Bunching and anti-bunching in electronic transport

TL;DR

This paper introduces a $g^{(2)}$-function for electronic transport to analyze electron bunching and anti-bunching, revealing that super- and sub-Poissonian statistics do not always correspond to these phenomena.

Contribution

It extends the $g^{(2)}$-function concept from quantum optics to electronic transport, providing new insights into electron current statistics in nano-structures.

Findings

Super-Poissonian statistics do not necessarily mean electron bunching.

Sub-Poissonian statistics do not necessarily mean anti-bunching.

The $g^{(2)}$-function offers detailed information about electron transport phenomena.

Abstract

In quantum optics the $g^{(2)}$-function is a standard tool to investigate photon emission statistics. We define a $g^{(2)}$-function for electronic transport and use it to investigate the bunching and anti-bunching of electron currents. Importantly, we show that super-Poissonian electron statistics do not necessarily imply electron bunching, and that sub-Poissonian statistics do not imply anti-bunching. We discuss the information contained in $g^{(2)}(\tau)$ for several typical examples of transport through nano-structures such as few-level quantum dots.