Magic-angle twisted bilayer graphene under orthogonal and in-plane magnetic fields
Abstract: We investigate the effect of a magnetic field on the band structure of bilayer graphene with a magic twist angle of 1.08{\deg}. The coupling of a tight-binding model and the Peierls phase allows the calculation of the energy bands of periodic two-dimensional systems. For an orthogonal magnetic field, the Landau levels are dispersive, particularly for magnetic lengths comparable to or larger than the twisted bilayer cell size. A high in-plane magnetic field modifies the low-energy bands and gap, which we demonstrate to be a direct consequence of the minimal coupling.
- J. M. B. Lopes dos Santos, N. M. R. Peres, and A. H. Castro Neto, Graphene Bilayer with a Twist: Electronic Structure, Physical Review Letters 99, 256802 (2007).
- R. Bistritzer and A. H. MacDonald, Moiré bands in twisted double-layer graphene, Proceedings of the National Academy of Sciences 108, 12233 (2011a).
- J. Liu, J. Liu, and X. Dai, Pseudo Landau level representation of twisted bilayer graphene: Band topology and implications on the correlated insulating phase, Physical Review B 99, 155415 (2019).
- A. Khalifa, G. Murthy, and R. K. Kaul, Absence of edge states in the valley Chern insulator in moiré graphene, Physical Review B 107, 085138 (2023).
- E. Y. Andrei and A. H. MacDonald, Graphene bilayers with a twist, Nature Materials 19, 1265 (2020).
- O. Antebi, A. Stern, and E. Berg, In-plane orbital magnetization as a probe for symmetry breaking in strained twisted bilayer graphene, Physical Review B 105, 104423 (2022).
- P. Moon and M. Koshino, Energy spectrum and quantum Hall effect in twisted bilayer graphene, Physical Review B 85, 195458 (2012).
- Y. Hasegawa and M. Kohmoto, Periodic Landau gauge and quantum Hall effect in twisted bilayer graphene, Physical Review B 88, 125426 (2013).
- K. Hejazi, C. Liu, and L. Balents, Landau levels in twisted bilayer graphene and semiclassical orbits, Physical Review B 100, 035115 (2019).
- B. Lian, F. Xie, and B. A. Bernevig, Landau level of fragile topology, Physical Review B 102, 041402(R) (2020).
- Y.-H. Zhang, H. C. Po, and T. Senthil, Landau level degeneracy in twisted bilayer graphene: Role of symmetry breaking, Physical Review B 100, 125104 (2019).
- Z. F. Wang, F. Liu, and M. Y. Chou, Fractal L]andau-Level Spectra in Twisted Bilayer Graphene, Nano Letters 12, 3833 (2012).
- B. Roy and K. Yang, Bilayer graphene with parallel magnetic field and twisting: Phases and phase transitions in a highly tunable Dirac system, Physical Review B 88, 241107(R) (2013).
- M. Van der Donck, F. M. Peeters, and B. Van Duppen, Transport properties of bilayer graphene in a strong in-plane magnetic field, Physical Review B 93, 115423 (2016).
- N. Kheirabadi, E. McCann, and V. I. Fal'ko, Magnetic ratchet effect in bilayer graphene, Physical Review B 94, 165404 (2016).
- T. Stauber, T. Low, and G. Gómez-Santos, Chiral Response of Twisted Bilayer Graphene, Physical Review Letters 120, 046801 (2018a).
- Y. H. Kwan, S. A. Parameswaran, and S. L. Sondhi, Twisted bilayer graphene in a parallel magnetic field, Physical Review B 101, 205116 (2020).
- T. Stauber, T. Low, and G. Gómez-Santos, Linear response of twisted bilayer graphene: Continuum versus tight-binding models, Physical Review B 98, 195414 (2018b).
- M. Kammermeier, P. Wenk, and U. Zülicke, In-plane magnetoelectric response in bilayer graphene, Physical Review B 100, 075421 (2019).
- N. Kheirabadi and A. Langari, Quantum nonlinear planar Hall effect in bilayer graphene: An orbital effect of a steady in-plane magnetic field, Physical Review B 106, 245143 (2022).
- W. Qin and A. H. MacDonald, In-Plane Critical Magnetic Fields in Magic-Angle Twisted Trilayer Graphene, Physical Review Letters 127, 097001 (2021).
- G. Tarnopolsky, A. J. Kruchkov, and A. Vishwanath, Origin of Magic Angles in Twisted Bilayer Graphene, Physical Review Letters 122, 106405 (2019).
- M. Koshino and N. N. T. Nam, Effective continuum model for relaxed twisted bilayer graphene and moiré electron-phonon interaction, Physical Review B 101, 195425 (2020).
- G. Trambly de Laissardière, D. Mayou, and L. Magaud, Numerical studies of confined states in rotated bilayers of graphene, Physical Review B 86, 125413 (2012).
- S. Fang and E. Kaxiras, Electronic structure theory of weakly interacting bilayers, Physical Review B 93, 235153 (2016).
- X. Lin and D. Tománek, Minimum model for the electronic structure of twisted bilayer graphene and related structures, Physical Review B 98, 081410(R) (2018).
- J. D. Jackson, Classical Electrodynamics (Wiley, 1998) p. 832.
- R. Peierls, Zur Theorie des Diamagnetismus von Leitungselektronen, Zeitschrift für Physik 80, 763 (1933).
- A. Cresti, Convenient Peierls phase choice for periodic atomistic systems under magnetic field, Physical Review B 103, 045402 (2021).
- F. Guinea, Spin-orbit coupling in a graphene bilayer and in graphite, New Journal of Physics 12, 083063 (2010).
- E. McCann and V. I. Fal’ko, Landau-Level Degeneracy and Quantum Hall Effect in a Graphite Bilayer, Physical Review Letters 96, 086805 (2006).
- R. Bistritzer and A. H. MacDonald, Moiré butterflies in twisted bilayer graphene, Physical Review B 84, 035440 (2011b).
- Y.-W. Liu and L. He, Recent progresses on graphene-based artificial nanostructures: a perspective from scanning tunneling microscopy, Quantum Frontiers 2, 2 (2023).
- J. C. Slater and G. F. Koster, Simplified LCAO Method for the Periodic Potential Problem, Physical Review 94, 1498 (1954).
- The MathWorks Inc., MATLAB version: 9.3.0 (R2017b) (2017).
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