Mathematics of magic angles in a model of twisted bilayer graphene

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.

We added a trace formula summing up powers of magic angles and elaborated on our numerical methods

References in corpus (3)

• Continuum models for twisted bilayer graphene: the effects of lattice deformation and hopping parameter
• Spectral characterization of magic angles in twisted bilayer graphene
• Existence of the first magic angle for the chiral model of bilayer graphene

Cited by in corpus (18)

• Towards the hidden symmetry in Coulomb interacting twisted bilayer graphene: renormalization group approach
• Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models
• Lattice model for the Coulomb interacting chiral limit of the magic angle twisted bilayer graphene: symmetries, obstructions and excitations
• Bistritzer-MacDonald dynamics in twisted bilayer graphene
• Interacting models for twisted bilayer graphene: a quantum chemistry approach
• Bridging the small and large in twisted transition metal dicalcogenide homobilayers: a tight binding model capturing orbital interference and topology across a wide range of twist angles
• Chiral model of twisted bilayer graphene realized in a monolayer
• Flat Bands and High Chern Numbers in Twisted Multilayer Graphene
• Diagrammatic perturbation approach to moiré bands in twisted bilayer graphene
• Exact ground state of interacting electrons in magic angle graphene
• Topologically protected flatness in chiral moiré heterostructures
• Optical response of alternating twisted trilayer graphene
• Robustness of flat bands on the perturbed Kagome and the perturbed Super-Kagome lattice
• Ideal topological flat bands in chiral symmetric moiré systems from non-holomorphic functions
• Semiclassical quantization conditions in strained moiré lattices
• Classically forbidden regions in the chiral model of twisted bilayer graphene. With an appendix by Zhongkai Tao and Maciej Zworski
• Unconventional Fractional Phases in Multi-Band Vortexable Systems
• Moiré-driven equilibrium of perturbations in moiré systems