Mathematics of magic angles in a model of twisted bilayer graphene
Mathematical Physics
2022-05-18 v4 Materials Science
Superconductivity
math.MP
Spectral Theory
Quantum Physics
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.
Keywords
Cite
@article{arxiv.2008.08489,
title = {Mathematics of magic angles in a model of twisted bilayer graphene},
author = {Simon Becker and Mark Embree and Jens Wittsten and Maciej Zworski},
journal= {arXiv preprint arXiv:2008.08489},
year = {2022}
}
Comments
We added a trace formula summing up powers of magic angles and elaborated on our numerical methods