Twist disorder in twisted bilayer graphene

Recent experiments in twisted bilayer graphene have set off a flurry of work due to the observation of purportedly correlated phases at the so-called ``magic-angle.'' The nearly pristine samples of graphene used in the experiment mainly have one significant source of disorder: the twist angle is not uniform throughout the sample. Current models in the literature are inadequate to fully capture this effect, so we introduce and study a new microscopic model in which the twist angle enters as a free parameter in real space. After benchmarking the results of the model with the continuum model, we simulate the effects of twist-angle disorder by constructing “patches” of uniform twist angle. We find that while the minibandwidth and gap are renormalized substantially, the Fermi velocity is not significantly altered. We discuss the implications of this for existing and ongoing experiments on twisted bilayer graphene.