Multiple Mechanisms for Emerging Conductance Plateaus in Fractional Quantum Hall States

TL;DR

This paper explores multiple mechanisms behind conductance plateaus in fractional quantum Hall states, showing that similar conductance values can arise from different processes and proposing shot noise measurements to distinguish them.

Contribution

It demonstrates that conductance plateaus can result from various mechanisms and introduces shot noise analysis as a method to differentiate these underlying processes.

Findings

Different mechanisms can produce identical conductance plateaus.

Shot noise measurements can distinguish between these mechanisms.

New conductance plateau at 5e^2/9h predicted.

Abstract

Two-terminal conductance quantization in the context of quantum Hall (QH) physics is intimately related to the current carried by a discrete number of chiral edge modes. Upon pinching off a QH bar, one may engineer setups where some modes are fully transmitted (while the others are fully reflected), giving rise to the orthodox theory of quantized conductance plateaus. Here, we note that the observation of quantized plateaus \emph{does not} uniquely indicate the underlying mechanism. Our study demonstrates explicitly that (i) such plateaus may be the manifestations of entirely different mechanisms; (ii) conductance measurements alone will not suffice to distinguish one from the other. We further show that measurements of shot noise (auto- and cross-correlation) at the plateau may discriminate among different mechanisms. While our observations apply to a broad class of QH states, we demonstrate their applicability employing a prototypical example: the bulk state of filling factor $\nu=2/3$. We present distinctly different scenarios that lead to a conductance plateau $G_{2-\text{terminal}} = e^2/3h$ (observed previously), and likewise qualitatively different mechanisms leading to $e^2/2h$ (recently observed). We also predict the possibility of a new conductance plateau at $5e^2/9h$, following a non-orthodox scenario.