Classically forbidden regions in the chiral model of twisted bilayer graphene. With an appendix by Zhongkai Tao and Maciej Zworski

Abstract

We establish exponential decay, as the angle of twisting goes to $0$, of eigenstates in a model of twisted bilayer graphene (TBG), near the hexagon connecting stacking points. That is done by adapting microlocal methods Kawai-Kashiwara and Sjöstrand used to establish analytic hypoellipticity by Trépreau and Himonas. That replaces ellipticity, absent here, which is the usual mechanism behind classically forbidden regions. We also discuss numerical evidence of exponential decay in other regions (the center of the hexagon) and analytic complications involved in establishing that decay.

We added a reference to a recent development and made some minor corrections

References in corpus (7)

• Chiral Approximation to Twisted Bilayer Graphene: Exact Intra-Valley Inversion Symmetry, Nodal Structure and Implications for Higher Magic Angles
• Mathematics of magic angles in a model of twisted bilayer graphene
• WKB estimate of bilayer graphene's magic twist angles
• Bistritzer-MacDonald dynamics in twisted bilayer graphene
• 3/2 magic-angle quantization rule of flat bands in twisted bilayer graphene and relationship with the Quantum Hall effect
• Existence of the first magic angle for the chiral model of bilayer graphene
• A simple derivation of moiré-scale continuous models for twisted bilayer graphene