# Non-renewal statistics for electron transport in a molecular junction with electron-vibration interaction

## TL;DR

This paper investigates how electron-vibration interactions in a molecular junction lead to non-renewal statistics in electron tunnelling times, revealing correlations influenced by vibrational dynamics and coupling strength.

## Contribution

It introduces a master equation approach to analyze non-renewal statistics in electron transport, highlighting the role of vibrational dynamics and strong electron-vibration coupling.

## Key findings

- Non-renewal statistics emerge when vibrational dynamics are treated exactly.
- Strong electron-vibration coupling is necessary for temporal correlations.
- Rare tunnelling events in Franck-Condon blockade are positively correlated.

## Abstract

Quantum transport of electrons through a molecule is a series of individual electron tunnelling events separated by stochastic waiting time intervals. We study the emergence of temporal correlations between successive waiting times for the electron transport in a vibrating molecular junction. Using master equation approach, we compute joint probability distribution for waiting times of two successive tunnelling events. We show that the probability distribution is completely reset after each tunnelling event if molecular vibrations are thermally equilibrated. If we treat vibrational dynamics exactly without imposing the equilibration constraint, the statistics of electron tunnelling events become non-renewal. Non-renewal statistics between two waiting times $\tau_1$ and $\tau_2$ means that the density matrix of the molecule is not fully renewed after time $\tau_1$ and the probability of observing waiting time $\tau_2$ for the second electron transfer depends on the previous electron waiting time $\tau_1$. The strong electron-vibration coupling is required for the emergence of the non-renewal statistics. We show that in Franck-Condon blockade regime the extremely rare tunnelling events become positively correlated.