Scanning tunneling microscopy fingerprints of point defects in graphene: A theoretical prediction

Scanning tunneling microscopy (STM) is one of the most appropriate techniques to investigate the atomic structure of carbon nanomaterials. However, the experimental identification of topological and nontopological modifications of the hexagonal network of $s{p}^2$ carbon nanostructures remains a great challenge. The goal of the present theoretical work is to predict the typical electronic features of a few defects that are likely to occur in $s{p}^2$ carbon nanostructures, such as atomic vacancy, divacancy, adatom, and Stone-Wales defect. The modifications induced by those defects in the electronic properties of the graphene sheet are investigated using first-principles calculations. In addition, computed constant-current STM images of these defects are calculated within a tight-binding approach in order to facilitate the interpretation of STM images of defected carbon nanostructures.

Figure 1

Fully optimized structures of five different defects. (a) Top view of a nonreconstructed vacancy, keeping the $D_{3h}$ symmetry of graphene. (b) Top and side views of the reconstructed vacancy with $C_s$ symmetry. (c) Top view of the divacancy. (d) Top and side views of the adatom equilibrium bridgelike position. (e) Top view of a Stone-Wales defect. Some carbon atoms are numbered; see text.

Figure 2

Electronic properties of the $D_{3h}$ vacancy. (a) Comparison between the electronic band structure calculated with DFT-LDA (left) and our modified TB model (right). For both calculations, the Fermi level is set to zero. (b) Isodenstity surfaces of specific defect states at $\Gamma$ point, calculated with DFT-LDA. The shaded spots label the two $\sigma$ states (degenerated in $\Gamma$) and the white spot represents the $\pi$ band.

Figure 3

Electronic properties of the $C_s$ vacancy. (a) Comparison between the electronic band structure calculated with DFT-LDA (left) and our modified TB model (right). For both calculations, the Fermi level is set to zero. (b) Isodensity surfaces of specific defect states at $\Gamma$ point calculated with DFT-LDA. Degeneracy of the former $\sigma$ states is broken, according to the bonding and antibonding character of the state between the two atoms that move closer.

Figure 4

Isodensities of different vacancies: (a) $D_{3h}$, (b) $C_s$, and (c) divacancy.

Figure 5

Electronic properties of the divacancy. (a) Comparison between the electronic band structure calculated with DFT-LDA (left) and our modified TB model (right). For both calculations, the Fermi level is set to zero. (b) Isodenstity surfaces of specific defect states at $\Gamma$ and $K$ point, labeled in the band structure and calculated with DFT-LDA.

Figure 6

Electronic properties of the adatom. (a) Comparison between the electronic band structure calculated with DFT-LDA (left) and our modified TB model (right). For both calculations, the Fermi level is set to zero. (b) Isodenstity surfaces of specific defect states at $\Gamma$ point, labeled in the band structure and calculated with DFT-LDA.

Figure 7

(Color online) Band structure of a graphene sheet, calculated using both ab initio (full lines) and tight-binding (dashed lines) techniques, with the Fermi level set to zero.

Figure 8

(Color online) Computed constant-current STM images of defects in graphene calculated with a positive tip potential of $0.2\mathrm{V}$: (a) nonreconstructed $D_{3h}$ and (b) reconstructed $C_s$. (c) Average of the three equivalent $C_s$ structures rotated by $\pm 2\pi ∕3$. All atomic coordinates are expressed in Å.

Figure 9

(Color online) Computed constant-current STM images of defects in graphene calculated with a positive tip potential of $0.2\mathrm{V}$: (a) divacancy and (b) Stone-Wales defect. All atomic coordinates are expressed in Å.