Correlated Disorder and Flat Bands in Moiré Heterostructures

Moiré heterostructures are a versatile platform for hosting a variety of correlated phases. Yet, device reproducibility is a major issue mainly because of disorder. In our work [1], we explore the fate of single-particle bands under correlated disorder in various channels, and identify some that remain perfectly immune to certain types of perturbations due to a chiral anomaly/symmetry. The latter being close to realized in twisted bilayer graphene and transition metal dichalcogenides. We employ a microscopic tight-binding model for correlation lengths in between the atomic and Moiré lattice vectors, and conversely, for correlation lengths larger than the Moiré lattice vector, we derive an effective model that respects the topology of the low energy bands. Lastly, we identify a chiral limit that hints at possible connections between the moire bands and Landau levels of graphene [2].