Super-Poissonian noise, negative differential conductance, and relaxation effects in transport through molecules, quantum dots, and nanotubes

We consider charge transport through a nanoscopic object, e.g., single molecules, short nanotubes, or quantum dots, that is weakly coupled to metallic electrodes. We account for several levels of the molecule/quantum dot with level-dependent coupling strengths, and allow for relaxation of the excited states. The current–voltage characteristics as well as the current noise are calculated within first-order perturbation expansion in the coupling strengths. For the case of asymmetric coupling to the leads we predict negative-differential-conductance accompanied with super-Poissonian noise. Both effects are destroyed by fast relaxation processes. The nonmonotonic behavior of the shot noise as a function of bias and relaxation rate reflects the details of the electronic structure and level-dependent coupling strengths.

Figure 1

Sketch of the couplings and processes in the considered model.

Figure 2

Current $I$ and shot noise $S$ vs voltage for $k_{B}T=0.05\mathrm{meV}$, ${ϵ}_1=-0.5\mathrm{meV}$, ${ϵ}_2=0.5\mathrm{meV}$, $U=1.5\mathrm{meV}$, $E_c=1\mathrm{meV}$, symmetric bias $({\mu }_L=-{\mu }_R=\mathrm{eV}∕2)$, and ${\Gamma }_1^L={\Gamma }_2^L={\Gamma }_1^R=\Gamma$. The height of the plateaus labeled by $i=0$, 1, 2 are discussed in the text and depend on the choice of the coupling parameters. For suppressed coupling ${\Gamma }_2^R$ current and shot noise break down leading to negative differential conductance (NDC) at a threshold energy. The curves are normalized to $I_{\max }=(e∕\hslash )2\Gamma$ and $S_{\max }=(e^2∕\hslash )2\Gamma$, respectively.

Figure 3

Fano factor $F$ vs bias voltage for the same parameters as in Fig. 2 and various coupling parameters ${\Gamma }_2^R$. The NDC effect results in a super-Poissonian value for the Fano factor.

Figure 4

Current $I$ and shot noise $S$ vs voltage for the same parameters as in Fig. 2 but fixed coupling ${\Gamma }_2^R=0.01\Gamma$. Coupling to a bosonic bath allows for relaxation processes. The coupling parameter ${\alpha }_{\mathrm{ph}}$ is varied relative to $\Gamma$. The NDC effect is destroyed by strong relaxation.

Figure 5

Fano factor vs bias voltage for the same parameters as in Fig. 4 and various couplings to a bosonic bath ${\alpha }_{\mathrm{ph}}$. The super-Poissonian value of the Fano factor vanishes due to strong relaxation processes.

Figure 6

Fano factor (left axis), current, and shot noise (right axis) vs coupling to the bosonic bath for the same set of parameters as in Fig. 4, 5. The values $I_1$, $S_1$, $F_1$ of the first plateau do not depend on the bosonic coupling parameter, whereas on the second plateau (NDC region) both the shot noise and the Fano factor show a nonmonotonic dependence.

Figure 7

Contour plot of the Fano factor (plateau $F_2$) with the choice ${\Gamma }_1^{L,R}=\Gamma -{\Gamma }_2^{L,R}$ and ${\alpha }_{\mathrm{ph}}=0$. The totally symmetric situation is given for ${\Gamma }_1^L={\Gamma }_1^R=0.5\Gamma$. The Fano factor can become arbitrarily large if the system is sufficiently asymmetric.