Enhanced Fano factor in a molecular transistor coupled to phonons and Luttinger-liquid leads

We study how the electron-phonon coupling and intralead electron interaction affects the transport properties of a molecular quantum dot coupled to leads. We consider the effects on the steady-state current and dc noise for both equilibrated and unequilibrated on-dot phonons. The density matrix formalism is applied in the high-temperature approximation and the resulting semiclassical rate equation is numerically solved for various strengths of electron-electron interactions in the leads and electron-phonon coupling. We have found that the Fano factor, which measures the noise to current ratio, is enhanced as the intralead electron interaction is increased, while both the current and its noise are smeared out and suppressed due to the interaction. Interestingly, the Fano factor exhibits super-Poissonian behavior as the electron-phonon coupling becomes greater than order one.

Figure 1

Tunneling current plotted as a function of source-drain voltage with $\lambda =1.0$. E and NE stand for equilibrated and nonequilibrated phonons, respectively, and S and A stand for symmetric and asymmetric biases, respectively. $\beta$ is the exponent in the Luttinger-liquid distribution, which, in the noninteracting limit, is 1 and bigger than 1 for both repulsive and attractive interactions. The current is plotted in units of $eT∕\hslash$.

Figure 2

Tunneling current plotted as a function of source-drain voltage with $\lambda =0.5$.

Figure 3

Tunneling current plotted as a function of source-drain voltage with $\lambda =2.0$.

Figure 4

Phonon probability distribution plotted with $\lambda =1.0$ in the case of nonequilibrium phonons. Here, ${\mu }_L=-{\mu }_R=2{\omega }_0$.

Figure 5

dc noise plotted as a function of source-drain voltage with $\lambda =1.0$. It is plotted in units of $e^{2}T∕\hslash$.

Figure 6

dc noise plotted as a function of source-drain voltage with $\lambda =0.5$.

Figure 7

dc noise plotted as a function of source-drain voltage with $\lambda =2.0$.

Figure 8

Fano factor plotted as a function of source-drain voltage with $\lambda =1.0$.

Figure 9

Fano factor plotted as a function of source-drain voltage with $\lambda =0.5$.

Figure 10

Fano factor plotted as a function of source-drain voltage with $\lambda =2.0$.

Figure 11

dc noise plotted as a function of source-drain voltage with $\lambda =1.0$ and $\beta =1$ at two different temperatures.