Fig. 1: Control alignment of top hBN and graphene by rotating 30°.

a Alignment of top hBN (T-hBN), graphene and bottom hBN (B-hBN). The Zigzag (ZG) edge of T-hBN is aligned with the ZG edge or Armchair (AR) edge of graphene and is then aligned with the ZG or AR edge of B-hBN, leading to eight possible combinations: C1 (0°/0°) & C1* (0°/60°), C2 (0°/30°) & C2* (0°/90°), C3 (30°/30°) & C3* (30°/90°) and C4 (30°/0°) & C4* (30°/60°), where C (or C*) represents the configuration when the T-hBN and B-hBN have the same (or opposite) lattice symmetry. The middle cartoons are two basic moiré patterns of 0° G/hBN and 30° G/hBN. b, c Calculated interaction energies for G/hBN heterostructure around 0° and 30°. Total energy (red circles) contributions from intralayer (elastic energy/blue triangles) and interlayer interactions (adhesive energy/black squares). d–f Side view and bottom view of 30° rotational alignment. PCA refers to the principle crystallographic axes of crystals. G1 and G2 refer to graphene 1 and graphene 2 which come from the same flake. g Optical image of G/hBN stack on Polydimethylsiloxane (PDMS) stamp. The red dash line profiles the outline of 0° G1/hBN and the green dash line profiles the outline of 30° G2/hBN. Scale bar, 20 μm. h Spatial map of the full width at half maximum (FWHM) of 2D-band for the dashed area in (g). The red color map refers to 0° G1/hBN, while the green color map refers to 30° G2/hBN. Scale bar, 5 μm. i The STM topography image of 0° G1/hBN shows ~14 nm moiré patterns (left, 500 mV,15pA), and the topography image of 30° G2/hBN shows the characteristic of quasicrystal (right, 100 mV, 100pA). Scale bar, 10 nm.