Electronic and structural characterization of divacancies in irradiated graphene

We provide a thorough study of a carbon divacancy, a point defect expected to have a large impact on the properties of graphene. Low-temperature scanning tunneling microscopy imaging of irradiated graphene on different substrates enabled us to identify a common twofold symmetry point defect. Our first-principles calculations reveal that the structure of this type of defect accommodates two adjacent missing atoms in a rearranged atomic network formed by two pentagons and one octagon, with no dangling bonds. Scanning tunneling spectroscopy measurements on divacancies generated in nearly ideal graphene show an electronic spectrum dominated by an empty-states resonance, which is ascribed to a nearly flat, spin-degenerated band of $\pi$-electron nature. While the calculated electronic structure rules out the formation of a magnetic moment around the divacancy, the generation of an electronic resonance near the Fermi level reveals divacancies as key point defects for tuning electron transport properties in graphene systems.

Figure 1

Divacancy in four different graphene systems: (a) 1-monolayer (ML) G/SiC(0001) ($V=+20$ mV), (b) 2-ML G/SiC(0001) ($V=+500$ mV), (c) HOPG ($V=+500$ mV), and (d) 4–5 ML G/SiC($000\overline{1}$) ($V=+190$ mV). (a)–(d) $\text{Size}=6\times 6$ nm${}^2$. All bias voltages refer to the sample. (e) STM image ($26\times 26$ nm${}^2$) showing two divacancies in 4–5 ML G/SiC($000\overline{1}$) ($V=+280$ mV). The direction of graphene lattice vectors ${\mathbf{a}}_{\mathbf{i}}$ of the outermost layer is indicated at the top right-hand part of the image.

Figure 2

(a) Simulated STM image of a commensurate moiré (2,3) formed by two graphene layers rotated $\Theta =13.{17}^{\circ }$ from an AA stacking. The unit cell (solid yellow rhombus) has a periodicity of 10.7 Å. Parameters: $5\times 5$ nm${}^2$, $V=+200$ mV. (b) Electronic band structure calculated for monolayer graphene (dashed blue line), bilayer AB (green solid line), and the (2,3) moiré (red dotted line). (c) Corresponding DOS for the calculated structures. (d) Typical $dI/dV$ spectrum acquired on the surface of 4–5 ML graphene/SiC($000\overline{1}$) at 6 K. Plots showed in (c) and (d) have the same energy range as in (b).

Figure 3

(a) Relaxed structure of the calculated divacancy where all sigma bonds saturate, leading to the (585) structure. The dotted lines show the mirror planes in the defect. (b) $2.57\times 2.57$ nm${}^2$ unit cell used for the calculation. The right-hand panel shows the comparison between experimental [(c) and (d)] and calculated [(e) and (f)] STM images at both sample bias polarities. All images have a size of $3.3\times 3.3$ nm${}^2$.

Figure 4

Consecutive tunneling differential conductance spectra acquired on the divacancies labeled as A and B in Fig. 1e. A reference $dI/dV$ curve taken on the bare surface is also shown.

Figure 5

(a) Calculated band structures and the corresponding DOS of pristine monolayer graphene (dots) and monolayer graphene with a (585) divacancy (solid). (b) Comparison between the experimental STS curves shown in Fig. 4 for the divacancy B with the calculated DOS around $E_F$.