Defect formation in a graphene overlayer on ruthenium under high pressure

Due to its highly corrugated moiré structure and the nanometer modulation of its electronic properties, graphene deposited on ruthenium substrates (G-Ru for short) is a versatile playground for molecular deposition and chemical reactivity. Under local ultrahigh pressure conditions, one can expect an even richer behavior, reinforced by the likely appearance of defects. We have theoretically investigated the formation of such defects on G-Ru by using density functional theory methods. We show that defects can be produced in the high areas of the moiré, either by generating reactive centers in graphene through the creation of vacancies or by modifying the relative carbon-ruthenium positions through conformational changes. The energetic cost to induce these defects is rather small, of the order of a few eV, so that defects are expected to appear when impacting a STM tip or applying high pressure by a diamond AFM tip in these regions. The different types of defects can be clearly distinguished from each other in our simulated STM images.

Figure 1

(a) Top views and side views of four possible relative coordinates of graphene on Ru in a $(1\times 1)$ matched reconstruction. The atoms of the “A” and “B” layers of the Ru HCP lattice are depicted by blue and purple spheres, respectively. In the top views the yellow line marks a possible choice for the unit cell, whereas the green dashed line marks the cut adopted in the side views. In the side views the green dashed circles mark the positions of the third layer (“C”) in an FCC lattice. (b) Optimized G-Ru moiré obtained using a $(11\times 11)$ graphene supercell over a $(10\times 10)$ Ru supercell. Both the top view and the side view are given; only the topmost Ru layer is shown for clarity. In the top view the box sizes are $55\times 35$ Å, whereas the yellow line identifies a possible choice for the unit cell. The graphene corrugation is rendered by its color, as indicated in the legend; the zero of the color scale corresponds to the average vertical C-Ru distance in the low part of the moiré, namely $\sim 2.3$ Å. The colored hexagons highlight the regions in which the relative in-plane positions of C and Ru correspond to the matching unit cells of panel (a).

Figure 2

Graphene defects analyzed in this work. (a) The Stone-Wales defect (7-55-7), (b)–(d) other conformational graphene defects, (e) single vacancy, (f)–(h) double vacancies. For each configuration the top view and the side view are given; in the top views the gray shading represents the normal honeycomb pattern. The out-of-plane displacement ($\mathrm{\Delta }z$) of the atoms in nonplanar arrangements is rendered depicting the atoms with a proportional shade of red; dashed lines mark C-C bonds longer than 1.5 Å.

Figure 3

Optimized graphene defects in the graphene/Ru(0001) system localized in the hcp-fcc region of the moiré: (a) the Stone-Wales defect (SW-2); (b) the conformational defect 58-77-85; (c) a single C vacancy (SV-B2); (d) a type-1 double C vacancy (DV-T1-1). For each configuration the top view and the side view are given and only the topmost Ru layer is shown for clarity. The same box size, plot region, and color code of Fig. 1 are used to ease comparison.

Figure 4

Simulated STM images for different values of the bias voltage $V_b$ and tunneling currents $I_t$ for the G-Ru systems given in Fig. 3. Each image represents the same zone of simulated sample; the box sizes are $67\times 50$ Å. The common color scale is only representative of the apparent corrugation, as different convention for the $z=0$ value were adopted. The moiré unit cell is depicted as a red dashed line in the top left corner image and identifies the same region given by the yellow line in Fig. 1.

Figure 5

Optimized graphene defects in the graphene/Ru(0001) system localized in the hcp-fcc region of the moiré not shown in the main text. For each configuration the top view and the side view are given and only the topmost Ru layer is shown for clarity. The same box size, plot region, and color code of Fig. 1 are used to ease comparison.

Figure 6

Simulated STM images for different values of the bias voltage $V_b$ and tunneling currents $I_t$ for all the G-Ru systems analyzed in this work, not given in Fig. 4. Each image represents the same zone of simulated sample; the box sizes are 67 $\times 50$ Å. The common color scale is only representative of the apparent corrugation, as different convention for the $z=0$ value were adopted.