alongside, same era.
Dante M. Kennes, Johannes Lischner, and Christoph Karrasch, “Strong correlations and d + 𝑖𝑑 d+\mathit{id} superconductivity in twisted bilayer graphene,” Phys. Rev. B 98
2018
Cited alongside, same era.
2018
Cited alongside, same era.
Alex Thomson, Shubhayu Chatterjee, Subir Sachdev, and Mathias S. Scheurer, “Triangular antiferromagnetism on the honeycomb lattice of twisted bilayer graphene,” Phys. Rev. B 98
2018
Cited alongside, same era.
2018
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M. Fleischmann, R. Gupta, D. Weckbecker, W. Landgraf, O. Pankratov, V. Meded, and S. Shallcross, “Moiré edge states in twisted graphene nanoribbons,” Phys. Rev. B 97
2018
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A. Alexandradinata and Leonid Glazman, “Semiclassical theory of landau levels and magnetic breakdown in topological metals,” Phys. Rev. B 97
2018
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Matthew Yankowitz, Shaowen Chen, Hryhoriy Polshyn, Yuxuan Zhang, K. Watanabe, T. Taniguchi, David Graf, Andrea F. Young, and Cory R. Dean, “Tuning superconductivity in twisted bilayer graphene,” Science 363
2019
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Bitan Roy and Vladimir Juričić, “Unconventional superconductivity in nearly flat bands in twisted bilayer graphene,” Phys. Rev. B 99
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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.
Teemu J. Peltonen, Risto Ojajärvi, and Tero T. Heikkilä, “Mean-field theory for superconductivity in twisted bilayer graphene,” Phys. Rev. B 98
2018
Cited alongside, same era.
M. Fidrysiak, M. Zegrodnik, and J. Spałek, “Unconventional topological superconductivity and phase diagram for an effective two-orbital model as applied to twisted bilayer graphene,” Phys. Rev. B 98
2018
Cited alongside, same era.
Liujun Zou, Hoi Chun Po, Ashvin Vishwanath, and T. Senthil, “Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and wannier obstructions,” Phys. Rev. B 98
2018
Cited alongside, same era.
Ying Su and Shi-Zeng Lin, “Pairing symmetry and spontaneous vortex-antivortex lattice in superconducting twisted-bilayer graphene: Bogoliubov-de gennes approach,” Phys. Rev. B 98
2018
Cited alongside, same era.
Huaiming Guo, Xingchuan Zhu, Shiping Feng, and Richard T. Scalettar, “Pairing symmetry of interacting fermions on a twisted bilayer graphene superlattice,” Phys. Rev. B 97
2018
Cited alongside, same era.
Yury Sherkunov and Joseph J. Betouras, “Electronic phases in twisted bilayer graphene at magic angles as a result of van hove singularities and interactions,” Phys. Rev. B 98
2018
Cited alongside, same era.
2019
Closest in time.
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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Y.-Z. You and A. Vishwanath, “Superconductivity from Valley Fluctuations and Approximate SO(4) Symmetry in a Weak Coupling Theory of Twisted Bilayer Graphene,” npj Quantum Materials 4
2019
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Long Zhang, “Lowest-energy moire band formed by dirac zero modes in twisted bilayer graphene,” Science Bulletin 64
2019
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J M Pizarro, M J Calderón, and E Bascones, “The nature of correlations in the insulating states of twisted bilayer graphene,” Journal of Physics Communications 3
2019
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J. González and T. Stauber, “Kohn-luttinger superconductivity in twisted bilayer graphene,” Phys. Rev. Lett. 122
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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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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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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A. O. Sboychakov, A. V. Rozhkov, A. L. Rakhmanov, and Franco Nori, “Many-body effects in twisted bilayer graphene at low twist angles,” Physical Review B 100
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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Qing-Kun Tang, Lin Yang, Da Wang, Fu-Chun Zhang, and Qiang-Hua Wang, “Spin-triplet f -wave pairing in twisted bilayer graphene near 14 -filling,” Physical Review B 99
2019
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Bikash Padhi and Philip W. Phillips, “Pressure-induced metal-insulator transition in twisted bilayer graphene,” Physical Review B 99
2019
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Vladyslav Kozii, Hiroki Isobe, Jörn W. F. Venderbos, and Liang Fu, “Nematic superconductivity stabilized by density wave fluctuations: Possible application to twisted bilayer graphene,” Physical Review B 99
2019
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Jian Kang and Oskar Vafek, “Strong coupling phases of partially filled twisted bilayer graphene narrow bands,” Phys. Rev. Lett. 122
2019
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Stephen Spurrier and Nigel R. Cooper, “Theory of quantum oscillations in quasicrystals: Quantizing spiral fermi surfaces,” Physical Review B 100
2019
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