Self-Passivating Edge Reconstructions of Graphene

Planar reconstruction patterns at the zigzag and armchair edges of graphene were investigated with density-functional theory. It was unexpectedly found that the zigzag edge is metastable and a planar reconstruction spontaneously takes place at room temperature. The reconstruction changes electronic structure and self-passivates the edge with respect to adsorption of atomic hydrogen from a molecular atmosphere.

Figure 1

The geometries of graphene edges: (a) reconstructed zigzag [zz(57)], (b) armchair (ac), (c) reconstructed armchair [ac(677)], (d) zigzag (zz), and (e) pentagonal armchair [ac(56)]. The numbers in parentheses denote the number of vertices in edge polygons. Some bond lengths (in Å) and bond angles are shown on the right: The bond angles are $\alpha =143°$, $\beta =126°$, $\gamma =148°$, and $\delta =147°$. All geometries are strictly in-plane.

Figure 2

The edge energies of carbon nanoribbons. Energies are plotted as a function of the ribbon width for the edges in Fig. 1.

Figure 3

Hydrogen adsorption energies. The upper symbols correspond to ${\epsilon }_{\mathrm{ads}}$ with coverage of one hydrogen per edge atom, and lower faint symbols are shifted by subtracting the ${\mathrm{H}}_2$ binding energy; positive ${\epsilon }_{\mathrm{ads}}-E_{{\mathrm{H}}_2}$ means the hydrogen atom is more strongly bound to the edge than to the ${\mathrm{H}}_2$ molecule.

Figure 4

The electronic structure of zigzag and zz(57) edges. (a) and (b) show the band structure for 34 Å wide zigzag and zz(57) nanoribbons, respectively, with a unit cell width of 4.9 Å. Note that for the zigzag this is twice the minimum unit cell, and the reciprocal space is thus only half of the normal representation. The dashed line is the Fermi level. The colored (thick) bands were identified directly by visual inspection of the wave functions. (c) and (d) show the height profiles of simulated scanning tunneling microscope images in the constant current mode of the respective edges (height variations $>2\AA$), formed by integrating the electron density from occupied bands within 0.1 eV of the Fermi energy. The degeneracies at the gamma point are 2 and 4 for the dangling bonds and the flat band, respectively.