Mathematics of magic angles in a model of twisted bilayer graphene

无序隧道势的扭曲双层石墨烯中无小魔角的缺失

Absence of small magic angles for disordered tunneling potentials in twisted bilayer graphene

本研究通过引入小随机扰动，利用Sjöstrand方法证明在足够小的扭曲角下，Bistritzer-MacDonald哈密顿量以压倒性概率不呈现平坦带，从而不存在所谓的魔角，并证明了手性极限下特征值的概率Weyl定律。

魔角扭曲双层石墨烯平带相互作用哈密顿量的多体基态流形

The Many-Body Ground State Manifold of Flat Band Interacting Hamiltonian for Magic Angle Twisted Bilayer Graphene

本研究完整刻画了魔角扭曲双层石墨烯平带相互作用哈密顿量的基态流形，证明其恰为铁磁Slater行列式的线性张成。

Chiral tunneling through generic one-dimensional potential barriers in bilayer graphene

We study tunneling of charge carriers in single- and bilayer graphene. We propose an explanation for non-zero "magic angles" with 100% transmission for the case of symmetric potential barrier, as well as for their almost-survival for slightly asymmetric barrier in the bilayer graphene known previously from numerical simulations. Most importantly, we demonstrate that these magic angles are not protected in the case of bilayer and give an explicit example of a barrier with very small electron transmission probability for any angles. This means that one can lock charge carriers by a p-n-p (or n-p…