Figure 1

Graphical outline of this article. (Top) Three mechanisms that strongly affect the edge states in ZGNRs: (a) the atomic structure of the $z_{211}$ passivated edge, (b) the atomic structure of the $\mathit{zz}(57)$ reconstructed edge, and (c) edge closure. (Bottom) The edge magnetism in (d) ideal ZGNRs is not stable at room temperature. The low-temperature magnetism is destabilized (or even totally disappears) whenever the system has (e) edge defects or (f) is charge doped.Reuse & Permissions

Figure 2

Atomic structures (top) and nonmagnetic band structures (bottom) of a 12-ZGNR with (a) unpassivated edges and (b) monohydrogenated edges. The fatness of the bands is proportional to the orbital character of the corresponding wave function on the encircled edge atom (top). Orange (light gray) represents the $\pi$ character of the bands, and blue (dark gray) represents their $\sigma$ character. Gray horizontal lines were added to the atomic structure (top) in order to indicate the boundaries of the corresponding unit cell along the periodic direction (see also Fig. 5). Because of the presence of (partially) flat bands near $E_F$ in the nonmagnetic band structure, there will be a magnetic transition into an antiferromagnetic ground state with a band gap (not shown).Reuse & Permissions

Figure 3

Atomic structures and band structures of a 12-ZGNR with a $\mathit{zz}(57)$ edge reconstruction for (a) unpassivated edges and (b) monohydrogenated edges (see Fig. 2). The system is metallic and nonmagnetic and has edge states.Reuse & Permissions

Figure 4

Atomic structure and band structure of a 12-ZGNR with a $z_{211}$ edge (see Fig. 2). The system does not have edge states, it is nonmagnetic, and a semiconductor. Its band gap is 0.61 eV.Reuse & Permissions

Figure 5

The spin density of (a) an unpassivated 12-ZGNR in the AFM state and (b) an unpassivated 10-ZGNR with an edge vacancy in the FM state. The red (dark gray) contours on the right hand side represent positive spin densities within the graphene layer; the yellow (light gray) contours on the left-hand side represent negative densities. $A$ is the lattice constant along the periodic direction. (b) Due to the presence of the defect, there are no remaining magnetic moments on the left edge.Reuse & Permissions

Figure 6

The effect of charge doping in 12-ZGNR+H: $\Delta N$ is the number of excess electrons per edge atom, ${\mu }^{\mathrm{FM}}$ is the magnetic moment per edge atom in the FM state, and $\Delta E_F$ is the change of the Fermi energy with respect to the undoped case for both the NM and the FM state.Reuse & Permissions