Off-resonance transport through a quantum dot weakly coupled to Luttinger liquids at finite applied bias voltages

We study off-resonance transport through a quantum dot coupled to Luttinger-liquid leads at finite applied bias voltages in the sequential tunneling regime using a master equation approach. The off-resonance differential conductance shows a lead-interaction strength-dependent power-law behavior as a function of the applied bias in contrast to the behavior for the case of Fermi liquid leads where one observes a satellite Lorentzian peak at a bias value equal to the distance away from the resonance. A Fermi-liquid-lead-like Lorentzian behavior is, however, observed for the case of Luttinger-liquid leads for highly asymmetric coupling to leads. The finite-voltage differential conductance provides information about both the lead interaction strength parameter and the asymmetry parameter.

Figure 1

A single quantum dot attached to left and right leads held at chemical potentials ${\mu }_L$ and ${\mu }_R$, respectively.

Figure 2

Plot of the differential conductance $G$ [scaled by $G_L=(2\pi e^2∕\hslash )({\Gamma }_R∕\eta )T^{1∕g-2}$] as a function of the applied bias very close to the value $\mid \epsilon \mid =1$ for lead interaction strengths $g=g_L=g_R=1∕3$ at different temperatures.

Figure 3

Plot of the differential conductance $G$ (scaled by its value $G_0$ at bias $\Delta \mu ∕2=\mid \epsilon \mid =1$) as a function of the applied bias for lead interaction strengths $g=g_L=g_R=1∕2,1∕3$ and for different asymmetry parameters $\eta ={\Gamma }_L∕{\Gamma }_R$. We have set the parameters $\Lambda =4$ and $T=0.05$.

Figure 4

Plot of the differential conductance $G$ [scaled by the value $G_R=(2\pi e^2∕\hslash ){\Gamma }_R∕T$] as a function of the applied bias for lead interaction strengths $g=g_L=g_R=1∕3$ and for asymmetry parameters $\eta =0.01$ and $\eta =0.001$. We have set the parameters $\Lambda =4$ and $T=0.05$.

Figure 5

Differential conductance $G$ [scaled by $G_R=(2\pi e^2∕\hslash ){\Gamma }_R∕T$] as a function of the applied bias for interaction stengths $g_L=1∕2$, $g_R=1$ and $g_R=1∕2$, $g_L=1$ We set the parameters $T=0.05$, $\Lambda =4$, and $\eta =1$.