Correlated Tunneling in Intramolecular Carbon Nanotube Quantum Dots

We investigate correlated electronic transport in single-walled carbon nanotubes with two intramolecular tunneling barriers. We suggest that below a characteristic temperature the long-range nature of the Coulomb interaction becomes crucial to determine the temperature dependence of the maximum $G_{\mathrm{m}\mathrm{a}\mathrm{x}}$ of the conductance peak. Correlated sequential tunneling dominates transport yielding the power law $G_{\mathrm{m}\mathrm{a}\mathrm{x}}\propto T^{{\alpha }_{\mathrm{e}\mathrm{n}\mathrm{d}\mathrm{\text{−}}\mathrm{e}\mathrm{n}\mathrm{d}}-1}$, typical for tunneling between the ends of two Luttinger liquids. Our predictions are in agreement with recent measurements.

Figure 1

Spectral densities $J_{\Sigma /\Delta }^{\rho }(\omega )/\omega$ for finite interaction range ($a=200x_0^{-1},g_{\rho }=0.23$) with ${\omega }_{\sigma }\equiv \Delta E_{\sigma }/\hslash$. Left inset: Enlargement of the low frequency part. The important parameter is $1/g_{\Delta }=\underset{\omega \to 0}{lim}{J}_{\Delta }^{\rho }(\omega )/\omega$. Right inset: Contributions to the effective linewidth ${\Gamma }^{\mathrm{t}\mathrm{o}\mathrm{t}}$ and ${\gamma }^{\Delta }$, with the latter being originated from the finite range of the interaction (see text).

Figure 2

Lowest order correlated sequential tunneling (CST) paths in the $(N_{\rho },N_{\rho }^{\prime })$ plane for the transfer of one charge through the island corresponding to Eq. (9). Filled circles denote diagonal states of the reduced density matrix.

Figure 3

Conductance maximum $G_{\mathrm{m}\mathrm{a}\mathrm{x}}$ (right) and integrated conductance $G^{*}$ (left) as a function of temperature. Solid line: theoretical prediction with $\Delta E_{\sigma }=23\mathrm{m}\mathrm{e}\mathrm{V}$ and interaction strength $g_{\rho }=0.23$; $\blacksquare$, experimental results 7; dashed lines: power laws; see Eq. (2). Left inset: A single conductance peak for varying gate voltage for $T=4.4$, 20, 30 K. Right inset: Peak width versus temperature.