Robust ultra-low-friction state of graphene via moiré superlattice confinement

Two-dimensional (2D) materials possess outstanding lubrication property with their thicknesses down to a few atomic layers, but they are easily susceptible to sliding induced degradation or ubiquitous chemical modification. Maintaining the superior lubricating performance of 2D materials in a harsh working environment is highly desirable yet grandly challenging. Here we show that by proper alignment of graphene on a Ge(111) substrate, friction of graphene could be well preserved at an ultra-low level even after fluorination or oxidation. This behaviour is experimentally found to be closely related to the suppression of molecular-level deformation of graphene within the moiré superlattice structure. Atomistic simulations reveal that the formation of an interconnected meshwork with enhanced interfacial charge density imposes a strong anchoring effect on graphene even under chemical modification. Modulating molecular-level deformation by interfacial confinements may offer a unique strategy for tuning the mechanical or even chemical properties of 2D materials.


Supplementary Note 1: Characteristics of fluorinated graphene on Ge(111)
SF 6 plasma is a strong etching agent for Ge substrate but not so for graphene. In our experiments, we find that regions of the Ge surface covered by graphene film are generally protected from etching. Similar effects have been reported for graphene on Cu or Ni surfaces 1,2 .
As shown in Supplementary Figure 1a, when pure Ge(111) is exposed to SF 6 plasma, the surface will be severely etched. When Ge(111) is covered by the discontinuous graphene, the exposed Ge surface will be etched as subjected to SF 6 plasma (Supplementary Figure 1b). If the covered graphene film is continuous but with some defects, Fions will only etch the Ge substrate underneath the defects of graphene (Supplementary Figure 1c). In this study, the graphene growth condition is fully optimized to achieve super quality graphene, so the SF 6 etching phenomenon can be totally precluded, as shown in Supplementary Figure 1d Raman spectroscopy and X-ray photoelectron spectroscopy (XPS). Raman scattering (HORIBA JobinYvon HR800) was conducted using an Ar + laser with a wavelength of 514 nm and a spot size of 1 μm. The spectra were recorded with a 600 lines/mm grating. The ESCALAB 250 XPS manufactured by THERMO VG SCIENTIFIC LTD was employed to study the chemical states of the surface with the monochromatic Al K α x-ray source. All the measurements were performed in an ultra-high-vacuum chamber with a base pressure of 10 -10 Torr at room temperature. Fitting of the XPS spectra was performed using a Gussian-Lorentzian peak shape after performing Shirley background correction.
Raman spectrum collected from the as-grown graphene shows a G band at 1593 cm -1 and a 2D band at 2700 cm -1 (Supplementary Figure 2b). The 2D band exhibits a symmetric single Lorentzian line shape with a full-width half-maximum (FWHM) of 28.1 cm -1 and the intensity ratio of 2D to G bands is about 2.1, which corresponds to the features of monolayer graphene with good uniformity, as reported previously 3,4 . However, 2D peak almost disappears and G peak becomes broad after the fluorination (Supplementary Figure 2b) C atoms and C-O bonding from the carbon contaminations 7,8 . In the fluorinated graphene, the enhancement of the peak at 285.1 eV (sp 3 ) together with the attenuation of the peak at 284.6 eV (sp 2 ) is associated with the distorted sp 2 bonding C atoms which have one neighboring C atom bonded with one F atom, i.e., the C-CF bonds 6,9,10 . In addition, the pronounced F1s peak locates at 688.5 eV (inset in Supplementary Figure 2c) and the extra component at 289 eV in the C1s peak also prove the existence of F atoms and F-C bonds 11,12 . The atomic fractions of carbon and fluorine atoms estimated from the XPS data are ~74% and ~26%, respectively. Properties of the fluorinated graphene have been described in our previous work 13 .

Supplementary Note 2: Moiré pattern of graphene/Ge(111) heterostructure
For epitaxially grown graphene on Ge(111), lattice mismatch between graphene and Ge (111) is fixed (~39.5%). The orientation and periodical length of the moiré pattern are determined by the relative rotation angle between graphene and the underneath Ge(111) substrate 14 .
Occasionally, moiré patterns with multiple orientations can be observed in a same region (200

Supplementary Note 3: Adhesion measurements on as-grown and fluorinated graphene
Pull-off force curves were obtained from the regions with/without moiré pattern on as- To rule out the possible influence of capillary, we also carried out pull-off force measurements in dry N 2 environment (relative humidity around 5%) at room temperature. As shown in Supplementary Figures 8a and 8b, the moiré pattern can be observed in lateral force and topography images in the as-grown graphene/Ge(111). We performed the pull-off force measurements on two regions with and without moiré pattern using a SiN tip. As shown in Supplementary Figure 8c, no significant difference in the pull-off force curves is observed between these two representative regions (as marked by square and triangle). For the fluorinated graphene ( Supplementary Figures 8d and 8e), the pull-off force increases noticeably compared to the as-grown sample in both regions with/without moiré pattern (Supplementary Figure 8f).
However, there is still no significant difference in pull-off force between moiré and non-moiré regions. The data obtained from both Supplementary Figures 7 and 8 suggest that the friction contrast between the region with moiré pattern and the region without moiré pattern always exists for different measurement environments. In addition, the pull-off force is closely related to the surface chemical state, therefore, the possibility for less fluorination in the moiré pattern regions can be precluded, as discussed in the main text.

Supplementary Note 4: Morphology and frictional behaviors of oxidized graphene
Besides the fluorinated graphene, the frictional behavior of oxidized graphene/Ge (111) heterostructure has been studied as well. Oxidation of graphene was obtained directly through tip-lithography method. It was performed at ambient conditions (temperature of 24 o C and relative humidity of ~ 40%) by a contact mode AFM (Multimode 8 SPM system) with a Pt/Ir coated conductive tip (DPE-XSC11, MIKROMASCH). During scanning, a local dc bias voltage of +12 V between the AFM tip and the graphene sample was scanned over the region of 2×2 μm 2 .
The oxidation process was implemented by tip assisted electrochemical effects as reported previously 15 . Supplementary Figure 10a shows a schematic diagram of the AFM lithography setup for local oxidation of graphene. When a positive dc bias voltage (high enough) is applied on the conducted AFM tip, it is expected to decompose water molecules adsorbed on graphene in the ambient environment into ions (H + , OH -, and O 2-). Then, the tip acts as the anode to assist the oxidation of the underneath graphene 15 . Even though the oxidation seems to introduce negligible change in the surface morphology (Supplementary Figure 10b), the surface friction increases dramatically on the oxidized region, as shown in Supplementary Figure 10c. The observations are in accordance with the previous reports [15][16][17][18] . Zoom in the friction image of oxidized graphene (insert in Supplementary Figure 10c), there are clear islands with low friction as that on the fluorinated samples. Raman mapping on the oxidized region (Supplementary Figure 10d) shows the tip-assisted oxidation induces the appearance of sharp defect-related D band with a decaying 2D band, which suggests the breaking of the translational symmetry of C-C sp 2 bonds. We have also measured the friction behaviors versus the normal applied load on the oxidized graphene (Supplementary Figure 10e). Friction in the base region without moiré pattern increases significantly as the applied load increases, however, the island with moiré pattern always keep their low friction state, which is also observed in fluorinated graphene (Fig. 1f in the main text).
By taking a high-resolution friction image on the oxidized region (Supplementary Figure   11a), we confirmed that the ultra-low friction island region indeed exhibited a moiré pattern, while the moiré pattern was absent in the base region with high friction (Supplementary Figure   11b). These results support our hypothesis that the mechanism of ultra-low friction state preservation for the fluorinated graphene is qualitatively similar to that for the oxidized graphene.