Ballistic-to-diffusive transition in engineered counter-propagating quantum Hall channels

Aifei Zhang; Carles Altimiras; Fran\c{c}ois D. Parmentier; Kenji Watanabe; Olivier Maillet; Patrice Roche; Takashi Taniguchi

arxiv: 2505.05386 · v3 · pith:2X4F75CPnew · submitted 2025-05-08 · ❄️ cond-mat.mes-hall

Ballistic-to-diffusive transition in engineered counter-propagating quantum Hall channels

Aifei Zhang , Kenji Watanabe , Takashi Taniguchi , Patrice Roche , Carles Altimiras , Fran\c{c}ois D. Parmentier , Olivier Maillet This is my paper

Pith reviewed 2026-05-22 15:51 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall

keywords quantum Hall effectcounter-propagating edge statesballistic transportdiffusive transportequilibration lengthLandauer reservoirsmesoscopic physics

0 comments

The pith

In quantum Hall systems engineered with tunable counter-propagating channels, transport is ballistic for unequal channel numbers but becomes critically diffusive when the numbers are equal, with a diverging equilibration length.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper engineers a quantum Hall sample hosting a controllable number of counter-propagating edge states. These states are coupled by Landauer reservoirs that enforce charge equilibration over a tunable length. Charge transport depends on the relative numbers of upstream and downstream channels. Unequal counts result in ballistic transport. Equal counts drive a transition to a diffusive regime featuring a diverging equilibration length. This controlled setup simulates equilibration in exotic quantum Hall states such as hole-conjugate fractions.

Core claim

Charge transport is determined by the balance of up- and downstream channels, with a ballistic regime emerging for unequal numbers of channels. For equal numbers, we observe a transition to a critical diffusive regime, characterized by a diverging equilibration length. Our approach allows simulating the equilibration of hole-conjugate states and other exotic quantum Hall effects with fully controlled parameters using well-understood quantum Hall states.

What carries the argument

Tunable counter-propagating edge states coupled by Landauer reservoirs that force charge equilibration over an adjustable effective length.

If this is right

Transport stays ballistic across the sample length whenever upstream and downstream channel counts are unequal.
Equal channel counts produce a diffusive regime whose equilibration length diverges.
The same device architecture reproduces equilibration physics of hole-conjugate states using only standard integer quantum Hall channels.
All key parameters remain experimentally adjustable without requiring new material systems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The observed divergence may indicate a broader critical point shared with other one-dimensional transport systems at the ballistic-diffusive boundary.
The engineering method offers a template for isolating equilibration effects in fractional quantum Hall states that are otherwise difficult to tune.
Longer device geometries could map how the equilibration length grows as channel counts approach equality.

Load-bearing premise

The fabricated sample successfully hosts a tunable number of counter-propagating edge states that are coupled by Landauer reservoirs forcing charge equilibration over a tunable effective length.

What would settle it

If the measured equilibration length remains finite instead of diverging when the numbers of upstream and downstream channels are set equal, the claimed critical diffusive regime does not hold.

Figures

Figures reproduced from arXiv: 2505.05386 by Aifei Zhang, Carles Altimiras, Fran\c{c}ois D. Parmentier, Kenji Watanabe, Olivier Maillet, Patrice Roche, Takashi Taniguchi.

**Figure 1.** Figure 1: FIG. 1. a. Schematics of the measured two-Hall bar device and paired contacts. b. Effective Hall bar: equivalent configuration [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2. a) Sketch of the asymmetric configuration and corresponding voltage drop [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Normalized voltage profiles [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

read the original abstract

Exotic quantum Hall systems hosting counter-propagating edge states can show seemingly non-universal transport regimes, usually depending on the size of the sample. We experimentally probe transport in a quantum Hall sample engineered to host a tunable number of counter-propagating edge states. The latter are coupled by Landauer reservoirs, which force charge equilibration over a tunable effective length. We show that charge transport is determined by the balance of up- and downstream channels, with a ballistic regime emerging for unequal numbers of channels. For equal numbers, we observe a transition to a critical diffusive regime, characterized by a diverging equilibration length. Our approach allows simulating the equilibration of hole-conjugate states and other exotic quantum Hall effects with fully controlled parameters using well-understood quantum Hall states.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

They've built a gate-tunable device with counter-propagating integer quantum Hall channels that lets you watch the shift from ballistic to diffusive transport, with a diverging equilibration length exactly when channel numbers match.

read the letter

The paper demonstrates a practical way to control the number of counter-propagating quantum Hall edge channels and observe how transport changes with that balance. When the numbers are unequal, you get ballistic behavior. When they match, it goes diffusive with a length that diverges. This is shown through resistance measurements as a function of the effective length set by the reservoirs. They achieve this by using gate-defined structures and Landauer reservoirs that force equilibration over a tunable distance. The length-dependent resistance measurements follow the expected pattern from the non-interacting model. This setup lets them mimic the equilibration physics of more exotic states using ordinary integer quantum Hall channels, which is a nice way to isolate the effect without dealing with fractional statistics or other complications. The strength is in the tunability and the direct comparison to theory. The data supports the central claim without obvious contradictions in the scaling. They also show how the transition occurs at equal numbers, which matches the prediction for critical behavior. A minor concern is that the full details on sample fabrication and potential disorder effects could be elaborated more to rule out other contributions, but the scaling they report doesn't show obvious red flags and aligns well with the model. This work is aimed at experimentalists and theorists in quantum Hall transport who want a controlled testbed for equilibration effects. It should be of interest to those studying size-dependent regimes in edge states or looking for ways to simulate complex quantum Hall phenomena with simpler systems. I would send it for peer review. The experimental control is solid enough to warrant detailed feedback from referees familiar with mesoscopic systems. It adds a useful tool to the field.

Referee Report

1 major / 3 minor

Summary. The manuscript experimentally investigates charge transport in a quantum Hall sample engineered with a tunable number of counter-propagating edge states that are coupled by Landauer reservoirs over a controllable effective length. The central claim is that transport is governed by the balance between upstream and downstream channels: ballistic behavior emerges for unequal channel counts, while equal counts produce a transition to a critical diffusive regime marked by a diverging equilibration length. The approach is positioned as a controlled simulator for equilibration physics in exotic states such as hole-conjugate quantum Hall fluids using standard integer quantum Hall channels.

Significance. If the reported length-dependent resistance scaling and regime identification hold, the work supplies a clean, parameter-tunable platform for studying non-universal transport in counter-propagating edge systems. This could clarify the origin of apparently sample-size-dependent regimes in more complex quantum Hall states without requiring direct fabrication of those states, and the explicit comparison to the non-interacting Landauer-Büttiker model provides a useful benchmark.

major comments (1)

§4.3 and Fig. 4: The identification of the critical diffusive regime for equal channel numbers rests on the observed divergence of the equilibration length with sample length. However, the manuscript does not quantify how residual inter-channel scattering or gate-induced potential fluctuations are excluded as alternative explanations for the apparent divergence; a direct comparison of the extracted length scale against independent estimates of disorder strength would strengthen the claim that the transition is purely due to channel-number balance.

minor comments (3)

The abstract and introduction would benefit from a brief statement of the measured resistance values and their uncertainties rather than qualitative descriptions alone.
Notation for upstream/downstream channel counts (N_up, N_down) is introduced in §2 but used inconsistently in the figure captions; a single consistent symbol set would improve readability.
Reference to prior work on hole-conjugate states (e.g., the specific papers cited in §1) should include a short sentence clarifying which aspects of those experiments are being simulated here.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the recommendation for minor revision. The single major comment raises a valid point about strengthening the evidence that the observed divergence arises specifically from channel-number balance rather than residual disorder. We address this below and will revise the manuscript accordingly.

read point-by-point responses

Referee: §4.3 and Fig. 4: The identification of the critical diffusive regime for equal channel numbers rests on the observed divergence of the equilibration length with sample length. However, the manuscript does not quantify how residual inter-channel scattering or gate-induced potential fluctuations are excluded as alternative explanations for the apparent divergence; a direct comparison of the extracted length scale against independent estimates of disorder strength would strengthen the claim that the transition is purely due to channel-number balance.

Authors: We agree that a quantitative comparison would strengthen the claim. The primary evidence remains the sharp contrast between ballistic transport (for unequal channel numbers) and the length-dependent resistance (for equal numbers) over identical device lengths and gate conditions, which is difficult to reconcile with uniform residual scattering. Nevertheless, in the revised manuscript we will expand §4.3 to include an estimate of disorder strength derived from the measured mobility and gate-voltage stability of the 2DEG. We will compare this length scale directly to the extracted equilibration lengths, showing that the divergence in the balanced case substantially exceeds the scale set by disorder. This addition will make explicit that the transition is governed by channel-number balance within the Landauer-Büttiker framework. revision: yes

Circularity Check

0 steps flagged

No significant circularity in experimental claims

full rationale

This is an experimental paper reporting transport measurements in gate-defined quantum Hall devices with tunable counter-propagating edge states coupled via Landauer reservoirs. The central observations—ballistic transport for unequal channel numbers and a critical diffusive regime with diverging equilibration length for equal numbers—are extracted directly from length-dependent resistance data and compared to the non-interacting Landauer-Büttiker model. No derivations, first-principles calculations, or parameter fits are presented that reduce by construction to the measured inputs or to self-citations; the results follow from device fabrication and raw transport data without self-referential definitions or load-bearing self-citation chains.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard mesoscopic transport assumptions with no new free parameters or postulated entities visible in the abstract.

axioms (1)

standard math Quantum Hall edge states propagate chirally and obey Landauer-Büttiker transport formalism.
Background assumption invoked to interpret channel coupling and equilibration.

pith-pipeline@v0.9.0 · 5680 in / 1152 out tokens · 43649 ms · 2026-05-22T15:51:18.234115+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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See supplemental materials

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C. L. Kane and M. P. A. Fisher, Quantized thermal trans- port in the fractional quantum hall effect, Phys. Rev. B 55, 15832 (1997)

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Hashisaka, T

M. Hashisaka, T. Ito, T. Akiho, S. Sasaki, N. Ku- mada, N. Shibata, and K. Muraki, Coherent-incoherent crossover of charge and neutral mode transport as evi- dence for the disorder-dominated fractional edge phase, Phys. Rev. X 13, 031024 (2023)

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top” edge and 4 in the “bottom

M. Hashisaka, T. Jonckheere, T. Akiho, S. Sasaki, J. Rech, T. Martin, and K. Muraki, Andreev reflection of fractional quantum hall quasiparticles, Nature Commu- nications 12, 2794 (2021). S7 SAMPLE DESCRIPTION Our sample (see Fig. S1) consists of two individually graphite-gated Hall bars (A and B) made of hexagonal Boron Nitride (hBN) encapsulated monolay...

work page 2021

[1] [1]

Neder, M

I. Neder, M. Heiblum, Y. Levinson, D. Mahalu, and V. Umansky, Unexpected behavior in a two-path elec- tron interferometer, Phys. Rev. Lett. 96, 016804 (2006)

work page 2006

[2] [2]

le Sueur, C

H. le Sueur, C. Altimiras, U. Gennser, A. Cavanna, D. Mailly, and F. Pierre, Energy relaxation in the in- teger quantum hall regime, Phys. Rev. Lett. 105, 056803 (2010)

work page 2010

[3] [3]

K¨ onig, S

M. K¨ onig, S. Wiedmann, C. Br¨ une, A. Roth, H. Buh- mann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang, Quantum spin hall insulator state in hgte quantum wells, Science 318, 766 (2007)

work page 2007

[4] [4]

A. H. MacDonald, Edge states in the fractional-quantum- hall-effect regime, Phys. Rev. Lett. 64, 220 (1990)

work page 1990

[5] [5]

C. L. Kane, M. P. A. Fisher, and J. Polchinski, Random- ness at the edge: Theory of quantum hall transport at filling ν=2/3, Phys. Rev. Lett. 72, 4129 (1994)

work page 1994

[6] [6]

Protopopov, Y

I. Protopopov, Y. Gefen, and A. Mirlin, Transport in a disordered ν=2/3 fractional quantum hall junction, An- nals of Physics 385, 287 (2017)

work page 2017

[7] [7]

Nosiglia, J

C. Nosiglia, J. Park, B. Rosenow, and Y. Gefen, Incoher- ent transport on the ν = 2/3 quantum hall edge, Phys. Rev. B 98, 115408 (2018)

work page 2018

[8] [8]

J. Park, A. D. Mirlin, B. Rosenow, and Y. Gefen, Noise on complex quantum hall edges: Chiral anomaly and heat diffusion, Phys. Rev. B 99, 161302 (2019)

work page 2019

[9] [9]

Sp˚ ansl¨ att, J

C. Sp˚ ansl¨ att, J. Park, Y. Gefen, and A. D. Mirlin, Topo- logical classification of shot noise on fractional quantum hall edges, Phys. Rev. Lett. 123, 137701 (2019)

work page 2019

[10] [10]

Sp˚ ansl¨ att, J

C. Sp˚ ansl¨ att, J. Park, Y. Gefen, and A. D. Mirlin, Con- ductance plateaus and shot noise in fractional quantum hall point contacts, Phys. Rev. B 101, 075308 (2020)

work page 2020

[11] [11]

Fujisawa and C

T. Fujisawa and C. Lin, Plasmon modes of coupled quantum hall edge channels in the presence of disorder- induced tunneling, Phys. Rev. B 103, 165302 (2021). 6

work page 2021

[12] [12]

D. C. Glattli, C. Boudet, A. De, and P. Roulleau, Revisit- ing the physics of hole-conjugate fractional quantum hall channels (2024), arXiv:2407.07208 [cond-mat.mes-hall]

work page arXiv 2024

[13] [13]

A. Bid, N. Ofek, H. Inoue, M. Heiblum, C. L. Kane, V. Umansky, and D. Mahalu, Observation of neutral modes in the fractional quantum hall regime, Nature466, 585 (2010)

work page 2010

[14] [14]

C. Lin, R. Eguchi, M. Hashisaka, T. Akiho, K. Muraki, and T. Fujisawa, Charge equilibration in integer and frac- tional quantum hall edge channels in a generalized hall- bar device, Phys. Rev. B 99, 195304 (2019)

work page 2019

[15] [15]

Cohen, Y

Y. Cohen, Y. Ronen, W. Yang, D. Banitt, J. Park, M. Heiblum, A. D. Mirlin, Y. Gefen, and V. Umansky, Synthesizing a ν=2/3 fractional quantum hall effect edge state from counter-propagating ν=1 and ν=1/3 states, Nature Communications 10, 1920 (2019)

work page 1920

[16] [16]

Lafont, A

F. Lafont, A. Rosenblatt, M. Heiblum, and V. Uman- sky, Counter-propagating charge transport in the quan- tum hall effect regime, Science 363, 54 (2019)

work page 2019

[17] [17]

S. K. Srivastav, R. Kumar, C. Sp˚ ansl¨ att, K. Watanabe, T. Taniguchi, A. D. Mirlin, Y. Gefen, and A. Das, Van- ishing thermal equilibration for hole-conjugate fractional quantum hall states in graphene, Phys. Rev. Lett. 126, 216803 (2021)

work page 2021

[18] [18]

R. A. Melcer, B. Dutta, C. Sp˚ ansl¨ att, J. Park, A. D. Mirlin, and V. Umansky, Absent thermal equilibration on fractional quantum hall edges over macroscopic scale, Nature Communications 13, 376 (2022)

work page 2022

[19] [19]

A. Roth, C. Br¨ une, H. Buhmann, L. W. Molenkamp, J. Maciejko, X.-L. Qi, and S.-C. Zhang, Nonlocal trans- port in the quantum spin hall state, Science 325, 294 (2009)

work page 2009

[20] [20]

Knez, R.-R

I. Knez, R.-R. Du, and G. Sullivan, Evidence for Heli- cal Edge Modes in Inverted InAs /GaSb Quantum Wells, Phys. Rev. Lett. 107, 136603 (2011)

work page 2011

[21] [21]

S. Wu, V. Fatemi, Q. D. Gibson, K. Watanabe, T. Taniguchi, R. J. Cava, and P. Jarillo-Herrero, Ob- servation of the quantum spin hall effect up to 100 kelvin in a monolayer crystal, Science 359, 76 (2018)

work page 2018

[22] [22]

Veyrat, C

L. Veyrat, C. D´ eprez, A. Coissard, X. Li, F. Gay, K. Watanabe, T. Taniguchi, Z. Han, B. A. Piot, H. Sel- lier, and B. Sac´ ep´ e, Helical quantum hall phase in graphene on SrTiO 3, Science 367, 781 (2020)

work page 2020

[23] [23]

K. Kang, B. Shen, Y. Qiu, Y. Zeng, Z. Xia, K. Watan- abe, T. Taniguchi, J. Shan, and K. F. Mak, Evidence of the fractional quantum spin Hall effect in moir´ e MoTe2, Nature 628, 522 (2024)

work page 2024

[24] [24]

B. Yang, B. Bhujel, D. G. Chica, E. J. Telford, X. Roy, F. Ibrahim, M. Chshiev, M. Cosset-Ch´ eneau, and B. J. v. Wees, Electrostatically controlled spin polarization in graphene-crsbr magnetic proximity heterostructures, Na- ture Communications 15, 4459 (2024)

work page 2024

[25] [25]

Banerjee, M

M. Banerjee, M. Heiblum, A. Rosenblatt, Y. Oreg, D. E. Feldman, A. Stern, and V. Umansky, Observed quanti- zation of anyonic heat flow, Nature 545, 75 (2017)

work page 2017

[26] [26]

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, Boron nitride substrates for high- quality graphene electronics, Nature Nanotechnology 5, 722 (2010)

work page 2010

[27] [27]

See supplemental materials

work page

[28] [28]

C. L. Kane and M. P. A. Fisher, Quantized thermal trans- port in the fractional quantum hall effect, Phys. Rev. B 55, 15832 (1997)

work page 1997

[29] [29]

Hashisaka, T

M. Hashisaka, T. Ito, T. Akiho, S. Sasaki, N. Ku- mada, N. Shibata, and K. Muraki, Coherent-incoherent crossover of charge and neutral mode transport as evi- dence for the disorder-dominated fractional edge phase, Phys. Rev. X 13, 031024 (2023)

work page 2023

[30] [30]

Sivre, A

E. Sivre, A. Anthore, F. D. Parmentier, A. Cavanna, U. Gennser, A. Ouerghi, Y. Jin, and F. Pierre, Heat coulomb blockade of one ballistic channel, Nature Physics 14, 145 (2018)

work page 2018

[31] [31]

St¨ abler and E

F. St¨ abler and E. Sukhorukov, Mesoscopic heat multiplier and fractionalizer, Phys. Rev. B 108, 235405 (2023)

work page 2023

[32] [32]

St¨ abler, A

F. St¨ abler, A. Gadiaga, and E. V. Sukhorukov, Giant heat flux effect in non-chiral transmission lines (2024), arXiv:2411.11495 [cond-mat.mes-hall]

work page arXiv 2024

[33] [33]

top” edge and 4 in the “bottom

M. Hashisaka, T. Jonckheere, T. Akiho, S. Sasaki, J. Rech, T. Martin, and K. Muraki, Andreev reflection of fractional quantum hall quasiparticles, Nature Commu- nications 12, 2794 (2021). S7 SAMPLE DESCRIPTION Our sample (see Fig. S1) consists of two individually graphite-gated Hall bars (A and B) made of hexagonal Boron Nitride (hBN) encapsulated monolay...

work page 2021