Chirality and Current-Current Correlation in Fractional Quantum Hall Systems

TL;DR

This paper investigates current correlations in fractional quantum Hall edge channels, revealing how chiral propagation affects equilibrium correlations and how fractional statistics of quasi-particles manifest in measurable current correlations.

Contribution

It provides the first analysis of current-current correlations in fractional quantum Hall systems, highlighting signatures of fractional statistics in measurable quantities.

Findings

Zero frequency equilibrium correlation vanishes after the beam splitter.

Normalized current-current correlation reveals signatures of fractional statistics.

Chiral edge propagation influences current correlation behavior.

Abstract

We study current-current correlation in an electronic analog of a beam splitter realized with edge channels of a fractional quantum Hall liquid at Laughlin filling fractions. In analogy with the known result for chiral electrons, if the currents are measured at points located after the beam splitter, we find that the zero frequency equilibrium correlation vanishes due to the chiral propagation along the edge channels. Furthermore, we show that the current-current correlation, normalized to the tunneling current, exhibits clear signatures of the Laughlin quasi-particles' fractional statistics.