Figure 1

(a) The structure of a carbon tetrapod, the building block of schwarzite. The four extremities consist of $(9,0)$ nanotubes with a zigzag edge. (b) Introduction of trivalent carbon radicals, emphasized by the gray spheres, in the aromatic system of the otherwise tetravalent carbon atoms in the tetrapod core. The radicals are associated with heptagons, indicated by gray shading. The structure of (c) an $s{p}^2$- and (d) an $s{p}^3$-terminated $(9,0)$ nanotube, with the smaller spheres indicating the hydrogen atoms.Reuse & Permissions

Figure 2

Spin-resolved electronic densities of states of carbon nanostructures related to Fig. 1, with the majority spins represented in the upper panels and the minority spins in the lower panels. (a) Density of states of the ${\mathrm{C}}_{264}$ tetrapod of Fig. 1a. The solid line represents the projection of the density of states onto the 192 core carbon atoms. The dashed line represents that of the 72 carbon atoms at the zigzag edges. (b) Electronic density of states of a 126-atom segment of an $s{p}^2$ terminated $(9,0)$ nanotube, shown in Fig. 1c. The solid line represents the density of states of all the carbon atoms, and the dashed line its projection onto the 36 carbon atoms at the zigzag edge. The states denoted by “A” are doubly degenerate and localized at the edge. The counterparts of (a) and (b) for $s{p}^3$ terminated structures are shown in (c) for the ${\mathrm{C}}_{264}$ tetrapod and in (d) for the $(9,0)$ nanotube segment. The discrete level spectrum has been convoluted with a Gaussian with a full width at half maximum of 0.012 eV. The Fermi level lies at $E=0$.Reuse & Permissions

Figure 3

(a) Charge density associated with the four unpaired spins, which are unrelated to the edge states in an $s{p}^2$ terminated tetrapod. (b) The wave function of a spin-polarized edge state in an $s{p}^2$ terminated $(9,0)$ nanotube. We use color shading to represent the phase of the wave function.Reuse & Permissions