Full counting statistics of a single-molecular quantum dot

TL;DR

This paper derives an analytical formula for the full counting statistics of a single-molecular quantum dot, revealing how inelastic effects influence current and noise, with oscillatory Fano factor behavior at zero temperature.

Contribution

It introduces a new analytical approach to distinguish elastic and inelastic contributions in quantum dot transport using nonequilibrium Green functions.

Findings

Inelastic effects cause steps in current and jumps in noise at specific bias voltages.

Fano factor oscillates with bias voltage and can be less than 0.5.

Derived explicit formula for cumulant generating function.

Abstract

We investigate the full counting statistics of a single quantum dot strongly coupled to a local phonon and weakly tunnel-connected to two metallic electrodes. By employing the generalized nonequilibrium Green function method and the Lang-Firsov transformation, we derive an explicit analytical formula for the cumulant generating function, which makes one to be able to identify distinctly the elastic and inelastic contributions to the current and zero-frequency shot noise. We find that at zero temperature, the inelastic effect causes upward steps in the current and downward jumps in the noise at the bias voltages corresponding to the opening of the inelastic channels, which are ascribed to the vibration-induced complex dependences of electronic self-energies on the energy and bias voltage. More interestingly, the Fano factor exhibits oscillatory behavior with increasing bias voltage and its minimum value is observed to be smaller than one half.