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Quantum point contact devices are indispensable tools for probing the edgestructure of the fractional quantum Hall (FQH) states. Recent observations ofquantized conductance plateaus accompanied by shot noise in such devices, aswell as suppression of Mach-Zehnder interference, call for theoreticalexplanations. In this paper, we develop a theory of FQH edge state transportthrough quantum point contacts, which allows for a generic Abelian edgestructure and assumes strong equilibration between edge modes (incoherenttransport regime). We find that conductance plateaus are found whenever thequantum point contact locally depletes the Hall bar to a stable region with afilling factor lower than that of the bulk and the resulting edge statesequilibrate. The shot noise generated on these plateaus can be classifiedaccording to 13 possible combinations of edge charge and heat transport in thedevice. We also comment on a relation between the the emergence of quantizedplateaus and the suppression of Mach-Zehnder interference. Besides explainingrecent experimental findings, our results provide novel insights andperspectives on quantum point contact devices in the FQH regime.

Conductance plateaus and shot noise in fractional quantum Hall point contacts