Self-consistent full counting statistics of inelastic transport

We consider the full counting statistics (FCS) of inelastic transport through a molecular junction. A self-consistent procedure for FCS within the nonequilibrium Green function method is introduced. We show that in the case of FCS the self-consistent treatment provides a conserving approximation. The importance of renormalizing the molecular vibration for the counting statistics of electron transport is discussed within a generic two-level model. We consider weak electron-vibration coupling, and report that heating the molecular vibration may lead to either an increase or a decrease in the current through the junction depending on the model parameters. Super-Poissonian noise induced by the nonequilibrium vibration is observed at resonance. We argue that the origin of the effect is the avalanche transport previously discussed in the literature for a system with a strong electron-vibration interaction.

Figure 1

Sketches of the two generic models: a two-level bridge with off-diagonal (model A) and diagonal (model B) couplings between the electron and molecular vibration(s).

Figure 2

Graphical representation of the self-consistent Born approximation. Shown are Feynman diagrams for the Dyson equation of (a) the electron and (b) the molecular vibration Green functions. The double solid (wiggly) line represents the full electron (molecular vibration) Green function. The single solid (wiggly) line indicates this Green function in the absence of the electron-vibration interaction (7).

Figure 3

Comparison between the Born and the self-consistent Born approximations for the model B [see Fig. 1b]. We present (a) the current, Eq. (10), and (b) the Fano factor, Eq. (12), as functions of the applied bias $V$. The BA yields different results on the left $L$ (dotted lines, blue) and right $R$ (dashed lines, magenta) interfaces. The self-consistent results (solid lines, black) are calculated within the SCBA 1 scheme. See the text for parameters.

Figure 4

Comparison between the SCBA 1 and SCBA 2 schemes for models A and B. We present (a) the current, Eq. (10), and (b) the Fano factor, Eq. (12), as functions of the applied bias $V$. Parameters are as in Fig. 3.

Figure 5

SCBA calculations for model A with a set of intersite coupling strengths: $t<{\Gamma }_K$, $t\sim {\Gamma }_K$, and $t>{\Gamma }_K$. We present (a) the current, Eq. (10), and (b) the Fano factor, Eq. (12), as functions of the applied bias $V$. Types of calculations and values of the elastic hopping parameter $t$ are indicated in the inset. Other parameters are as in Fig. 3.