Theory of suppressed shot-noise at $\nu=2/(2p+\chi)$

TL;DR

This paper analyzes the edge states of fractional quantum Hall liquids at specific filling factors, explaining the transition between conductance plateaus and the suppression of shot-noise using chiral Tomonaga-Luttinger liquid theory.

Contribution

It introduces a theoretical framework for understanding shot-noise suppression at fractional quantum Hall states with filling factors =2/(2p+), including hierarchy constructions for =2/3.

Findings

Fractional charge q=e/(2p+) at =2/(2p+) plateau.

Charge q=e/(p+) at G=G_0/(p+) plateau.

Hierarchy construction explains shot-noise suppression at =2/3.

Abstract

We study the edge states of fractional quantum Hall liquid at bulk filling factor $\nu=2/(2p+\chi)$ with $p$ being an even integer and $\chi=\pm 1$. We describe the transition from a conductance plateau $G=\nu G_0=\nu e^2/h$ to another plateau $G=G_0/(p+\chi)$ in terms of chiral Tomonaga-Luttinger liquid theory. It is found that the fractional charge $q$ which appears in the classical shot-noise formula $S_{I}=2q <I_b>$ is $q=e/(2p+\chi)$ on the conductance plateau at $G=\nu G_0$ whereas on the plateau at $G=G_0/(p+\chi)$ it is given by $q=e/(p+\chi)$. For $p=2$ and $\chi=-1$ an alternative hierarchy constructions is also discussed to explain the suppressed shot-noise experiment at bulk filling factor $\nu=2/3$.