Non-Fermi-liquid behavior in transport across carbon nanotube quantum dots

A low energy theory for nonlinear transport in finite-size single-wall carbon nanotubes, based on a microscopic model for the interacting $p_z$ electrons and successive bosonization, is presented. Due to the multiple degeneracy of the energy spectrum diagonal as well as off-diagonal (coherences) elements of the reduced density matrix contribute to the nonlinear transport. A four-electron periodicity with a characteristic ratio between adjacent peaks, as well as nonlinear transport features, in quantitative agreement with recent experiments, are predicted.

Figure 1

Energy spectrum of a SWNT with open boundary conditions (right-hand side) described in terms of left $\left(\tilde{L}\right)$ and right $\left(\tilde{R}\right)$ branches. It is constructed from suitable combinations of travelling waves whose spectrum is shown on the left-hand side.

Figure 2

(a) Conductance vs electrochemical potential in the linear regime $eV\ll k_{B}T\ll {\epsilon }_0$. Despite asymmetric contacts, the two central peaks and the two outer peaks have equal height. (b) Current in the regime ${\epsilon }_0\gg \mid e{V}_l\mid \gg kT$. Asymmetry effects become visible. Four-electron periodicity is still observed. Parameters are $E_c=9.5\mathrm{meV}$, $k_{B}T=0.05\mathrm{meV}$, ${\epsilon }_0=2.9\mathrm{meV}$, ${\gamma }_s=5{\gamma }_d=4.9\times {10}^{10}{\mathrm{s}}^{-1}$.

Figure 3

(a) Current in a bias voltage-electrochemical potential plane for the symmetric contacts case. (b) Difference plot of the current with and without coherences. Here $k_{B}T=0.01\mathrm{meV}$ and $n_q{\epsilon }_0∕{\epsilon }_{c+q}\approx 0.21$. Other parameters as in Fig. 2a.