Full counting statistics and shot noise of cotunneling in quantum dots and single-molecule transistors

TL;DR

This paper introduces a simple master-equation scheme to evaluate full-counting statistics and shot noise in cotunneling through quantum dots and molecules, revealing super-Poissonian noise and effects of blocking states.

Contribution

A novel, straightforward method based on master equations for calculating FCS and shot noise in cotunneling, including elastic and inelastic processes, with analytical results for quantum dots.

Findings

Shot noise is super-Poissonian above the inelastic threshold.

Enhanced shot noise occurs with blocking states in resonant and cotunneling regimes.

The method reproduces known results and provides new analytical expressions.

Abstract

We develop a conceptually simple scheme based on a master-equation approach to evaluate the full-counting statistics (FCS) of elastic and inelastic off-resonant tunneling (cotunneling) in quantum dots (QDs) and molecules. We demonstrate the method by showing that it reproduces known results for the FCS and shot noise in the cotunneling regime. For a QD with an excited state, we obtain an analytic expression for the cumulant generating function (CGF) taking into account elastic and inelastic cotunneling. From the CGF we find that the shot noise above the inelastic threshold in the cotunneling regime is inherently super-Poissonian when external relaxation is weak. Furthermore, a complete picture of the shot noise across the different transport regimes is given. In the case where the excited state is a blocking state, strongly enhanced shot noise is predicted both in the resonant and cotunneling regimes.