Current noise in molecular junctions: effects of the electron-phonon interaction

TL;DR

This paper investigates how electron-phonon interactions influence current noise in molecular junctions, providing analytical formulas and demonstrating that inelastic noise spectroscopy can serve as a diagnostic tool.

Contribution

It offers a unified theoretical framework for calculating inelastic corrections to current noise in molecular junctions, including analytical formulas and the identification of key noise contributions.

Findings

Vertex corrections significantly affect inelastic noise.

Inelastic noise spectroscopy is a sensitive diagnostic tool.

Analytical formulas enable microscopic evaluation of noise corrections.

Abstract

We study inelastic effects on the electronic current noise in molecular junctions, due to the coupling between transport electrons and vibrational degrees of freedom. Using a full counting statistics approach based on the generalized Keldysh Green's function technique, we calculate in an unified manner both the mean current and the zero-frequency current noise. For multilevel junctions with weak electron-phonon coupling, we give analytical formulas for the lowest order inelastic corrections to the noise in terms of universal temperature- and voltage-dependent functions and junction-dependent prefactors, which can be evaluated microscopically, e.g. with ab-initio methodologies. We identify distinct terms corresponding to the mean-field contribution to noise and to the vertex corrections, and we show that the latter contribute substantially to the inelastic noise. Finally, we illustrate our results by a simple model of two electronic levels which are mutually coupled by the electron-phonon interaction and show that the inelastic noise spectroscopy is a sensitive diagnostic tool.