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

TL;DR

This paper proves exponential decay of eigenstates in a twisted bilayer graphene model as the twist angle approaches zero, using microlocal analysis techniques to identify classically forbidden regions.

Contribution

It adapts microlocal methods to analyze eigenstate decay in TBG, replacing traditional ellipticity-based approaches and providing new insights into forbidden regions.

Findings

Eigenstates decay exponentially near stacking points as twist angle approaches zero.

Numerical evidence suggests decay in other regions like the hexagon center.

Discussion of analytic challenges in proving decay in different regions.

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 Sj\"ostrand used to establish analytic hypoellipticity by Tr\'epreau 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.