Cotunneling and one-dimensional localization in individual disordered single-wall carbon nanotubes: Temperature dependence of the intrinsic resistance

We report on the temperature dependence of the intrinsic resistance of long individual disordered single-wall carbon nanotubes. The resistance grows dramatically as the temperature is reduced, and the functional form is consistent with an activated behavior. These results are described by a Coulomb blockade along a series of quantum dots. We occasionally observe a kink in the activated behavior that reflects the change of the activation energy as the temperature range is changed. This is attributed to charge hopping events between nonadjacent quantum dots, which is possible through cotunneling processes.

Figure 1

Four-point resistance. (a) Device schematic. (b)–(h) $R_{4pt}$ as a function of temperature. When the value of $V_g$ is not indicated, $V_g=0$. Device 3b is the same device as device 3, but it has been measured $1\text{month}$ before. Microscopic changes might have been occurred in between.

Figure 2

Four-point differential resistance as a function of $V_{4pt}$ for device 1 at 35, 45, 55, and $60\mathrm{K}$.

Figure 3

(Color online) Four-point resistance as a function of the gate voltage. (a) $R_{4pt}\left(V_g\right)$ for device 3b at 18, 25, 31, 39, 49, 60, 74, 96, 125, 158, and $191\mathrm{K}$. (b) $R_{4pt}\left(T\right)$ averaged over $V_g$ between $-0.3$ and $0.3\mathrm{V}$ and taken at different conductance maxima (m1 at $0.09\mathrm{V}$, m2 at $0.17\mathrm{V}$, m3 at $-0.25\mathrm{V}$, m4 at $-0.05\mathrm{V}$). (c) Two-point differential conductance as a function of $V_g$ and $V_{2pt}$ at $20\mathrm{K}$. The same measurement with $G_{4pt}$ is very noisy. $R_{4pt}\left(V_g\right)$ and $R_{2pt}\left(V_g\right)$ in the linear regime show the same features at $20\mathrm{K}$. Figures 1f and (a) and (c) in this figure are taken in three cooling runs. (d), (e) $G_{4pt}\left(V_g\right)$ for device 4.

Figure 4

Schematics of localized states along the nanotube. (a) States are randomly distributed. (b) Strong barriers that define quantum dots. (c) Proposed process to account for the kinks in Figs. 1f, 1g. Arrows represent hopping paths.