Multiple Mechanisms for Emerging Conductance Plateaus in Fractional Quantum Hall States

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.