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  • Open Access

Revisiting the physics of hole-conjugate fractional quantum Hall channels

D. C. Glattli*, C. Boudet, A. De, and P. Roulleau

  • *Contact author: christian.glattli@cea.fr
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Phys. Rev. Research 7, 043026 – Published 7 October, 2025

DOI: https://doi.org/10.1103/brnm-hv7c

Abstract

The fractional quantum Hall effect provides the first example of multiple quantum phases hosting quasiparticles not being fermions or bosons, but anyons. It is therefore important to investigate whether all these phases can be practical to detect these anyons. Here, we propose revisiting the intriguing physics of hole-conjugate Fractional Quantum Hall (FQH) phases with counter-propagating edge channels in the filling factor range 1/2≤ν≤1 whose properties may prevent anyon interference detection. In the seminal KFP model by Kane, Fisher, and Polchinski, upstream neutral and downstream charge modes, along with random incoherent interchannel tunneling, are considered essential for explaining the observed conductance at ν=2/3. In this work, we introduce a minimal model that qualitatively reproduces the edge physics of the ν=2/3 FQH phase without invoking neutral and charge modes. By inserting N fictive reservoirs—either Landauer reservoirs (LRs) or Energy-Preserving Reservoirs (EPRs)—along the counter-propagating channels to simulate edge channel mixing, we show that the conductance rapidly approaches the KFP fixed point of 2/3×(e2/h) for both EPRs and LRs. While LRs produce equal charge and thermal relaxation lengths, EPRs exhibit an infinite thermal relaxation length, consistent with recent observations. Our model also predicts current noise in small Hall bars that varies linearly with voltage at large bias, with an apparent Fano factor ≃0.19/N+1 for N LRs or an exponentially vanishing Fano factor for EPRs. Moreover, with a Quantum Point Contact at the center of the Hall bar, the model predicts the recently observed 0.5e2/h conductance plateau. Finally, early experiments reporting upstream excitations are found to be conveniently explained by upstream diffusive heat flow and delta-T noise, rather than by specific collective neutral modes. The results obtained in this study can be generalized to more complex hole-conjugate fractional quantum Hall phases.

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Phys. Rev. Research 7, 043026– Published 7 October, 2025
  • Received 5 December 2024
  • Accepted 1 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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