# Build-up of Vibron-Mediated Electron Correlations in Molecular Junctions

## TL;DR

This paper explores how electron correlations and vibrational dynamics develop over time in molecular junctions, revealing the role of vibron-assisted tunneling and phonon back-action in shaping electronic transport properties.

## Contribution

It provides a comprehensive analysis of time-dependent electron-vibron interactions and their impact on electron correlations in molecular junctions, highlighting the build-up mechanism and phonon effects.

## Key findings

- Damped oscillations in vibron displacement and current towards steady state.
- Electron-hole correlations build up after a critical time, deviating from binomial statistics.
- Phonon back-action amplifies and accelerates electron correlation formation.

## Abstract

We investigate on the same footing the time-dependent electronic transport properties and vibrational dynamics of a molecular junction. We show that fluctuations of both the molecular vibron displacement and the electronic current across the junction undergo damped oscillations towards the steady-state. We assign the former to the onset of electron tunneling events assisted by vibron-emission. The time-dependent build-up of electron-hole correlations is revealed as a departure of the charge-transfer statistics from the generalized-binomial one after a critical time tc. The phonon-back action on the tunneling electrons is shown to amplify and accelerate this build-up mechanism.