Conductance plateaus and shot noise in fractional quantum Hall point contacts

TL;DR

This paper develops a theoretical framework for understanding conductance plateaus and shot noise in fractional quantum Hall quantum point contacts, explaining recent experimental observations and their relation to edge state equilibration.

Contribution

It introduces a generic Abelian edge structure model assuming strong edge mode equilibration, explaining conductance plateaus and shot noise classifications in FQH devices.

Findings

Conductance plateaus occur when the local filling factor is lower than the bulk.

Shot noise can be classified into 13 types based on edge charge and heat transport.

Quantized plateaus are related to suppression of Mach-Zehnder interference.

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.