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

TL;DR

This paper demonstrates that small random perturbations in twisted bilayer graphene's tunneling potentials prevent the formation of flat bands at small angles, challenging the existence of magic angles.

Contribution

It introduces a probabilistic analysis showing the absence of magic angles under small random perturbations in the Bistritzer-MacDonald model.

Findings

No flat bands at small angles with high probability

Probabilistic Weyl law for eigenvalues under perturbations

Absence of magic angles in disordered tunneling potentials

Abstract

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.