Vol. 3, No. 1, 2022

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Mathematics of magic angles in a model of twisted bilayer graphene

Simon Becker, Mark Embree, Jens Wittsten and Maciej Zworski

Vol. 3 (2022), No. 1, 69–103
Abstract

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.

Keywords
spectral theory, semiclassical analysis, magic angles, condensed matter physics, quantum mechanics
Mathematical Subject Classification
Primary: 35J10
Milestones
Received: 11 October 2020
Revised: 7 November 2020
Accepted: 12 April 2021
Published: 11 May 2022
Authors
Simon Becker
Department of Applied Mathematics and Theoretical Physics
University of Cambridge
Cambridge
United Kingdom
Mark Embree
Department of Mathematics
Virginia Tech
Blacksburg, VA
United States
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