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.

arXiv comment7+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 (34)

• Topological Insulators
• Transport in an inhomogeneous interacting one--dimensional system
• Observation of half-integer thermal Hall conductance
• Sharp and Smooth Boundaries of Quantum Hall Liquids
• Randomness at the Edge: Theory of Quantum Hall transport at filling $\nu =2/3$
• Observation of neutral modes in the fractional quantum Hall regime
• Quantum Point Contacts
• Edge reconstruction in the $\nu =2/3$ fractional quantum Hall state
• A New Paradigm for Edge Reconstruction in Fractional Quantum Hall States
• Composite Edge States in the $\nu =2/3$ Fractional Quantum Hall Regime
• Transport in a disordered $\nu =2/3$ fractional quantum Hall junction
• Spontaneous breakdown of topological protection in two dimensions
• Incoherent transport on the $\nu =2/3$ quantum Hall edge
• Vanishing thermal equilibration for hole-conjugate fractional quantum Hall states in graphene
• Topological classification of shot noise on fractional quantum Hall edges
• Noise on the Non-Abelian $\nu =5/2$ Fractional Quantum Hall Edge
• Observation of ballistic upstream modes at fractional quantum Hall edges of graphene
• Absent thermal equilibration on fractional quantum Hall edges over macroscopic scale
• Determination of topological edge quantum numbers of fractional quantum Hall phases
• Fractional Edge Reconstruction in Integer Quantum Hall Phases
• Conductance plateaus and shot noise in fractional quantum Hall point contacts
• Phenomenological theory of heat transport in the fractional quantum Hall effect
• 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
• Transport in helical Luttinger liquids in the fractional quantum Hall regime
• Emergence of Neutral Modes in Laughlin-like Fractional Quantum Hall Phases
• Distinguishing particle-hole conjugated Fractional Quantum Hall states using quantum dot mediated edge transport
• Fingerprints of anti-Pfaffian topological order in quantum point contact transport
• Symmetry-related transport on a fractional quantum Hall edge
• Robustness of Helical Edge States Under Edge Reconstruction
• Edge Reconstruction of a Time-Reversal Invariant Insulator: Compressible-Incompressible Stripes

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