Magic angle (in)stability and mobility edges in disordered Chern insulators

Why do experiments only observe one magic angle in twisted bilayer graphene, despite standard models like the chiral limit of the Bistritzer-MacDonald Hamiltonian predicting an infinite number? In this article, we explore the relative stability of larger magic angles compared to smaller ones. Specifically, we analyze how disorder impacts these angles as described by the Bistritzer-MacDonald Hamiltonian in the chiral limit. Changing focus, we investigate the topological and transport properties of a specific magic angle under disorder. We identify a mobility edge near the flat band energy for small disorder, showing that this mobility edge persists even when all Chern numbers are zero. This persistence is attributed to the system’s $C_{2z}T$ symmetry, which enables non-trivial sublattice transport. Notably, this effect remains robust beyond the chiral limit and near perfect magic angles, aligning with experimental observations.