Disorder effects on flatbands in moiré superlattices.

Plenty of exotic phenomena in moiré superlattices arise from the emergence of flatbands, but their significance could be diminished by structural disorders that will significantly alter flatbands. Thus, unveiling the effects of disorder on moiré flatbands is crucial. In this work, we explore the disorder effects on two sets of flatbands in silicon-based mismatched moiré superlattices, where the level of disorder is controlled by varying the magnitude of random perturbations of the locations of silicon strips. The results reveal that, after ensemble averaging, the average spectral positions of the four flatbands exhibit stability despite variations in the degree of disorder. However, the δ-like density of states (DOS) related to flatbands in the perfect superlattice evolves into a finite-width envelope of high DOS. By increasing the level of disorder, the width of the DOS envelope increases accordingly. Particularly, we observe a fascinating contrast: the width of bandgap flatbands saturates after initial growth, while the width of dispersive-band-crossed flatbands exhibits a linear increase versus the disorder. This unveils fundamental differences in how flatbands respond to structural imperfections, offering crucial insights into their perturbation characteristics within moiré superlattices. Our work offers new perspectives on flatbands in partially disordered moiré superlattices.