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.

7+5 pages, 4+4 figures, 1 table; The Supplemental Material has a partial overlap with Low Temperature Physics 50, 1113 (2024)+arXiv:2307.05175(2023)

References in corpus (11)

• Observation of neutral modes in the fractional quantum Hall regime
• Spontaneous breakdown of topological protection in two dimensions
• Determination of topological edge quantum numbers of fractional quantum Hall phases
• Conductance plateaus and shot noise in fractional quantum Hall point contacts
• Contacts, equilibration, and interactions in fractional quantum Hall edge transport
• Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise
• Probing the neutral edge modes in transport across a point contact via thermal effects in the Read-Rezayi non-abelian quantum Hall states
• Does shot noise always provide the quasiparticle charge?
• Half-integer conductance plateau at the $\nu =2/3$ fractional quantum Hall state in a quantum point contact
• Fingerprints of anti-Pfaffian topological order in quantum point contact transport
• Distinguishing particle-hole conjugated Fractional Quantum Hall states using quantum dot mediated edge transport

Cited by in corpus (4)

• Half-integer thermal conductance in the absence of Majorana mode
• Experimentally Motivated Order of Length Scales Affect Shot Noise
• Elevated Hall Responses as Indicators of Edge Reconstruction
• Quantized Transport of $\nu =2/3$ Fractional Quantum Hall Edge with Disordered Superconducting Proximity