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REVIEW 3 major objections 6 minor 38 references

Individual quasiparticles entering the bulk of a graphene quantum Hall interferometer cause phase slips whose timescale can grow to minutes, revealing whether they join a central puddle or sit in a defect site.

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2026-08-04 18:29 UTC pith:67LP56JY

load-bearing objection Useful interferometry paper with a clever puddle-vs-defect lever-arm test; the 'several minutes' claim in the abstract is inferred, not measured, and the novelty framing underplays prior telegraph-noise observations. the 3 major comments →

arxiv 2509.09901 v1 pith:67LP56JY submitted 2025-09-11 cond-mat.mes-hall

Hard and soft phase slips in a Fabry-P\'erot quantum Hall interferometer

N. L. Samuelson , L. A. Cohen , W. Wang , S. Blanch , T. Taniguchi , K. Watanabe , M. P. Zaletel , A. F. Young This is my paper
classification cond-mat.mes-hall PACS 73.43.-f
keywords quantum Hall effectFabry-Pérot interferometergraphenephase slipsbulk-edge couplingquasiparticle dynamicstelegraph noiseAharonov-Bohm interference
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper reports that in a graphene quantum Hall Fabry-Pérot interferometer, the discrete jumps in the interference phase come from individual quasiparticles entering or leaving the interferometer's bulk, and that the time between these events can reach several minutes. The authors show that this timescale grows rapidly as the magnetic field approaches the plateau center, explaining why some phase slips appear smooth, some noisy, and some sudden. By sweeping different top gates, they distinguish two classes of bulk states: quasiparticles joining a central compressible puddle that couples uniformly to the edge, and quasiparticles trapped at localized defects that couple mainly to the nearest edge segment. The key consequence is that the interferometer phase can serve as a slow, sensitive probe of quasiparticle dynamics, not just an equilibrium property of the state.

Core claim

The central discovery is that the characteristic timescale τ of phase slips is the RC charging time, τ = R·C_bulk, for a quasiparticle to tunnel between the edge and a localized bulk state. In the measured regime this τ rises by nearly an order of magnitude over a 45–60 mT field range, implying effective tunneling resistances above 10^15 Ω and explaining why, at higher fields, individual charging events appear as sudden, seemingly random 'hard' phase slips in quasi-DC transport. Using the multi-gated geometry, the authors introduce a lever-arm protocol: for a bulk puddle, the gate-voltage spacing between phase-slip lines scales inversely with the gate length bordering the interferometer, so

What carries the argument

The central object is the Fabry-Pérot interference phase θ, which responds to the number of bulk quasiparticles N_qp through Coulomb bulk-edge coupling. The key identity is τ = R·C_bulk, the RC time for a quasiparticle to tunnel between edge and bulk through an effective resistance R; this τ sets whether a phase slip appears smooth, noisy, or hard. The discriminating protocol uses capacitive lever arms, measured as the gate-voltage spacing between phase-slip lines, to determine whether a quasiparticle state couples uniformly to all edge gates (a compressible puddle) or predominantly to one nearby gate (a localized defect).

Load-bearing premise

The hard-slip regime is not directly timed; the paper extrapolates a measured order-of-magnitude increase in τ over a 60 mT window to explain why slips appear instantaneous near 4.45 T, so the central claim stands or falls on whether τ really keeps growing to minutes there.

What would settle it

Directly time-resolve the hard-slip regime, for example with fast rf reflectometry or repeated rapid field sweeps, and look for two-state switching with dwell times of seconds to minutes. If the phase jumps occur synchronously with the field sweep, are reproducible from sweep to sweep, or switch faster than the RC model predicts, the slow-quasiparticle interpretation is ruled out. Alternatively, measure τ near 4.2 T at several temperatures: the RC model with tunneling across an incompressible strip predicts thermally activated growth, so a flat temperature dependence would contradict it.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • At ν = -1, the phase-slip timescale τ grows by nearly an order of magnitude over a 45–60 mT range; extrapolating this trend implies effective tunneling resistances above 10^15 Ω, so quasiparticles can remain out of equilibrium for minutes.
  • The lever-arm product ℓ_i·ΔV_i is constant within uncertainty for the puddle scenario at ν = -1, providing a quantitative certification that quasiparticles enter a uniformly coupled bulk puddle rather than random disorder sites.
  • At ν = -2, the phase slip position depends on only one nearby gate, directly showing that localized defect states coexist with puddle charging and can dominate in certain field and density regimes.
  • The same lever-arm protocol can be applied in fractional quantum Hall interferometers to separate Coulomb bulk-edge coupling from anyonic statistics, especially as the bulk puddle shrinks and τ increases.
  • The inferred puddle-edge separation of about 35 nm, larger than the magnetic length, accounts for the measured slow tunneling and predicts that the bulk-edge coupling is strongly screened by nearby gates.

Where Pith is reading between the lines

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

  • If the RC picture is correct, τ should be thermally activated—growing exponentially as the temperature is lowered—because tunneling across the incompressible strip is suppressed by an energy barrier; a temperature-dependence measurement of τ would test this directly.
  • The two-state telegraph noise near charge degeneracy is effectively a single-shot detector of bulk quasiparticle parity; with faster rf reflectometry readout, the same device could sense individual charging events on much shorter timescales, which may matter for non-abelian state experiments.
  • The lever-arm protocol could be developed into a general disorder-mapping tool: by sweeping each gate and recording the field position of each phase slip, one could localize individual traps inside the interferometer and measure their capacitive coupling with sub-micron resolution.
  • If hard slips truly reflect minutes-long stochastic quasiparticle dynamics, repeated identical field sweeps should produce irreproducible slip positions; observing reproducible slips would instead point to deterministic flux jumps or gate instabilities.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper reports transport measurements of a monolayer-graphene Fabry-Pérot interferometer in the integer quantum Hall regime at ν = -1 and ν = -2. The authors observe discrete phase slips in the interference pattern and interpret them as the addition/removal of single quasiparticles to the interferometer bulk. They identify a crossover from 'soft' to 'noisy' to 'hard' phase slips as the magnetic field approaches the plateau center. In the noisy regime, two-state telegraph noise is used to extract a quasiparticle switching time τ that grows rapidly with field. In the hard-slip regime, the authors infer that τ becomes much longer than the trace time, producing apparently instantaneous, irreversible jumps. A multi-gate lever-arm analysis is used to argue that in one regime quasiparticles enter a central compressible puddle, while in another regime they occupy a defect site close to one edge. The paper proposes that interferometry can probe quasiparticle dynamics through the time dependence of bulk occupancy, and suggests implications for future fractional quantum Hall experiments.

Significance. If the central dynamical interpretation holds, the paper offers a new and useful probe: time-resolved phase-slip measurements as a way to access quasiparticle equilibration dynamics in quantum Hall interferometers, and a practical gate-lever-arm protocol to distinguish bulk puddles from localized defect states. The reported data are of high quality in the noisy regime: the dwell-time histograms in Fig. S4 directly show exponential two-state switching, and the near-uniform magnitude of the hard-slip phase jumps (−0.092 ± 0.008 in units of 2π) is a clean signature of single-charge addition. The lever-arm protocol is a valuable diagnostic that could transfer to fractional quantum Hall systems. However, the paper's headline claim that equilibration times 'can become as long as several minutes' is inferred rather than measured, and this gap weakens the dynamical narrative as currently written. The puddle-vs-defect distinction, though plausible, rests on a consistency test with broad uncertainties.

major comments (3)
  1. [Abstract and §2 (Fig. 2f, Fig. 2c)] The claim that the equilibration time 'can become as long as several minutes' is not directly supported. The τ values in Fig. 2f are measured only over a ~60 mT range near B≈4.2 T, where τ is of order 0.1–1 s; the hard-slip regime of Fig. 2c lies at B≈4.45–4.49 T, outside this range. The text states that the increase in Fig. 2f 'provides a natural explanation' and that τ is then 'much larger than the T≈7s period'—but that is a lower bound τ≳7s, not a measured value of several minutes. The hard-slip traces alone cannot exclude reproducible threshold crossings or bistable impurity/gate/magnet processes with unrelated switching statistics. Please provide direct time-domain traces in the hard-slip regime (or repeated sweeps with timestamps) and report the actual waiting-time distribution, or revise the abstract and conclusion to state the measured lower bound rather than 'several minutes.'
  2. [§3, Fig. 3c-e] The puddle-vs-defect conclusion rests on the product ℓ_i ΔV_i being constant: {0.77±0.26, 0.68±0.22, 1.04±0.33} µm·V. These values agree within 1σ but carry 30–50% uncertainties, so the data are consistent with a single uniformly coupled puddle but do not strongly establish it. A central defect or multiple defects could also roughly satisfy this weak test. Please report the lever-arm values with a fuller uncertainty analysis (including correlated errors from the slope fits) and, if possible, compare the measured ratios to an electrostatic model prediction. Alternatively, soften the wording from 'consistent with' to 'not ruled out by this test.'
  3. [SI, 'Estimation of KIL' and §2 (puddle-edge separation)] The estimate w≈35 nm is obtained by inserting the measured KIL (derived from δθ via the Halperin–Stern–Neder–Rosenow charging model) into the SI electrostatic model, and is then used to argue that tunneling is suppressed and hence τ is long. This is a self-consistency check, not an independent measurement. The inferred puddle-edge separation therefore carries the assumptions of a uniform puddle, screening by the gates, and the validity of the KIL parametrization. Please present this explicitly as a model inference and discuss its sensitivity to uncertainties in d, ϵ_z, ϵ_xy, and KIL.
minor comments (6)
  1. [Conclusion] Typo: 'localaization of the bulk states' should be 'localization.'
  2. [Conclusion] Typo: 'diambiguate' should be 'disambiguate.'
  3. [SI, source-drain analysis] The text contains an unresolved reference 'Fig. ??a' in the paragraph discussing common-mode period; please fix.
  4. [Fig. 2f caption] The error bar is defined as |τ12−τ21|; please clarify whether this is intended as a standard error, and note that the asymmetry between τ12 and τ21 is itself a detuning indicator.
  5. [Fig. 4 caption and text] The insets are said to mark the inferred quasiparticle location with an 'x,' but the mark is not visible in the printed figure; please make it explicit.
  6. [Abstract/§2] The abstract asserts 'the equilibration time can become as long as several minutes' before the operational definition of equilibration time and its measurement window are introduced; consider rewording to match the actual data range.

Circularity Check

0 steps flagged

No significant circularity: phase-slip magnitudes, time-domain switching rates, and gate-lever-arm slopes are measured inputs; the bulk-edge-coupling model only interprets them.

full rationale

The derivation chain is measurement-driven rather than circular. Phase slip magnitudes are measured directly (Fig. 2g: eight jumps with mean δθ/2π = -0.092, s.d. 0.008); τ is extracted from time-domain telegraph noise (Fig. 2e/f) rather than from the hard-slip behavior it is invoked to explain; and the lever-arm test (Fig. 3) independently distinguishes a central compressible puddle from a localized defect by comparing phase-slip slopes ΔVi to gate lengths ℓi. The quantity KIL is obtained by applying the external Halperin–Stern–Neder–Rosenow theory (ref 8) to the measured δθ via KIL = KI·δθ/(2π), and the 35 nm puddle-edge separation is then an inversion of the SI electrostatics model using that KIL. This is a model-dependent interpretation, not a circular reduction: the input is δθ and the output is w, with no quantity defined in terms of the other. Self-citations (refs 17, 26, 28) appear only in broad citation lists or for fabrication/example details and are not load-bearing. One non-circular weakness should be noted: the hard-slip τ is not directly measured at B ≈ 4.45 T; the text says the Fig. 2f increase 'provides a natural explanation' and only bounds τ by the T ≈ 7 s trace period, so the abstract's 'several minutes' is an extrapolation. That is a robustness concern, not circularity.

Axiom & Free-Parameter Ledger

2 free parameters · 5 axioms · 0 invented entities

The central claims rest on standard quantum Hall interferometry and bulk-edge coupling theory plus measured device parameters. No new entities are postulated. The puddle-edge separation w is the only fitted quantity that is then used as an output; the RC resistance is derived from measured τ with an assumed capacitance.

free parameters (2)
  • puddle-edge separation w = 35 nm
    Inferred from the measured phase-slip magnitude via the half-plane model in SI Eq. (4); not independently measured.
  • effective RC resistance R = >1e15 ohm (when τ > 1 s)
    Inferred from measured τ using τ = R Cbulk with Cbulk ≈ 1 fF estimated from geometry. The capacitance is an input, not measured.
axioms (5)
  • domain assumption Phase slips follow the Halperin-Stern-Neder-Rosenow bulk-edge coupling energy E = KI δnI^2/2 + KL δnL^2/2 + KIL δnI δnL, with slip magnitude δθ = ±2π KIL/KI.
    Used in main text Eq. (2) and to convert the measured δθ to KIL. Standard theory, cited as ref 8.
  • domain assumption Quasiparticle charging obeys an RC circuit model τ = R Cbulk with Cbulk ≈ 1 fF estimated from geometry.
    Used to translate measured switching times into an effective resistance and to motivate the soft/hard interpretation. Stated in main text around Fig. 2f.
  • domain assumption The compressible puddle can be modeled as an infinite half-plane of uniform charge with hBN dielectric constants ϵz = 3.25, ϵxy = 6.6.
    Used in SI to estimate KIL and the puddle-edge separation w; the dielectric constants are taken from literature.
  • domain assumption Telegraph noise in the transmitted current is a two-state Markov process with a single characteristic time at charge degeneracy.
    Used in SI Fig. S4 to extract τ from dwell-time histograms.
  • standard math The Aharonov-Bohm phase relation θ/(2π) = AI B/Φ0 holds with fixed interference area per gate voltage.
    Defines the background phase; cited ref 1.

reviewed 2026-08-04 · how reviews work

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Cite this review

Pith. "Pith review of Hard and soft phase slips in a Fabry-P\'erot quantum Hall interferometer." pith.science (2026). https://pith.science/paper/67LP56JY

@misc{pith2026250909901,
  author       = {Pith},
  title        = {Pith review of: Hard and soft phase slips in a Fabry-P\'erot quantum Hall interferometer},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/67LP56JY}},
  note         = {Machine review of arXiv:2509.09901}
}
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read the original abstract

Quantum Hall Fabry-P\'erot interferometers are sensitive to the properties of bulk quasiparticles enclosed by the interferometer loop, with the interference phase containing information about both the quasiparticle statistics and the Coulomb-mediated bulk-edge coupling. Previous studies have explored the role of the bulk-edge coupling in an equilibrium picture where quasiparticles enter and exit the interferometer rapidly compared to the timescale over which the interferometer phase is measured. Here, we present data from a monolayer graphene quantum Hall interferometer in the integer quantum Hall regime at $\nu = -1$ and $\nu = -2$. Quantum interference shows phase slips associated with the entrance of quasiparticles to the interferometer bulk. Tracing the dependence of these phase slips on the magnetic field, we show that the equilibration time can become as long as several minutes. We further use our multi-gated geometry to identify two classes of phase slips. The first is associated with the addition of a quasiparticle to a bulk `puddle' of quasiparticles uniformly coupled to the entire chiral edge state, while the second is associated with the addition of a quasiparticle trapped by a defect site that couples predominantly to the closest portion of the edge.

Figures

Figures reproduced from arXiv: 2509.09901 by A. F. Young, K. Watanabe, L. A. Cohen, M. P. Zaletel, N. L. Samuelson, S. Blanch, T. Taniguchi, W. Wang.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: a shows an interference plot acquired for ν = −1. Since ∂AI /∂VP < 0 for ν = −1, we orient 2(a-c) to be right- [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

discussion (0)

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Reference graph

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.