a, Large-scale STM image (V tip = −1.008 V; I tip = 3.90 nA; T = 300 K) of hBN/Cu. b, Atomic-scale STM image (V tip = −0.003 V; I tip = 46.50 nA; T = 300 K) of hBN/Cu. c, Typical STM image (V tip = −0.003 V; I tip = 8.91 nA; T = 300 K) of hBN on Cu (111) with a relative rotation angle, θ, of approximately 3.3°, showing a moiré pattern with a period of 4.20 nm. d, Typical STM image (V tip = −0.032 V; I tip = 18.51 nA; T = 300 K) of hBN on Cu (111) with a θ of roughly 1.5°, showing a moiré pattern with a period of 7.75 nm. The unit cell of the moiré pattern is highlighted by a black rhombus. e, Magnified STM image (V tip = −0.039 V; I tip = 18.51 nA; T = 300 K) of hBN on Cu (111) with a θ of approximately 1.5°. f, Simulation of the moiré pattern for monolayer hBN on Cu (111) with a θ of roughly 1.5°. The unit cell of the moiré pattern for hBN/Cu (111) is highlighted by a black rhombus. The large-scale STM image in a shows a large-area flat terrace of hBN/Cu with a clean surface. The atomic-scale STM image in b reveals a honeycomb structure with a lattice constant of roughly 0.25 nm, which coincides well with the lattice parameters of hBN. Notably, in some typical regions of hBN/Cu (111), moiré patterns with different periods are observed. For instance, d and e show a moiré pattern with a period of around 7.75 nm, and c shows another with a period of roughly 4.20 nm. Such patterns arise from the lattice mismatch and/or relative rotation between hBN and the underlying Cu (111) substrate, and the moiré periods (D) correlate with the relative rotation angles (θ) between hBN and Cu (111) as23 \(D=(1+\delta )a/\sqrt{2(1+\delta )(1-\,\cos \theta )+{\delta }^{2}}\), where δ is the lattice mismatch (roughly 2%) between hBN and the Cu (111) lattice24, and a is the lattice constant of hBN. Consequently, the θ for the moiré pattern with a D of around 7.75 nm (d, e) is calculated to be around 1.5°, and the simulated moiré pattern generated from monolayer hBN stacking on Cu (111) with a θ of roughly 1.5° (f) fits well with the STM result (d, e). The θ for the moiré pattern with a D of around 4.20 nm is calculated to be roughly 3.3° (c). g–j, STM images showing the boundary between areas with and without moiré pattern. g, Typical STM image (V tip = −0.003 V; I tip = 8.10 nA; T = 300 K) of hBN/Cu at the boundary site. h, Magnified STM image (V tip = −0.003 V; I Tip = 8.10 nA; T = 300 K) of the boundary in g (highlighted by the black square), showing that the hBN lattices present perfect coherence at the boundary site. i, Magnified STM image (V tip = −0.003 V; I tip = 17.93 nA; T = 300 K) of hBN/Cu without moiré pattern in region 1 of g. j, Magnified STM image (V tip = −0.003 V; I Tip = 10.78 nA; T = 300 K) of hBN/Cu with moiré pattern in region 2 of g. The hBN atomic rows in region 1 and region 2 are along the same direction (black arrows). The STM image in g was captured at a typical boundary region, with moiré (region 2) and non-moiré (region 1) areas. The magnified atomic-resolution image at the boundary site in h shows that the hBN presents perfect lattice coherence at the patching boundary. The hBN atomic rows in the two adjacent regions are along the same direction (i, j). All images suggest that the hBN is aligned well and has mono-orientation, indicating epitaxial growth of hBN on Cu (111), and that the formation of moiré pattern does not affect the hBN orientation. We believe that the hBN completes its single-crystal growth at high temperatures, and that the strain associated with sample cooling after growth results in local moiré pattern.