Conductance plateaus and shot noise in fractional quantum Hall point contacts

Abstract

Quantum point contact devices are indispensable tools for probing the edge structure of the fractional quantum Hall (FQH) states. Recent observations of quantized conductance plateaus accompanied by shot noise in such devices, as well as suppression of Mach-Zehnder interference, call for theoretical explanations. In this paper, we develop a theory of FQH edge state transport through quantum point contacts, which allows for a generic Abelian edge structure and assumes strong equilibration between edge modes (incoherent transport regime). We find that conductance plateaus are found whenever the quantum point contact locally depletes the Hall bar to a stable region with a filling factor lower than that of the bulk and the resulting edge states equilibrate. The shot noise generated on these plateaus can be classified according to 13 possible combinations of edge charge and heat transport in the device. We also comment on a relation between the the emergence of quantized plateaus and the suppression of Mach-Zehnder interference. Besides explaining recent experimental findings, our results provide novel insights and perspectives on quantum point contact devices in the FQH regime.

21 pages, 10 figures

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• Thermal conductance and noise of Majorana modes along interfaced $\nu =5/2$ fractional quantum Hall states
• Observation of the scaling dimension of fractional quantum Hall anyons
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• Emergence of Neutral Modes in Laughlin-like Fractional Quantum Hall Phases
• Fingerprints of anti-Pfaffian topological order in quantum point contact transport
• Multiple Mechanisms for Emerging Conductance Plateaus in Fractional Quantum Hall States
• Localization and conductance in fractional quantum Hall edges
• Role of scaling dimensions in generalized noises in fractional quantum Hall tunneling due to a temperature bias
• Transport Signatures of Fractional Quantum Hall Binding Transitions
• Edge Reconstruction and Emergent Neutral Modes in Integer and Fractional Quantum Hall Phases
• Experimentally Motivated Order of Length Scales Affect Shot Noise
• Ballistic-to-diffusive transition in engineered counter-propagating quantum Hall channels
• Magnon transmission across $\nu =1|-1|1$ mono-layer graphene junction as a probe of electronic structure
• Extracting the scaling dimension of quantum Hall quasiparticles from current correlations
• Elevated Hall Responses as Indicators of Edge Reconstruction
• Shot noise signatures of candidate states for the fractional quantum Hall $\nu =12/5$ state