Crossover from the Luttinger-Liquid to Coulomb-Blockade Regime in Carbon Nanotubes

We develop a theoretical approach to the low-energy properties of one-dimensional electron systems aimed to encompass the mixed features of Luttinger-liquid and Coulomb-blockade behavior observed in the crossover between the two regimes. For this aim, we extend the Luttinger-liquid description by incorporating the effects of a discrete single-particle spectrum. The intermediate regime is characterized by a power-law behavior of the conductance, but with an exponent oscillating with the gate voltage, in agreement with recent experimental observations. Our construction also accounts naturally for the existence of a crossover in the zero-bias conductance, mediating between two temperature ranges where the power-law behavior is preserved but with a different exponent.

Figure 1

Plot of the EDF $n(\epsilon ;{\epsilon }_F)$ for different values of the temperature corresponding to $k_{B}T/\Delta \epsilon =0.25,0.6,1.0$. Solid lines are obtained from (2) and dashed lines by using the Fermi-Dirac distribution (3).

Figure 2

Plot of the exponent $\alpha$ as a function of the Fermi energy ${\epsilon }_F$ (in units of $\Delta \epsilon$) for different values of the temperature $T=1$, 40, and 150 K.

Figure 3

Log-log plot of the conductance vs the temperature.