Transport through a quantum dot with two parallel Luttinger liquid leads

We study transport through a quantum dot side-coupled to two parallel Luttinger liquid leads in the presence of a Coulombic dot-lead interaction. This geometry enables an exact treatment of the interlead Coulomb interactions. We find that for dots symmetrically disposed between the two leads the correlation of charge fluctuations between the two leads can lead to an enhancement of the current at the Coulomb-blockade edge and even to a negative differential conductance. Moving the dot off center or separating the wires further converts the enhancement to a suppression.

Figure 1

Schematic of a one-dimensional lead-dot-lead system showing two parallel leads.

Figure 2

(a) Luttinger exponent $Y_L$ of a symmetric junction ($Y_R=Y_L$) with nanotube leads as a function of the interlead distance $d$ for different $q$ values. (b) Luttinger exponents $Y_L,Y_R$ as a function of the displacement $\delta \equiv d_L-d/2$ of the quantum dot relative to the leads. (Here $\delta =0$ represents a symmetric junction.)

Figure 3

Comparison of current-voltage characteristics of a quantum dot symmetrically side-coupled to two parallel Luttinger liquid leads (a) for a model including interlead Coulomb interactions and (b) for the same model but with interlead Coulomb interactions set to zero. Voltages and thermal energies are given in units of the corresponding on-site energy. For the results shown in (a), the interaction parameters are obtained from Eq. (30) using Eqs. (17), (18) and (22) with $V_c\simeq 0.9$, $M=4$ (channels), $d_{\alpha }=d/2=\Lambda$, and with the logarithms evaluated at $q=0.1\hspace{0.5em}\Lambda {}^{-1}$ (these parameters were shown in Ref. 8 to be appropriate for a carbon nanotube with $\Lambda$ of the order of the tube diameter). The results shown in (b) are obtained for the same parameters except $V_{\alpha \mathrm{\alpha ̄}}$ [cf. Eq. (16)] set to zero. The local Coulomb interaction is assumed to be twice as large as the on-site energy in both panels.

Figure 4

(a) Current-voltage characteristics of a symmetric junction with nanotube leads for different interlead distances $d$. (b) Current-voltage characteristics for different displacements $\delta \equiv d_L-d/2$ of the quantum dot. (Here $\delta =0$ represents a symmetric junction.) We assume the same parameter values as used in Fig. 3.