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arxiv: 1907.00532 · v3 · pith:5QTURMJ4new · submitted 2019-07-01 · ❄️ cond-mat.mes-hall

Negative Excess Shot Noise by Anyon Braiding

Byeongmok Lee , Cheolhee Han , H.-S. Sim This is my paper

Pith reviewed 2026-05-25 12:16 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords anyon braidingnegative excess noisefractional quantum Hallquantum point contactAbelian statisticsshot noise
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0 comments X

The pith

Anyon braiding at a quantum point contact reduces autocorrelation noise below thermal equilibrium by 2 e^* I at large voltages.

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

The paper predicts that when anyons are dilutely injected from an additional biased edge into a fractional quantum Hall setup containing a quantum point contact, the measured autocorrelation noise falls below the thermal equilibrium value. The amount of the reduction is 2 e^* I. This negative excess noise arises because a thermally excited anyon at the contact braids around an injected anyon, encoding the fractional statistics of Abelian anyons. A sympathetic reader would care because the effect is opposite in sign to the positive excess noise used in conventional fractional-charge detection and supplies a distinct experimental signature of anyonic statistics.

Core claim

The autocorrelation noise of the electrical tunneling current I at the QPC, when anyons are dilutely injected from an additional edge biased by a voltage into the equilibrium setup, is reduced below the thermal equilibrium noise by the value 2 e^* I at large voltages. This negative excess noise is a signature of the Abelian fractional statistics, resulting from the effective braiding of an anyon thermally excited at the QPC around another anyon injected from the additional edge.

What carries the argument

Effective braiding of anyons at the quantum point contact, in which the statistical phase acquired when one anyon encircles another converts directly into a negative contribution to the noise autocorrelation.

If this is right

  • The negative excess noise is opposite in sign to the positive excess noise 2 e^* I of conventional fractional-charge detection.
  • The reduction appears specifically under the condition of dilute injection from the additional edge.
  • The sign and magnitude of the excess noise encode the Abelian nature of the fractional statistics.
  • The effect is visible only at large voltages where the injected anyons dominate the nonequilibrium contribution.

Where Pith is reading between the lines

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

  • The same geometry might be adapted to compare noise signatures across different filling factors to map how the statistical angle affects the reduction.
  • If non-Abelian anyons were injected instead, the noise reduction might be replaced by a different functional form that could be tested by changing the edge filling factor.
  • Varying the injection density while keeping voltage fixed would test whether the linear scaling with I survives outside the dilute limit assumed in the derivation.

Load-bearing premise

Dilute anyon injection from the additional edge lets the braiding phase translate into the negative noise term without extra scattering or nonequilibrium processes changing the result.

What would settle it

Measure the noise power spectral density at the QPC while raising the bias voltage on the additional edge and check whether the excess noise equals exactly -2 e^* I at high voltages.

Figures

Figures reproduced from arXiv: 1907.00532 by Byeongmok Lee, Cheolhee Han, H.-S. Sim.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Setup at [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. TVB interference for [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
read the original abstract

Anyonic fractional charges $e^*$ have been detected by autocorrelation shot noise at a quantum point contact (QPC) between two fractional quantum Hall edges. We find that the autocorrelation noise can also show a fingerprint of Abelian anyonic fractional statistics. We predict the noise of electrical tunneling current $I$ at the QPC of the fractional-charge detection setup, when anyons are dilutely injected, from an additional edge biased by a voltage, to the setup in equilibrium. At large voltages, the nonequilibrium noise is {\it reduced} below the thermal equilibrium noise by the value $2 e^* I$. This negative excess noise is opposite to the positive excess noise $2e^* I$ of the conventional fractional-charge detection and also to usual positive autocorrelation noises of electrical currents. This is a signature of the Abelian fractional statistics, resulting from the effective braiding of an anyon thermally excited at the QPC around another anyon injected from the additional edge.

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.

Referee Report

1 major / 0 minor

Summary. The manuscript predicts that in a fractional quantum Hall edge setup with a quantum point contact (QPC), dilutely injecting anyons from an additional voltage-biased edge produces a negative excess autocorrelation noise that saturates to -2e^*I below the equilibrium thermal noise at large bias. This reduction is presented as a direct signature of Abelian anyonic statistics arising from the braiding phase experienced by a thermally excited anyon at the QPC around an injected anyon.

Significance. If the central result holds under the stated conditions, the work supplies a new, statistics-specific noise signature that is opposite in sign to the conventional positive excess noise used for fractional-charge detection. The derivation is grounded in the anyon tunneling model and braiding phase, providing a falsifiable prediction for noise measurements in the fractional quantum Hall regime.

major comments (1)
  1. [Abstract and setup paragraph] Abstract and setup paragraph: the headline saturation to a negative excess of exactly -2e^*I at large voltage is stated to hold “when anyons are dilutely injected,” yet no explicit bound is supplied that relates bias voltage V, tunneling amplitude, and filling factor to guarantee that the mean inter-anyon spacing remains larger than the QPC size or coherence length in the V→∞ limit. Because the injection rate scales with I, violation of diluteness would allow multiple braidings or non-equilibrium corrections that could cancel or reverse the claimed negative term; this assumption is load-bearing for the large-V claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and the constructive comment on the diluteness assumption. We address the point below and will revise the manuscript to strengthen the justification of the large-voltage limit.

read point-by-point responses

  1. Referee: [Abstract and setup paragraph] Abstract and setup paragraph: the headline saturation to a negative excess of exactly -2e^*I at large voltage is stated to hold “when anyons are dilutely injected,” yet no explicit bound is supplied that relates bias voltage V, tunneling amplitude, and filling factor to guarantee that the mean inter-anyon spacing remains larger than the QPC size or coherence length in the V→∞ limit. Because the injection rate scales with I, violation of diluteness would allow multiple braidings or non-equilibrium corrections that could cancel or reverse the claimed negative term; this assumption is load-bearing for the large-V claim.

    Authors: We agree that the diluteness condition is load-bearing for the saturation result and that an explicit bound relating V, tunneling amplitude, and filling factor would make the large-V claim more rigorous. In the revised manuscript we will add a dedicated paragraph in the setup section deriving the required inequality: the mean inter-anyon spacing (set by the anyon velocity and the injection rate from the additional edge) must exceed both the QPC size and the coherence length. The injection rate scales with the bias voltage on the additional edge (denoted I_inj in the new text to distinguish it from the QPC tunneling current I); the resulting bound will be expressed in terms of V, the tunneling amplitude at the injector, and the filling factor. For sufficiently weak tunneling the condition remains satisfiable even as V increases, thereby excluding multiple-braiding and non-equilibrium corrections within the stated regime. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The derivation starts from the standard anyon tunneling Hamiltonian at the QPC and computes the noise correlator by incorporating the Abelian braiding phase acquired when a thermally excited anyon encircles an injected anyon from the biased edge. The negative excess term -2e^*I emerges directly as the large-bias limit of that phase factor in the current-noise expression, without any parameter being fitted to the target noise value itself and without the central result being presupposed by a self-citation or by re-labeling an input. The dilute-injection condition is stated as an explicit modeling assumption rather than derived from the noise formula, so the claimed reduction does not reduce to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on standard anyon theory for fractional quantum Hall edges; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Anyons in the fractional quantum Hall regime carry fractional charge e* and obey Abelian braiding statistics
    Invoked to obtain the braiding-induced negative noise term.

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Reference graph

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