Electron-phonon interaction and full counting statistics in molecular junctions

TL;DR

This paper derives an analytic formula for the full counting statistics of electron transport in molecular junctions interacting with phonons, revealing how inelastic processes influence current fluctuations and distribution shapes.

Contribution

It introduces a novel analytic approach to describe irreducible moments of charge transfer distributions considering electron-phonon interactions in molecular junctions.

Findings

Distribution shifts from Gaussian to Poissonian above inelastic threshold.

Domains in parameter space characterized by sign changes in moments.

Analytic expressions for moments of charge transfer distribution.

Abstract

The full counting statistics of a molecular level weakly interacting with a local phonon mode is derived. We find an analytic formula that gives the behavior of arbitrary irreducible moments of the distribution upon phonon excitation. The underlying competition between quasi-elastic and inelastic processes results in the formation of domains in parameter space characterized by a given sign in the jump of the irreducible moments. In the limit of perfect transmission, the corresponding distribution is distorted from Gaussian statistics for electrons to Poissonian transfer of holes above the inelastic threshold.