标题： 扭曲双层石墨烯中无小魔角的无序隧穿势 显示英文标题

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

摘要： 我们考虑描述扭曲双层石墨烯的Bistritzer-MacDonald哈密顿量中标准高对称性隧穿势的小随机扰动。 使用Sjöstrand为研究非自伴伪微分算子谱渐近性而开发的方法，我们证明了对于足够小的扭转角度，哈密顿量在极大概率下不会表现出平坦能带，因此不存在所谓的\textit{魔法天使}。 此外，我们在手征极限下，针对Bistritzer-MacDonald哈密顿量的非自伴隧穿算子，在小随机扰动下证明了一个概率Weyl定律。 显示英文摘要

摘要： We consider small random perturbations of the standard high-symmetry tunneling potentials in the Bistritzer-MacDonald Hamiltonian describing twisted bilayer graphene. Using methods developed by Sj\"ostrand for studying the spectral asymptotics of non-selfadjoint pseudo-differential operators, we prove that for sufficiently small twisting angles the Hamiltonian will not exhibit a flat band with overwhelming probability, and hence the absence of the so-called \textit{magic angels}. Moreover, we prove a probabilistic Weyl law for the eigenvalues of the non-selfadjoint tunneling operator, subject to small random perturbations, of the Bistritzer-MacDonald Hamiltonian in the chiral limit.