Thermally Induced Graphene Rotation on Hexagonal Boron Nitride

In this Letter, we report the observation of thermally induced rotation of graphene on hexagonal boron nitride ($h$-BN). After the rotation, two thermally stable configurations of graphene on $h$-BN with a relative lattice twisting angle of 0° (most stable) and 30° (metastable), respectively, were found. Graphene on $h$-BN with a twisting angle below (above) a critical angle of $\sim 12\pm 2°$ tends to rotate towards 0° (30°) at a temperature of $>100°\mathrm{C}$, which is in line with our theoretical simulations. In addition, by manipulating the annealing temperature and the flake sizes of graphene, moiré superlattices with large spatial periods of graphene on $h$-BN are achieved. Our studies provide a detailed understanding of the thermodynamic properties of graphene on $h$-BN and a feasible approach to obtaining van der Waals heterostructures with aligned lattices.

Figure 1

As-transferred graphene and as-fabricated graphene flake arrays on $h$-BN and ${\mathrm{SiO}}_2$. (a) Optical image of mechanically transferred graphene with part (top) on $h$-BN and part (bottom) on ${\mathrm{SiO}}_2$. Inset: side view schematic diagram. (b) and (c) AFM morphology images of as-fabricated graphene flake arrays on $h$-BN [(b)] and ${\mathrm{SiO}}_2$ [(c)], separately captured from red and black square areas in (a). The scale bars in (b) and (c) are 500 nm.

Figure 2

Stable configurations of $G/h\text{−}\mathrm{BN}$ and graphene on graphite stackings. (a) and (b) AFM images of two $G/h\text{−}\mathrm{BN}$ stacking configurations with relative angle difference of 30°. Sample in (a) is as-prepared sample as that in Fig. 1. Flake in (b) results from clockwise rotation of the flake in a by 30° in a manipulation process. The scale bars in (a) and (b) are 400 nm. (c) and (d) Englarged AFM images of yellow square areas in (a) and (b), respectively. The unit cell of the moiré pattern is marked by a red hexagon. The scale bars in (c) and (d) are 40 nm. (e) and (f) Schematic maps of atomic structures in (c) and (d), respectively. Mismatch in lattice between graphene and $h$-BN is exaggerated to 10%. (g) and (h) AFM images of graphene on graphite stacking configurations with relative angle $\theta$: $\sim 30°$ and $\sim 0°$, respectively. Graphene on top and graphite at bottom are denoted by black and white arrows, respectively. The scale bars in (g) and (h) are 400 nm.

Figure 3

Unstable configurations and thermal-induced rotations of graphene on $h$-BN. (a) and (d) AFM images of as-prepared 30°-twisted $G/h\text{−}\mathrm{BN}$ samples. (b) and (e) Unstable configurations resulting from manipulations [clockwise rotation of 10° (b) and 22° (e), respectively] on corresponding graphene flake in (a) and (d). (c) and (f) Configurations after annealing treatment ($400°\mathrm{C}$ for 1 h) on samples shown in (b) and (e), respectively. In (a)–(f), dashed white lines mark the edges of graphene in as-prepared 30°-twisted $G/h\text{−}\mathrm{BN}$ samples and the scale bars are 400 nm. (g) Enlarged AFM image of the yellow square area in (f). The scale bar in (g) is 10 nm. (h) Adhesive energy of $G/h\text{−}\mathrm{BN}$ stacking as a function of stacking angles from first principles simulation. The energy of the 0° configuration is set to zero. The blue curve is a fit of the energy. Green and black arrows denote the thermal-induced rotations to 30° [evolution from (b) to (c)] and $\sim 0°$ [evolution from (e) to (f)], respectively. The two strips show the experimentally estimated position of energy barrier ($12\pm 2°$).

Figure 4

Sliding energy corrugation-interface friction and the dependences of graphene rotation on annealing time and flake size. (a) Sliding energy corrugation (adhesive energy corrugation when graphene translates on $h$-BN) from first principles simulation plotted against twisted angle. Blue and green dots separately correspond to sliding along armchair and zigzag directions of the underlying $h$-BN. The dashed line shows the experimentally estimated position of the energy barrier (12°). Inset: schematic map of graphene translation along the zigzag and armchair directions for 0°-twisted $G/h\text{−}\mathrm{BN}$. (b) Typical relationships between the twisted angle and annealing time in rotations towards 30° and 0°. Two consecutive annealing processes (at $200°\mathrm{C}$) were carried out. The black and blue lines are linear fits. The error bars are $\pm 1°$. (c) Relationship between wavelength of obtained superlattice (near 0°) and size of graphene flake. The annealing temperature is $1000°\mathrm{C}$. The black curve is a fit. The error bars are $\pm 0.5\mathrm{nm}$. Inset: Relationship between twisting angle ($\theta$) and size of graphene flake. (d) Raman spectra of superlattices with a different wavelength.

Figure 5

Moiré patterns in phase diagram and electrical measurements. (a) and (b) Fast Fourier Transform filtered phase diagram of $G/h\text{−}\mathrm{BN}$ superlattices with $\lambda$: 13 nm [(a)] and 10 nm [(b)], respectively. Lower parts are the profiles along the red and blue lines. The scale bars in (a) and (b) are 40 nm. (c) Transfer characteristics of samples shown in (a) and (b). Inset: Transfer curve of epitaxial graphene on $h$-BN with precise lattice alignment ($\theta =0°$).