Full Counting Statistics of Strongly Non-Ohmic Transport through Single Molecules

We study analytically the full counting statistics of charge transport through single molecules, strongly coupled to a weakly damped vibrational mode. The specifics of transport in this regime—a hierarchical sequence of avalanches of transferred charges, interrupted by “quiet” periods—make the counting statistics strongly non-Gaussian. We support our findings for the counting statistics as well as for the frequency-dependent noise power by numerical simulations, finding excellent agreement.

Figure 1

Hierarchical character of transport. Left: Three generations of self-similar MC plots for $\lambda =4$ and $eV=3\hslash {\omega }_v$, showing the net-transferred charge $N$ and phonon state $q$ as functions of time. (${\omega }_v$: phonon frequency; $\rho$: density of states of the leads; $t_0$: molecule-lead coupling). Right: Comparison of the fixed-point distribution for the transferred charge per generation-$q$ avalanche to numerical simulations for $q=0,1,2$ (mean values ${\overline{N}}^{(0)}=91.2$, ${\overline{N}}^{(1)}=11.1$, and ${\overline{N}}^{(2)}=2.9$).

Figure 2

Evolution of the full counting statistics $P_T(Q)$ for four different time intervals $T$ with $\lambda =4.0$ and $eV=3\hslash {\omega }_v$. The MC data (solid lines) are in excellent agreement with the analytical full counting statistics, Eq. (6) (dashed lines), with ${\overline{N}}^{(0)}=91.2$, ${\overline{n}}_T=2.4·{10}^{-6}T/T_0$ (no fit), and $T_0=(2\pi \rho t_0^2/\hslash {)}^{-1}$.