Mathematics of magic angles in a model of twisted bilayer graphene

Simon Becker, Mark Embree, Jens Wittsten, Maciej Zworski

Published 2020-08-19Version 1

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.