Supplementary information Supplementary Figure S1STM images of four GNBs and their corresponding STS spectra. a-d, STM images of four GNBs are shown in the left side. The experimental STS data with respective Gaussian fits are shown in the right side. The STS data without fitting is shown in inset with the corresponding pseudo-magnetic field derived from the Landau energy levels. e, Normalized peak energy versus for the peaks observed on four different GNBs which follow the expected scaling behavior described by the equation shown in the text. (set a, b, c, d for a, b, c, d bubbles) Tunneling parameters (a-d) V =0.2 V, I = 0.4 na.
Supplementary Figure S2STS spectra of graphene blisters and GNB. The STS curves (A-C) collected on graphene Moiré blisters show only one weak peak at -0.43 ± 0.04 ev which was assigned to bulk states of Ru 21. This is clear evidence that the bubbles engineered in this work are distinctly different to the Moiré blisters in terms of electronic properties.
Supplementary Figure S32-D High resolution STM images of a series of GNBs. a, d, triangular GNB from the delamination of three blisters. b, e, trapezoid-shaped GNB from the delamination of five blisters. c, f, hexagonal GNB from the delamination of seven blisters. f-i, hexagonal GNBs grow with the increase in reaction time, from 10 to16 minutes (2 minutes in space) at 600K (constant molecular O 2 partial pressure at 1.5 10-7 mbar). All the scale bars are 2 nm. Tunneling parameters (a-i) V =0.2 V, I = 0.4 na.
Supplementary Figure S4 The calculation of strain in GNB and its strain distribution. a, STM image of a hexagonal GNB. b, The height profile along the highly-symmetrical line indicated in a. c, The corresponding histogram showing the strain distribution in hexagonal GNB shown in a. d, Illustration showing the method used for calculating strain in GNB. e-f, Determining the Moiré lattice constant using STM. The scale bar in e is 15 nm. Tunneling parameters (a) V =0.2 V, I = 0.4 na.
Supplementary Figure S5The apparent height of a hexagonal GNB at different sample bias. a-n, A series of STM images of one hexagonal GNB at different sample bias. o, The apparent heights measured from the corresponding STM images. p, The plot of apparent height versus sample bias.
Supplementary Figure S6STM images of GNB and blisters at different bias. Atomic resolution of GNB and graphene Moiré pattern on Ru(0001) was obtained simultaneously with sample bias at ±0.2 V and ±0.1 V.
Supplementary Figure S7The apparent height of GNBs relative to that of decoupled graphene regions. a-b, the coexistence of the triangular decupled graphene moiré pattern with triangular GNB. c-d, STM images of GNBs with the line profile to show the relative height between GNBs. The scale bars in a, c are 5 and 20 nm.
Supplementary Figure S8Atomic resolution STM images of GNBs. a-c, 3D and 2D STM images of 6-fold honeycomb lattice in GNBs with relative lower corrugation. d-f, 3D and 2D STM images of 3-fold triangular lattice observed in highly-strained GNBs. The scale bars in b, f are 1 nm and in c, e are 0.25 and 3 nm respectively. Tunneling parameters (a-f) V =0.2 V, I = 0.4 na
Supplementary Figure S9STM images of a compact (2 2)-O adlayer on Ru(0001). a-b, the contrast reversal in the STM images of O(2 2) superstructure on Ru(0001) occurs with different tunneling parameters. c-d, the contrast reversal in oxidized Ru surface was also observed in the graphene antidots. All the scale bars are 3 nm
Supplementary Figure S10STM images of the occasional irregularities on the graphene moiré pattern. a, Large scale STM image shows the missing of blisters b-f, Magnified view of several flat regions (no blisters, marked by green circles) reveals there is no mono- or multi-vacancy in graphene lattice. The scale bar in a is10 nm and the scale bars in b-f are 2 nm. Tunneling parameters (a-f): V = 0.1 V, I = 0.5 na
Supplementary Figure S11STM images of the surface vacancies on Ru(0001). The clean Ru surface was exposed to a flux of low energy Ar+ ions beam (500 ev, 0.5 µa) for 2 minutes (a-c) or 10 minutes (d-f). After annealing at 400 o C for 10 mins, a low (750 ± 50)/µm 2 and high density (1.5 ± 0.2) 10 5 /µm 2 of surface vacancies was achieved respectively. (g) Surface vacancies on Ru created at room temperature. (h) After annealing at 1000 K for 5 minutes. The scale bars in a, d are 5 nm, and in b-c, e-f are 2 nm and in g-h are 10 nm. Tunneling parameters (a-f): V = 0.02 V, I = 0.4 na
Supplementary Methods Graphene nanobubbles growth and methods Subsequently, ethylene gas (National Oxygen Pte Ltd, purity 99.99%) at a partial pressure of 2.5 10-7 mbar was leaked into the chamber for 10 minutes on the Ru(0001) surface decorated with surface vacancies, and the substrate was annealed at 800-1000 K in order to grow extended graphene covering the whole substrate by chemical vapor deposition. The graphene monolayer that was grown as such possessed the occasional irregularities on the Moiré pattern and the angular distortions and translational domains as shown in Fig. 5 and Supplementary Fig. S10. Graphene nanobubbles start to break out at random sites on graphene at temperature ranging from 550 K to 600 K after the as-prepared graphene with defect (missing blisters) was exposed to molecular oxygen (SOXAL purity 99.999%) with partial pressure 1 10-7 mbar to 2.5 10-7 mbar for 10 to 16 minutes. Using the grid function in the scanning software, 9 surface areas (100 100 nm) were selected. Surface vacancies on Ru(0001) and the GNBs were counted accordingly in each area. The same experiment was also repeated twice to obtain these statistical results as shown in Fig. 5j and Supplementary Fig. S11. Scanning Tunneling Spectroscopy (STS) measurement The STS curve as shown in Supplementary Fig. S1 are an arithmetic average of values measured at 40-100 equally spaced points (depends on GNBs size) over the GNBs surface. The reproducibility and consistency of the experimental spectra is vigorously checked by using new tips prepared by in-situ ion sputtering, thereby ruling out any contribution arising from tip artifacts. The Gaussian fitting (with a quadratic background) was used for the statistical analysis of peaks positions in experimental STS spectra. 3-D STM images of four GNBs with their corresponding STS spectra. Individual GNBs exhibit a series of Landau energy related peaks in the STS spectra 1. These peaks do not appear in the spectra of other regions without the GNB and are not observed in the STS of the Moiré blisters (Supplementary Fig. S2). Gaussian fits with a simple quadratic background was used to locate the peak positions shown in STS
spectra. The original averaged STS data without fitting was shown in the inset of the right panel of Supplementary Fig. S1. The pseudo-magnetic field determined from n = 1 was placed in corresponding panel of STS spectrum for each GNB. Normalized peak energy versus for these peaks observed on four different GNBs follow the expected scaling behavior described by the equation in the text (Supplementary Fig. S1e). The STS curves (A-C) collected on graphene Moiré blisters show only one weak peak at -0.43 ± 0.04 ev which was assigned to bulk states of Ru 21. They are not related to Landau Levels because there are no characteristic series of peaks in STS data of these Moiré blisters to begin with and they have a very small strain which cannot induce strong pseudomagnetic field. On the contrary, there are a series of peaks in STS curves (black plot below) collected on different kinds of GNBs, which show the characteristics dependence. These are strong and consistent features which can be assigned to Landau Levels, in agreement with the previous report in Science paper 8. 2-D STM images series of geometric GNBs grown at different conditions The triangle- and trapezoid-shaped GNBs are derived from the coalescence of 3 and 5 surface blisters, respectively, after dosing 90 Langmuir (L) of O 2 at 550 K as shown in Supplementary Fig. S3(a, d) and (b, e). At 600 K, hexagon-shaped GNBs are generated from the merging of 7 surface blisters (Supplementary Fig. S3c, f). It proceeds from a unique blister which acts as the epicenter for the rippling of graphene (Supplementary Fig. S3c) along six directions. With increasing reaction time, the hexagonal GNB grows in size from 2.7, 4.6, 5.4 to 8.1 nm, which corresponds to the incorporation of 7, 13, 19 and 37 blisters respectively, as observed in Supplementary Fig. S3f-i. Calculation of strain in GNBs The lattice constant in graphene can be measured from STM imaging, while the strain in GNBs can be calculated based on changes in the bond length of stretched
graphene lattice 29 as shown in the equation below. where is the stretched graphene lattice; is unstrained, standard graphene lattice (2.4612 Å for triangular lattice imaged in highly strained GNBs); is the in-plane distance between two adjacent lattice; is apparent height between two adjacent lattice measured from STM. (Refer to Supplementary Fig. S4d) The lattice constant derived from STM imaging has been verified to be highly accurate (Supplementary Fig. S4e-f) after comparing it with surface X-ray diffraction (SXRD) results 30 (marginal difference: 2.474 Å versus 2.4895 Å, 0.6% difference in percentage). For example, = 2.72 Å and = 0.2 Å, The strain calculated is shown in Supplementary Fig. S4c. The strain is higher for the regions closer to the edges of GNB, while strain is smaller in the centre of GNB as shown in the histogram (Supplementary Fig. S4c). Such distribution of strain agrees with simulated results in the previous report 8. The apparent heights of GNBs at different tunneling bias Firstly, the strain calculated in the paper is based on the stretched graphene lattice measured from STM images. The apparent height between two adjacent lattice points has much smaller contribution (0-0.3 Å) to the final strain shown in Supplementary Fig. S4, compared to the stretched in-plane distance (2.5-2.76 Å) measured between two adjacent lattice points. (Refer to Supplementary Fig. S4) Secondly, the justification of using the minimal apparent height measured from STM images for the calculation of strain is explained in detail below. The justification for using the minimal apparent height measured from STM images for the calculation of strain is explained in detail below. As shown in Supplementary Fig. S5, the apparent height of one perfect hexagonal GNB changes from 0.385 nm to 0.52 nm when the tunneling bias voltage changes from
-1.2 V to +1.2 V, corresponding to a change of ~35%. This is the largest change in apparent height of all the GNBs we examined and the majority of bubbles we tested have a change of apparent height in the range of ~ (0.75-0.68)/0.68 = 10.2%. A change of 54% in bias-dependent apparent height of Moiré humps was reported (from 0.11 nm to 0.05 nm when the tunneling bias voltage goes from -0.8 V to + 0.8 V) 20 and a change of 64% was observed in our measurement (from 0.11 nm to 0.04 nm when the tunneling bias changes from -1.2 to +1.2 V). Another observation is that the apparent height of GNBs slightly increases with rising of sample bias in both negative and positive sample bias (Supplementary Fig. S5). The minimal apparent height in GNBs is observed with the sample bias in the range of -0.2 V to 0.2 V. In this range, the atomic resolution STM images of graphene Moiré blisters and GNBs can be achieved simultaneously as shown in Supplementary Fig. S6. This indicates the surface states from graphene are dominant in both the blisters and GNBs and the bulk states of Ru have negligible contribution in the tunneling current. Therefore, the apparent height of GNBs, relative to that of graphene Moiré superlattice in this case should approach the real height of GNBs. That is the reason that we choose to use the minimal apparent height measured from STM images for the calculation of strain discussed in Supplementary Fig. S4. In addition, we can provide further evidence to demonstrate that using the minimum apparent height of GNB in the calculation of strain is appropriate. As shown in Supplementary Fig. S7, the decoupled graphene regions and highly-corrugated GNB are captured together in one image under the same tunneling conditions. It is well-known that the influence of Ru substrate on the LDOS is insignificant in the decoupled graphene regions by O intercalation (triangular one in Supplementary Fig. S7 a-b and hexagonal area in Supplementary Fig. S7 c-d). As reported by Sutter et al., the strong metal-carbon coupling is lifted by the selective oxidation of a ruthenium surface and the characteristic Dirac cones of isolated monolayer graphene is restored in this case. The graphene honeycomb lattice is also obtained in the decoupled areas from the work of Sutter et al. 17. Therefore, the difference of apparent height between GNB and decoupled region can be viewed as the real difference of topographical height
between them since they have a more or less similar LDOS now. The relative apparent height of GNBs measured from STM images (Supplementary Fig. S7e-f) is 0.5-0.6 nm, which, in principle, can be considered as the real difference of height between GNBs and decoupled regions. Therefore, the real height of GNBs (have to add the height from the bottom part) should be in the range of 0.7-0.8 nm, since the real height of coupled and decoupled graphene is about 0.15 nm and 0.3 nm, respectively. On the basis of this calculation, we can conclude that using minimum apparent height for the calculation of strain in GNBs can minimize the difference between apparent height and real topographical height. Triangular lattice observed in highly-strained GNBs We have observed the co-existence of 6-fold graphene honeycomb lattice as well as the 3-fold triangular lattice in GNBs, this indicates that the exact symmetry depends on the strain (or curvature) of GNBs. 3-fold triangular lattice is present in highly-strained GNBs, while the 6-fold honeycomb lattice is present in the lesser strained GNBs, as shown in Supplementary Fig. S8. These observations agree with previous report. Xu and Heath et al. reported that the local curvature of graphene wrinkles (10 nm in width and 3 nm in height) could provide sufficient perturbation to break the 6-fold symmetry of graphene lattice, giving rise to a 3-fold 3-for-6 triangular pattern 31. STM images of the O(2 2) superstructure on Ru(0001) Following the explosion of GNB and the creation of a hole on the graphene sheet after dosing 100 Langmuir (L) of O 2 at 650 K, the sub-surface area beneath the GNB can be imaged through the hole. These areas show the presence of a well ordered oxygen adlayer. For example, oxygen adatoms in the (2 2) superstructures on Ru (0001) with a lattice spacing of 0.54 nm are visualized as dark circular spots due to the electronegative oxygen atom which causes a reduction of the local density of states at Fermi level. Upon increasing the tunneling current from 0.1 na to 1.0 na (decreasing the tunneling gap resistance), a complete change of contrast occurs: the oxygen depressions turn into protrusions as shown in Supplementary Fig. S9. The contrast reversal observed here was attributed to the modulation of tip status by picking up a mobile oxygen atom from surface.
Investigating the irregularities in the graphene Moiré pattern on Ru(0001) The Moiré superstructure of graphene on Ru(0001) contains regions which appear to be irregular in terms of missing the hump part of the superstructure. We carefully imaged the irregular Moiré patterns but did not find any point defects such as pentagon-heptagon pairs or mono- or multi-vacancies (Supplementary Fig. S10b-f). Therefore, we deduce that these defects (i.e., missing blisters) on the Moiré pattern are due to irregularities at the interface between graphene and ruthenium, translating into angular distortions and translational domains on the graphene 10 _ENREF_8, as shown in Supplementary Fig. S10b. Creating surface vacancies on Ru(0001) by the argon beam sputtering To create surface vacancies, as-prepared clean Ru(0001) was intentionally exposed to a weak flux of low-energy argon ion beam (500 ev, 0.5 µa) for 2 minutes or 10 minutes. After annealing at 400 o C for 10 minutes, surface vacancies with densities of (750 ± 50)/µm 2 or (1.5 ± 0.2) 10 5 /µm 2 were generated respectively, as shown in Supplementary Fig. S11. We observed that that the density of missing blisters is around 1-2 times less than that of the initial vacancies prepared. This data indicates the surface vacancies could be repaired partially (33%-60% of surface vacancies are repaired based on the data presented in the main text). As shown in Supplementary Fig. S11g-h, 80% of vacancies were repaired after annealing at 1000 K for 5 minutes. On the contrary, more surface vacancies on Ru (33%-60%) remain if there is graphene layer growing on top of the defect-engineered Ru, which will result in missing blisters in the graphene Moiré pattern. Therefore, we can conclude that the growth of graphene on top of defect-engineered Ru will slow the relaxation of Ru vacancies in high temperature. Supplementary References 29 N'Diaye, A.T., Coraux, J., Plasa, T.N., Busse, C. & Michely, T. Structure of epitaxial graphene on Ir(111). New. J. Phys. 10, 043033 (2008) 30 Martoccia, D. et al. Graphene on Ru(0001): A 25x25 supercell. Phys. Rev. Lett. 101, 126102 (2008). 31 Xu, K., Cao, P.G. & Heath, J.R. Scanning Tunneling Microscopy Characterization of the Electrical Properties of Wrinkles in Exfoliated Graphene Monolayers. Nano Lett 9, 4446-4451 (2009)