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Mathematics of magic
angles in a model of twisted bilayer graphene
Simon Becker, Mark Embree, Jens Wittsten and Maciej Zworski |
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Vol. 3 (2022), No. 1, 69–103
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Abstract |
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We provide a mathematical account of the recent letter by Tarnopolsky, Kruchkov and Vishwanath (Phys. Rev. Lett.122:10 (2019), art. id. 106405). The new contributions are a spectral characterization of magic angles, its accurate numerical implementation and an exponential estimate on the squeezing of all bands as the angle decreases. Pseudospectral phenomena due to the nonhermitian nature of operators appearing in the model considered in the letter of Tarnopolsky et al. play a crucial role in our analysis. |
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Keywords
spectral theory, semiclassical analysis, magic angles,
condensed matter physics, quantum mechanics
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Mathematical Subject Classification
Primary: 35J10
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Milestones
Received: 11 October 2020
Revised: 7 November 2020
Accepted: 12 April 2021
Published: 11 May 2022
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Authors |
| Simon Becker | |
| Department of Applied Mathematics
and Theoretical Physics University of Cambridge Cambridge United Kingdom |
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| Mark Embree | |
| Department of Mathematics Virginia Tech Blacksburg, VA United States |
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| Jens Wittsten | |
| Department of Engineering University of Borås Borås Sweden |
Centre for Mathematical
Sciences Lund University Lund Sweden |
| Maciej Zworski | |
| Department of Mathematics University of California at Berkeley Berkeley, CA United States |
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