Tunable inter-moiré physics in consecutively twisted trilayer graphene

By electrostatically tuning the strength and hierarchy of the inter-moir\'e interaction in a consecutively twisted trilayer graphene (tTLG) device with two distinct moir\'e superlattices, the authors observe here a new type of inter-moir\'e Hofstadter butterfly. The periodical pattern of the butterfly corresponds to one of the intermediate quasicrystal length scales of the reconstructed moir\'e of moir\'e (MoM) superlattice. This study sheds new light on emergent physics from competing atomic orders in twisted multilayer 2D material platforms.