Multiscale arrangements between moiré structures in twisted bilayer graphene/hBN double moiré lattices

Coexistence of two moiré structures in a tri-layer heterostructure can lead to the formation of a complex lattice structure. Twisted bilayer graphene (TBG)/hexagonal boron nitride (hBN) double moiré lattice where the top graphene (Gr_t)/bottom graphene (Gr_b) moiré and Gr_b/hBN moiré structures coexist is an ideal platform to study such phenomena. Here, we report twist-dependent interactive arrangements between the Gr_t/Gr_b and Gr_b/hBN moiré structures in helical- and alternate-twisted Gr_t/Gr_b/hBN heterostructures. Experimental observation using conductive atomic force microscopy (C-AFM) showed clearly different moiré patterns for the helical- and alternate-twisted heterostructures. In the helical- (alternate-) TBG/hBN lattice, the AA domains of the TBG moiré structure were located on the AB’ (AA’) domains of the Gr/hBN moiré structure. Theoretical simulation considering the effects of the lattice relaxation in each moiré structure on the total moiré structure well reproduced the experimental results. Furthermore, large-scale ordered structures characterized by extremely ordered large domains separated by long-straight domain boundaries were observed in the moiré lattices. Our work proved a new rule to control the moiré structure in multi-moiré systems.