Mathematics of magic angles in a model of twisted bilayer graphene
Simon Becker, Mark Embree, Jens Wittsten, Maciej Zworski
TL;DR
This paper offers a rigorous mathematical analysis of magic angles in twisted bilayer graphene, including spectral characterization, numerical methods, and band squeezing estimates, enhancing understanding of the electronic properties at these angles.
Contribution
It introduces a spectral characterization of magic angles, develops accurate numerical methods, and provides exponential estimates on band squeezing, advancing the mathematical understanding of twisted bilayer graphene.
Findings
Spectral characterization of magic angles
Accurate numerical implementation of the model
Exponential estimates on band squeezing
Abstract
We provide a mathematical account of the recent Physical Reviews Letter by Tarnopolsky--Kruchkov--Vishwanath. 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 non-hermitian nature of operators appearing in the model play a crucial role in our analysis.
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