The fate of disorder in twisted bilayer graphene near the magic angle

Abstract

In disordered lattices, itinerant electrons typically undergo Anderson localization due to random phase interference, which suppresses their motion. By contrast, in flat-band systems where electrons are intrinsically localized owing to their vanishing group velocity, the role of disorder remains elusive. Twisted bilayer graphene (TBG) at the magic angle $\sim 1.1^\circ$ provides a representative flat-band platform to investigate this problem. Here, we perform an atomistic tight-binding quantum transport calculation on the interplay between disorder and flat-bands in TBG devices. This non-phenomenological approach provides direct evidence that moderate disorder enhances conductance, whereas stronger disorder restores localization, revealing a disorder-driven delocalization-to-localization transport behavior. The underlying physical mechanism is understood by an effective inter-moir{\'e} tunneling strength via spectral flow analysis of a disordered TBG cylinder. Moreover, by comparing magic-angle and large-angle TBG, we demonstrate qualitatively distinct disorder responses tied to the presence of flat-bands. Our quantitative results highlight the unconventional role of disorder in flat-band moir{\'e} materials and offer insights into the observation of the fractional quantum anomalous Hall effect in disordered moir{\'e} systems.