Charge transfer statistics of a molecular quantum dot with a vibrational degree of freedom

TL;DR

This paper investigates the full counting statistics of electron transport through a molecular quantum dot with vibrational modes, revealing how inelastic processes influence noise and cumulants.

Contribution

It explicitly identifies quasielastic and inelastic contributions to transport statistics and their effects on shot noise and cumulants in a vibrational quantum dot.

Findings

Inelastic processes cause a sign change in shot noise correction at universal transmission values.

When inelastic current correction vanishes, all odd cumulants also vanish.

The analysis applies to arbitrary transmission with weak electron-phonon coupling.

Abstract

We analyze the full counting statistics (FCS) of a single-site quantum dot coupled to a local Holstein phonon for arbitrary transmission and weak electron-phonon coupling. We identify explicitly the contributions due to quasielastic and inelastic transport processes in the cumulant generating function and discuss their influence on the transport properties of the dot. We find that in the low-energy sector, the inelastic term causes a sign change in the shot noise correction at certain universal values of the transmission. Furthermore, we show that when the correction to the current due to inelastic processes vanishes, all odd order cumulants vanish as well.