Anisotropy of the Stone-Wales defect and warping of graphene nanoribbons: A first-principles analysis

Stone-Wales (SW) defects, analogous to dislocations in crystals, play an important role in mechanical behavior of $s{p}^2$-bonded carbon based materials. Here, we show using first-principles calculations that a marked anisotropy in the interaction among the SW defects has interesting consequences when such defects are present near the edges of a graphene nanoribbon: depending on their orientation with respect to edge, they result in compressive or tensile stress, and the former is responsible to depression or warping of the graphene nanoribbon. Such warping results in delocalization of electrons in the defect states.

Figure 1

(Color online) Stone Wales defect in bulk graphene; (a) ${\text{SW}}_{\parallel }$, (b) ${\text{SW}}_{\angle }$ $\left(\theta =60°\right)$, (c) ${\text{SW}}_{\angle }$ $\left(\theta =120°\right)$, where $\theta$ is the angle of the bond [rotated to create the defect, marked in red (light gray in the grayscale)] with the horizontal axis in the anticlockwise direction. (d) Planar stresses acting on the supercell.

Figure 2

(Color online) (a) Pristine AGNR and (b)–(f) SW reconstructed AGNRs. (g) Pristine ZGNR and (h)–(l) SW reconstructed ZGNRs. Red, appearing light gray in the grayscale, dots, and lines denote the hydrogen atoms and bonds rotated to create SW defects, respectively.

Figure 3

(Color online) Warped structure of various different edge reconstructed nanoribbons. Red, green, and blue represent elevated “flat” and depressed regions, respectively. In grayscale, light and dark gray represents “flat” and warped regions, respectively. Atoms of a warped GNR are labeled as “flat” if $\left|z\right|<0.1\text{Å}$, $z$ being the height of the constituent carbon atoms. For a GNR of strictly flat geometry, $z=0$ for all the carbon atoms.

Figure 4

(Color online) DOS and STM image of pristine AGNR visualized with XCRYSDEN (Ref. 26). $E=0$ denotes the Fermi energy. We have applied a thermal broadening equivalent to room temperature to plot the DOS in this figure and throughout the rest of the paper. Consult text for the definition of $\rho$, ${\rho }_e$, and ${\rho }_i$. The horizontal bar represents the color scale used in the STM image. The image has been simulated for a sample bias of $-0.3\text{eV}$ and reflects the spatial distribution of the local-density of states LDOS below Fermi energy.

Figure 5

(Color online) DOS and STM image of $A_{\perp 757}^{2L}$ simulated with a sample bias of $+0.2\text{eV}$. The STM image shows the spatial distribution of LDOS above the Fermi energy.

Figure 6

(Color online) DOS and STM image of (a) $A_{\angle 57}^L$ and (b) $A_{\angle 57w}^L$. The STM images have been simulated with sample bias of $+0.2$ and $+0.4\text{eV}$ for (a) and (b), respectively. They show the spatial distribution of LDOS above the Fermi energy.

Figure 7

(Color online) DOS up to $E_F\left(=0.0\right)$ and STM image of pristine ZGNR simulated with a sample bias of $-0.2\text{eV}$. The image illustrates the spatial distribution of LDOS below the Fermi energy.

Figure 8

(Color online) DOS and STM image of $Z_{\angle 57}^{2L}$, simulated with a sample bias of $-0.2\text{eV}$. The image shows the spatial distribution of occupied LDOS.