Electronic Bisection of a Single-Wall Carbon Nanotube by Controlled Chemisorption

Conversion of two diametrically opposed atomic rows on a carbon nanotube to $s{p}^3$ hybridization produces two identical weakly coupled one-dimensional electronic systems within a single robust covalently bonded package: a biribbon. Arm-chair tubes, when so divided, acquire a pair of narrow spin-polarized bands at the Fermi energy; interaction across the $s{p}^3$ dividers produces a tunable band splitting in the THz range. For semiconducting tubes, the eigenvalues of the low-energy electronic states are surprisingly unaffected by the bifurcation; however, the tubes’ response functions to external electric fields are dramatically altered. These modified tubes could be produced by uniaxial compression transverse to the tube axis followed by site-selective chemisorption.

Figure 1

Uniaxial compression of a nanotube transverse to its axis in the presence of a reactive species such as hydrogen or fluorine should facilitate chemisorption onto diametrically opposed rows of carbon atoms in the regions of highest curvature. The aperture angle $\theta$ of the $s{p}^3$ junction appears in the discussion of structural energetics.

Figure 2

Chemisorption patterns on zigzag (8,0) and arm-chair (6,6) nanotubes, opened up into ribbons. Open circles indicate adsorption sites and the absence of an accessible $p_z$ orbital. Heavy bonds symbolize electronic $\pi$ hopping in the tight-binding picture. The light bonds are inactive.

Figure 3

Band structures for (9,0) and (11,0) biribbons. Insets show $0.003{\AA }^{-3}$ electron density isosurfaces for the highest occupied zone-edge state.

Figure 4

Spin-resolved band structures of (12,12) and (6,6) biribbons and a bent (unrelaxed) graphitic ribbon which is half of the (6,6) biribbon, terminated with extra hydrogens at the locations of the missing carbon atoms. Solid (black and green online) lines show bands for different spin polarizations. Dashed lines for (6,6) case are from an unpolarized calculation. Compared to unpolarized calculation, spin splitting gains around 0.15 eV per unit cell [29]. Close relationship between the ribbon and the (6,6) biribbon is evident from the electron probability density shown in the insets ($0.003{\AA }^{-3}$ isosurfaces for highest occupied zone-edge states are shown). The carbon-carbon bonds in the circumferential direction lengthen gradually from 1.40 Å at the zigzag edge to 1.58 Å at the bearded edge, nearly the same as the change from a double bond to a single bond.

Figure 5

Minimum direct gap as a function of the total electric field across the (11,0) biribbon in the directions indicated, for a (non-self-consistent) tight-binding calculation. The resulting charge transfer across the tube indicates that the corresponding external electric field is approximately 1.2 (2) times as large as the total field if it is along the short (long) axis.

Figure 6

The energy per carbon atom from density functional theory (dots) and an analytical fit (lines) for biribbons.