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All Magic Angles in Twisted Bilayer Graphene are Topological
Open accessAbstract
We show that the electronic structure of the low-energy bands in the small angle-twisted bilayer graphene consists of a series of semimetallic and topological phases. In particular, we are able to prove, using an approximate low-energy particle-hole symmetry, that the gapped set of bands that exist around all magic angles have a nontrivial topology stabilized by a magnetic symmetry, provided band gaps appear at fillings of ±4 electrons per moiré unit cell. The topological index is given as the winding number (a Z number) of the Wilson loop in the moiré Brillouin zone. Furthermore, we also claim that, when the gapped bands are allowed to couple with higher-energy bands, the Z index collapses to a stable Z_{2} index. The approximate, emergent particle-hole symmetry is essential to the topology of graphene: When strongly broken, nontopological phases can appear. Our Letter underpins topology as the crucial ingredient to the description of low-energy graphene. We provide a four-band short-range tight-binding model whose two lower bands have the same topology, symmetry, and flatness as those of the twisted bilayer graphene and which can be used as an effective low-energy model. We then perform large-scale (11000 atoms per unit cell, 40 days per k-point computing time) ab initio calculations of a series of small angles, from 3° to 1°, which show a more complex and somewhat different evolution of the symmetry of the low-energy bands than that of the theoretical moiré model but which confirm the topological nature of the system.
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Cited by
Fractional Chern insulators in magic-angle twisted bilayer graphene
Xie, Y., Pierce, A. T., Park, J. M., Parker, D. E., Khalaf, E., Ledwith, P., Cao, Y., Lee, S. H., Chen, S., Forrester, P. R., et al. (2021) · Nature · doi:10.1038/s41586-021-04002-3 · Cited by 523
Colloquium : Quantum anomalous Hall effect
Chang, C.-Z., Liu, C.-X., & MacDonald, A. H. (2023) · Reviews of Modern Physics · doi:10.1103/revmodphys.95.011002 · Cited by 508
Faithful tight-binding models and fragile topology of magic-angle bilayer graphene
Po, H. C., Zou, L., Senthil, T., & Vishwanath, A. (2019) · Physical Review B · doi:10.1103/physrevb.99.195455 · Cited by 394
Superconductivity, superfluidity and quantum geometry in twisted multilayer systems
Törmä, P., Peotta, S., & Bernevig, B. A. (2022) · Nature Reviews Physics · doi:10.1038/s42254-022-00466-y · Cited by 319
Self-citationFractional Chern insulator states in twisted bilayer graphene: An analytical approach
Ledwith, P. J., Tarnopolsky, G., Khalaf, E., & Vishwanath, A. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.023237 · Cited by 266
Metadata
- Authors
- Song, Z., Wang, Z., Shi, W., Li, G., Fang, C., & Bernevig, B. A.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2019-07-16
- Volume
- 123
- Issue
- 3
- Pages
- 036401-036401
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2884381403
- Cited by
- 489
- References
- 50
- FWCI
- 29.33
- Type
- journal article
- Language
- en
- Open access
- green
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