Dual-Scale Stick-Slip Friction on $\text{Graphene}/h\text{−}\mathrm{BN}$ Moiré Superlattice Structure

Using atomic force microscopy, we have shown that friction on $\text{graphene}/h\text{−}\mathrm{BN}$ superlattice structures may exhibit unusual moiré-scale stick slip in addition to the regular ones observed at the atomic scale. Such dual-scale slip instability will lead to unique length-scale dependent energy dissipation when the different slip mechanisms are sequentially activated. Assisted by an improved theoretical model and comparative experiments, we find that accumulation and unstable release of the in-plane strain of the graphene layer is the key mechanism underlying the moiré-scale behavior. This work highlights the distinct role of the internal state of the van der Waals interfaces in determining the rich dynamics and energy dissipation of layer-structured materials.

Figure 1

(a) A schematic of the friction measurement. The inset shows the moiré pattern with a period of $\sim 15\mathrm{nm}$ obtained from STM. (b) Lateral force image (upper panel) and the corresponding line traces (lower panel) show a hexagonal pattern originating from moiré-scale stick slip. Scale bar, 20 nm. (c) Close-up lateral force image (upper panel) and the corresponding line traces (lower panel) acquired from the dashed rectangle region of panel (b). Scale bar, 5 nm. (d) Close-up lateral force image (upper panel) and the corresponding line traces (lower panel) acquired from the dashed rectangle region of panel (c). Scale bar, 5 Å. (e) Friction versus normal load data acquired from areas with $5\mathrm{nm}\times 5\mathrm{nm}$ (atomic-scale) and $40\mathrm{nm}\times 40\mathrm{nm}$ (moiré-scale) sizes. Error bars represent the standard deviation at each load. As the typical size of the graphene islands was much larger than the tip contact size ($\sim$ a couple of nm), we did not expect them to move or rotate globally with respect to the $h\text{−}\mathrm{BN}$ substrate.

Figure 2

(a) Trace (gray line) and retrace (blue line) lateral force curves obtained with a sliding velocity of $4\mu \mathrm{m}/\mathrm{s}$ under normal loads of 1.4, 5.7, 14.3, and 25.7 nN, respectively. (b) The corresponding trace and retrace lateral force and friction images of (a). Scale bar, 10 nm.

Figure 3

(a) A schematic showing a tip sliding on a composite structure containing two periodic layers with different periods. The tip is moved by a support through a linear spring and the upper layer is fixed laterally through another linear spring. (b) Typical trace (gray line) and retrace (blue line) lateral force curves obtained in numerical calculations with $U_1=70\mathrm{meV}$, and varying $U_2$ of 700, 2100, and 2800 meV, respectively. (c) Variation of the tip displacement $x_1$ with the support displacement for $U_2=2800\mathrm{meV}$. Inset shows a magnified curve profile and the slip stages are highlighted with red segments. (d) Schematics showing the atomic configurations corresponding to two typical moments of (i) and (ii) as marked in the lower panel (upper panel). Variation of the upper layer displacement $x_2$, with the support displacement obtained in numerical calculation with $U_1=70\mathrm{meV}$ and $U_2=2800\mathrm{meV}$ (lower panel).

Figure 4

(a) A schematic showing a bilayer graphene island on $h\text{−}\mathrm{BN}$ substrate. The bilayer graphene is aligned with $h\text{−}\mathrm{BN}$. The inset shows the lattice orientation of $h\text{−}\mathrm{BN}$. (b) Typical lateral force images obtained on the first and second graphene layers, showing clear moiré-scale stick-slip friction. Insets show the lattice orientation of the first and second graphene layers. Scale bar, 5 Å (inset). (c) A schematic showing a bilayer graphene island on $h\text{−}\mathrm{BN}$ substrate. There is a twist angle of 21° between the first graphene layer and $h\text{−}\mathrm{BN}$, and the second graphene layer is aligned with $h\text{−}\mathrm{BN}$. (d) Typical lateral force images obtained on the first and second graphene layers. Insets show the lattice orientation of the first and second graphene layers. Scale bar, 5 Å (inset). (e) A schematic showing a trilayer graphene island on $h\text{−}\mathrm{BN}$ substrate. There is a twist angle of 27° between the second graphene layer and $h\text{−}\mathrm{BN}$. The first and third graphene layer are both aligned with $h\text{−}\mathrm{BN}$. (f) Typical lateral force images obtained on the first, second, and third graphene layers. Insets show the lattice orientation of the first, second, and third graphene layers, respectively. Scale bar, 5 Å (inset).