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Origin of Magic Angles in Twisted Bilayer Graphene
Open accessAbstract
Twisted bilayer graphene (TBG) was recently shown to host superconductivity when tuned to special "magic angles" at which isolated and relatively flat bands appear. However, until now the origin of the magic angles and their irregular pattern have remained a mystery. Here we report on a fundamental continuum model for TBG which features not just the vanishing of the Fermi velocity, but also the perfect flattening of the entire lowest band. When parametrized in terms of α∼1/θ, the magic angles recur with a remarkable periodicity of Δα≃3/2. We show analytically that the exactly flat band wave functions can be constructed from the doubly periodic functions composed of ratios of theta functions-reminiscent of quantum Hall wave functions on the torus. We further report on the unusual robustness of the experimentally relevant first magic angle, address its properties analytically, and discuss how lattice relaxation effects help justify our model parameters.
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Cites
Tuning superconductivity in twisted bilayer graphene
Yankowitz, M., Chen, S., Polshyn, H., Zhang, Y., Watanabe, K., Taniguchi, T., Graf, D., Young, A. F., & Dean, C. R. (2019) · Science · doi:10.1126/science.aav1910 · Cited by 2,290
Mumford, D. (1983) · Progress in mathematics · doi:10.1007/978-1-4899-2843-6 · Cited by 773
Cited by
Tuning superconductivity in twisted bilayer graphene
Yankowitz, M., Chen, S., Polshyn, H., Zhang, Y., Watanabe, K., Taniguchi, T., Graf, D., Young, A. F., & Dean, C. R. (2019) · Science · doi:10.1126/science.aav1910 · Cited by 2,290
Electronic-structure methods for twisted moiré layers
Carr, S., Fang, S., & Kaxiras, E. (2020) · Nature Reviews Materials · doi:10.1038/s41578-020-0214-0 · Cited by 303
Metadata
- Authors
- Tarnopolsky, G., Kruchkov, A. J., & Vishwanath, A.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2019-03-15
- Volume
- 122
- Issue
- 10
- Pages
- 106405-106405
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2887373946
- Cited by
- 791
- References
- 2
- FWCI
- 32.13
- Type
- journal article
- Language
- en
- Open access
- green
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- Tarnopolsky, G., Kruchkov, A. J., & Vishwanath, A. (2019). Origin of Magic Angles in Twisted Bilayer Graphene. Physical Review Letters. https://doi.org/10.1103/physrevlett.122.106405
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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