Mathematics of magic angles in a model of twisted bilayer graphene
Simon Becker, Mark Embree, Jens Wittsten, Maciej Zworski
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.
Topics & Concepts
MAGIC (telescope)Bilayer grapheneHermitian matrixExponential functionMagic angleCharacterization (materials science)PhysicsMathematicsTheoretical physicsMathematical analysisGrapheneOpticsPure mathematicsQuantum mechanicsSpectral lineMatrix Theory and AlgorithmsElectromagnetic Scattering and AnalysisNumerical methods in inverse problems