Electron transport in carbon nanotube shuttles and telescopes

Using a scattering technique, combined with density-functional theory, a computational study of the electron-transport properties of multiwall carbon nanotube (MWNT) telescopes and shuttles is presented. When the inner nanotube of a MWNT is displaced by an amount $\delta x$ with respect to the outer tube, we predict that the interwall $\pi \text{−}\pi$ coupling, ${\gamma }_{\pi \text{−}\pi }$, is significantly modified, leading to unexpected conductance oscillations for values of $\delta x$ of the order of the interatomic spacing. An analytical model is presented, which provides a mapping between ${\gamma }_{\pi \text{−}\pi }$ and electron-transport measurements.

Figure 1

(a) A telescoping MWNT in which a small-diameter NT is inserted a distance $L$ into a larger diameter NT. The NTs are each connected to reservoirs on the left- and right-hand sides of the structures. In both cases, electrons are scattered at the points, separated by a distance $L$, where an NT terminates. (b) A “shuttle” system, in which a large-diameter SWNT (the shuttle) of length $L$ is placed outside a small-diameter inner-wall NT, which in turn is connected to external reservoirs.

Figure 2

(a) Ab initio (6,6)@(11,11) band structure close to the Fermi energy (0 eV). (b) Gap opening due to interwall interaction. (c) Band structure with no interwall interaction. (d) The difference $\delta k_{\pi \text{−}\pi }=k_2-k_1$ and average of the Fermi wave vectors $k_1$ and $k_2$ in the $\pi$ bands as a function of $\delta x$.

Figure 3

Ab initio conductance $G\left(E_F\right)$ as a function of $\delta x$ in a (6,6)@(11,11) telescope for scattering regions of length (a) $N=10$, and (b) $N=250$. Analytic description of $T\left(E\right)$ for the telescope model of length (c) $N=10$ and (d) $N=250$.

Figure 4

(a) Ab initio conductance of the shuttle (6,6)@(11,11) nanotube as a function of $\delta x$ for scattering lengths (a) $N=10$ and (b) $N=250$. Analytic desciption of transmission for the shuttle model of lengths (c) $N=10$ and (d) $N=250$.

Figure 5

Transmission coefficient vs energy for a telescope (a) and shuttle (b).

Figure 6

Model representation of a (a) telescoping nanotube, and (b) shuttle nanotube.