First-principles study of the electrical conductance of telescopically aligned carbon nanotubes

We perform a comparative study for the quantum transport of telescoping carbon nanotubes, where the (5,5) and (10,10) nanotubes are coaxially aligned, using first-principles local-density-functional and tight-binding calculations. In both calculations, the intertube conductance initially increases as the hybridized length in the contact region increases, and then decreases, exhibiting a maximum conductance. However, the calculated conductances from first principles are generally smaller than those from the single $\pi$-orbital tight-binding model. In the first-principles calculations, we obtain the maximum intertube conductance that does not exceed $G_0(=2e^2∕h)$, while individual tubes have two conducting channels, giving the conductance of $2G_0$. On the other hand, the single $\pi$-orbital tight-binding model gives the maximum conductance close to $2G_0$, similar to previous calculations. Using a double-wall nanotube, we examine the effect of interwall interactions on conductance and find that the ${\pi }^{*}$ states of the inner and outer tubes are strongly coupled in the tight-binding model, allowing for an extra conducting channel, while the ${\pi }^{*}$ channel is closed in the first-principles calculations.

Figure 1

The atomic structure of the telescoping nanotube which consists of the (5,5) and (10,10) nanotubes. The hybridized double-wall region is given by the coordinates of $z=0$ and $L$.

Figure 2

The conductances (solid lines) and the DOS (dotted lines) calculated from the first-principles LDA for the $(5,5)∕(10,10)$ telescoping nanotubes with the hybridized lengths of $L=5a$, $16a$, and $30a$.

Figure 3

(Color online) Comparison of the conductances at the Fermi level calculated from the first-principles LDA (black line) and the single $\pi$-orbital tight-binding (blue dashed line) model for the $(5,5)∕(10,10)$ telescoping nanotubes with varying the hybridized length up to $L=30a$. The single-band TB conductances are also shown, which are obtained by reducing the strength of the interwall coupling $W$ to $0.7W$ (red dashed line) and $0.5W$ (green dashed line) in the TB Hamiltonian.

Figure 4

(a) The conductances calculated from the first-principles LDA for the $(5,5)∕(10,10)$ telescoping nanotube with the hybridized length of $L=22a$ remain almost unchanged by breaking the mirror symmetries. (b) The conductances calculated from the single-band TB model are compared for the $(5,5)∕(10,10)$ telescoping nanotubes with the mirror symmetries (solid lines) and the symmetry breaking (dashed lines) by rotating the inner tube $(\Delta \theta =6°)$ about the tube axis.

Figure 5

(Color online) Comparison of the band structures obtained from the first-principles LDA (black dots), single $\pi$-orbital TB (blue lines), and multiband TB (red lines) calculations for the $(5,5)∕(10,10)$ double-wall nanotubes with preserving the mirror symmetries [in (a) and (b)] and breaking the symmetry by rotating the inner tube by 6° about the tube axis [in (c) and (d)].

Figure 6

(Color online) Comparison of the band structures of the symmetry-preserved double-wall nanotube (black solid lines) and individual (5,5) (red circles) and (10,10) (blue dots) nanotubes from the (a) LDA, (b) single $\pi$-orbital TB, and (c) multiband TB calculations.