Coherent Bunching of Anyons and their Dissociation in Interference Experiments

Bikash Ghosh; David F. Mross; Maria Labendik; Moty Heiblum; Vladimir Umansky

REVIEW 3 major objections 5 minor 1 cited by

Coherent Bunching of Anyons and their Dissociation in Interference Experiments

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read At filling factors 2/3, 3/5, and 4/7, a chiral interferometer measures flux periods set by the bulk filling ν, implying that bunched quasiparticles, not elementary ones, carry the interference.

desk verdict A likely real experimental effect in FQH interferometry whose interpretation as charge-bunched anyons is not yet nailed down; the dissociation claim rests on an unverified fixed-area conversion. read the letter →

arxiv 2412.16316 v2 pith:VM4NYVOQ submitted 2024-12-20 cond-mat.mes-hall

Bikash Ghosh , Maria Labendik , Vladimir Umansky , Moty Heiblum , David F. Mross This is my paper · ORCID

classification cond-mat.mes-hall PACS 73.43.-f72.70.+m73.23.-b

keywords fractionalquantumHalleffectAharonov-BohminterferenceanyonsquasiparticlebunchingFanofactorMach-Zehnderinterferometerparticle-holeconjugatestatestop-gatedissociation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper reports that in a chiral Mach-Zehnder interferometer at the fractional quantum Hall fillings $\nu=2/3$, $3/5$, and $4/7$, the Aharonov-Bohm flux period is $\Delta\Phi=\Phi_0/\nu$ rather than $\Delta\Phi=(e/e^*)\Phi_0$, and the shot-noise Fano factor at a single point contact (the inferred charge of the partitioned particles) is $F=\nu$ rather than $F=e^*/e$. Because independent elementary quasiparticles would give both quantities in terms of the elementary charge $e^*$, the authors conclude that coherent bunches of two, three, or four elementary quasiparticles, carrying charge $e_b=\nu e$ each, are the objects that tunnel and interfere. Charging a small top gate in the interferometer bulk dissociates the bunches and restores the elementary-charge flux period, while the Fano factor stays at $\nu$, which the authors attribute to neutral edge modes adding incoherent noise. The two observations, bunching and dissociation, are not expected by current theory, and the authors suggest the same physics may appear in other fractional quantum Hall states at lower temperatures.

What carries the argument

The load-bearing object is the bunched quasiparticle, defined operationally by the identity $\Delta\Phi=\Phi_0/F$: the flux period and the Fano factor are consistent only with a tunneling charge $e_b=\nu e$, i.e., a Laughlin quasiparticle comprising two, three, or four elementary anyons. The device that exposes it is the optical Mach-Zehnder interferometer (OMZI), whose two point contacts partition co-propagating edge modes so that all incoming charge must pass through the interference loop, producing clean Aharonov-Bohm 'pajama' patterns. The top gate is the control knob: left uncharged it leaves the bunches intact, and charged it forms a dot or antidot whose local quasiparticles dissociate the bunches and change the flux period without changing the point-contact noise. Neutral edge modes serve as the auxiliary mechanism invoked to keep $F=\nu$ in the dissociated regime.

What would settle it

Measure the same three fillings with a second interferometer of a different known area, or with an in-situ tunable area: if the periods are truly flux periods $\Phi_0/\nu$ and $(e/e^*)\Phi_0$, the magnetic-field period must scale inversely with the enclosed area; if it does not, the fixed-area conversion is the source of the apparent effect. A second, complementary check is to sweep temperature through the range where earlier work saw $F$ change from $\nu$ to $e^*/e$: the bunched periodicity should disappear in the same temperature window.

Watch

Extended reading notes

Core claim

The paper's central claim is that the objects that tunnel and interfere in these particle-hole-conjugated states are Laughlin quasiparticles of charge $e_b=\nu e$, not the elementary quasiparticles of charge $e^*=e/3$, $e/5$, or $e/7$. The evidence is the joint pattern $\Delta\Phi=\Phi_0/\nu$ and $F=\nu$ with the top gate uncharged, which satisfies $\Delta\Phi=\Phi_0/F$ exactly as if a single object of charge $\nu e$ carried the current. When the top gate is charged to form a dot or antidot, the flux period jumps to $\Delta\Phi=(e/e^*)\Phi_0$, the value fixed by the elementary quasiparticles, while $F$ stays at $\nu$; the authors read this as dissociation of the bunches, with neutral modes supplying the extra noise so that the Fano factor no longer tracks the interfering charge. The dissociation is not all-or-nothing: at intermediate top-gate voltages the two periodicities coexist, and at $\nu=3/5$ the system evolves continuously from bunched to dissociated and back as the gate voltage is swept.

Load-bearing premise

The analysis converts every measured magnetic-field period into a flux period using a fixed enclosed area of $3\,\mu\mathrm{m}^2$, and assumes the Aharonov-Bohm phase is accumulated solely by the tunneling charge with no contribution from anyonic statistical phase or from quasiparticles under the top gate.

Editorial extensions

If this is right

With no top-gate charge, the relationship $\Delta\Phi=\Phi_0/F$ identifies the interfering charge as $\nu e$, so AB periodicity alone cannot be used to read off the elementary charge $e^*$ in these states at low temperature.
A single local gate can switch the interferometer between a bunched regime and a dissociated regime, giving experimental control over which quasiparticle species sets the interference period.
In the dissociated regime the Fano factor no longer tracks the interfering charge, showing that shot noise and AB periodicity can disagree when neutral modes contribute, a combination that any complete theory of these edges must reproduce.
The same low-temperature bunching should appear in Jain particle states and in even-denominator fractional quantum Hall states, with correspondingly modified flux periods.
Braiding experiments in non-Abelian states will need to account for the fact that the coherently interfering object can be a Laughlin quasiparticle, which is Abelian, even when elementary quasiparticles of the state are not.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper: if bunching is generic, previous interferometric determinations of fractional charge that operated near the same temperatures may have actually measured $\nu e$ rather than $e^*$; re-examining those datasets for the $\Phi_0/\nu$ period would test this.
Beyond the paper: the dissociation threshold should depend on the top gate's area and on the density of localized quasiparticles it creates; a systematic sweep of dot size and gate voltage could distinguish a number-fluctuation mechanism from a direct electrostatic effect on the bunches.
Beyond the paper: a testable prediction is that lengthening the interferometer arms, or equilibrating the edges, should change the neutral-mode contribution and therefore reduce $F$ toward $e^*/e$ in the dissociated regime while leaving the flux period unchanged.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

First thing to know: this is a genuinely new experimental observation, not a rehash. Prior shot-noise-only works already measured F=ν at these fillings; what's new is the AB flux period Φ0/ν with the top gate uncharged and the gate-controlled crossover back to (e*/e)Φ0. The agreement between period and Fano factor at V_TG=0, plus the edge-mode control, makes the bunched-charge interpretation there reasonably credible. Data are public, two devices, real value.

The dissociation claim is where I get less comfortable. Charging the top gate changes the period to (e/e*)Φ0, and the ratio is exactly the factor q=ν/(e*/e) (2, 3, 4). A top gate that shrinks the effective interference area by the same factor q would produce the same period change while the interfering charge stays νe. The top gate sits at the center of the interferometer and is used to form an antidot/dot, so a change in effective loop area is not a contrived alternative. The modulation-gate periodicity is the diagnostic that would separate area from charge, but in the dissociated regime at ν=3/5 and 4/7 it disagrees with the fixed-area charge-change prediction, and the paper says this is not understood. That is a load-bearing soft spot, not a cosmetic one.

Also, in the dissociated regime the Fano factor remains F=ν while the AB period says e*. The authors explain this via neutral modes, but the neutral-mode contribution was not measured in this setup. They say so themselves. The relation ΔΦ=Φ0/F, which works at V_TG=0, is violated after charging, so the two measurements no longer point to the same charge.

To be fair: the paper flags all of this. It does not hide the missing pieces, and the fixed-area assumption is explicit. The gate-controlled crossover in Fig. 5 is interesting, and the one-by-one dissociation is a nice check. I just would not sign on to the coherent-bunched-anyons conclusion as established.

Who should read it: anyone working on FQH interferometry or quasiparticle charge. It deserves a serious referee; the experimental result is likely real, and the interpretation has holes that referees can push on. My own verdict would be conditional: publish after the area alternative is addressed, or with the interpretation softened. I'd cite the data, but not the strong claim.

Referee Report

3 major / 5 minor

Summary. The manuscript reports Aharonov-Bohm (AB) interference and shot-noise measurements in a chiral Mach-Zehnder interferometer at the fractional quantum Hall fillings ν=2/3, 3/5, and 4/7. With the top gate uncharged, the authors observe magnetic flux periodicities ΔΦ=Φ0/ν and single-QPC Fano factors F=ν, which they interpret as coherent tunneling and interference of bunched quasiparticles with charge νe. When the top gate is charged, the AB periodicity changes to ΔΦ=(e/e*)Φ0, which they interpret as dissociation into elementary quasiparticles, while the Fano factor remains F=ν. The paper states that these two observations are not expected by current theories and discusses possible implications for other fractional quantum Hall states.

Significance. If the interpretation holds, the results would establish that the interfering quasiparticle charge in a fractional quantum Hall interferometer can be set by the bulk filling rather than by the elementary fractional charge, and that a local gate can switch between the two regimes. The manuscript provides public data, uses two devices, and includes useful controls such as different edge-mode configurations (Supp. S7) and a second smaller top-gate device (Supp. S11). However, the load-bearing conversion from magnetic-field periods to flux periods rests on a fixed loop area that is not independently verified in the dissociated regime, and the Fano-factor behavior in that regime is not fully consistent with the proposed picture. The strength of the evidence is therefore currently insufficient for the strongest claims made in the title and abstract.

major comments (3)

[Paragraph beginning 'Next, we charged the top gate...' and the paragraph beginning 'The modulation gate voltage…] The central dissociation claim depends on converting every magnetic-field period into a flux period using the fixed geometric area A=3 µm². If charging the top gate shrinks the effective loop area by the factor q=ν/(e*/e), the same period change would be observed with the quasiparticle charge unchanged; for ν=4/7 the required area of roughly 0.75 µm² is close to the top-gate area, making this a concrete alternative. The modulation-gate data provide an internal check, but they contradict the fixed-area charge-change prediction: in the dissociated regime the observed ΔVMG values at ν=3/5 and 4/7 are 17.4 mV and 15.5 mV, whereas scaling the bunched-regime values (10.3 mV and 9.5 mV) by q=3 and 4 predicts approximately 30.9 mV and 38 mV. The authors state this discrepancy is not understood. As written, the dissociation evidence is therefore not distinguished from a gate-induced area change, and the conclusion that the AB periodicity changes because the quasiparticle charge changes is not independently supported.
[Paragraph beginning 'The present experiment focused on the low-temperature regime...' and Supp. S6] The Fano factor in the dissociated regime remains F=ν while the AB periodicity corresponds to the elementary charge e*, and the paper appeals to neutral modes to reconcile this. The manuscript itself notes that intermediate transmission plateaus were not observed in the OMZI's QPCs, so the neutral-mode contribution was not established. The sentence 'the agreement between the Fano factor and AB periodicity through the relation ΔΦ≈Φ0/F at VTG=0 strongly suggests an incoherent origin of the increased Fano factor (due to neutral modes)' is internally inconsistent: if the Fano factor had an incoherent neutral-mode origin, it would not determine the AB periodicity. The authors should clarify this argument and provide additional evidence, such as the VTG dependence of F measured in the full interferometer, before concluding that the tunneling charge changes while the Fano factor does not.
[Paragraph beginning 'Our observations present a new paradigm...' and the Conclusions] The interpretation of the data as coherent bunched quasiparticles of charge νe assumes that the AB phase is accumulated solely by the charge of the interfering quasiparticle, with no contribution from anyonic statistical phases or from bulk quasiparticles beneath the top gate. The paper notes that localized quasiparticles are expected to produce phase slips, yet none were observed in these particle-hole conjugated states. This absence, together with the unexplained modulation-gate behavior, leaves the proposed bunching/dissociation picture without a quantitative theoretical account. The authors should either provide a more detailed model for the observed periodicities or explicitly frame the result as an empirical observation that challenges current theories, rather than as a demonstrated property of bunched anyons.

minor comments (5)

[Throughout] The notation for the flux quantum is inconsistent: the abstract and figure captions use Φ0, while the main text frequently uses F0. Please unify the notation.
[Paragraph following Fig. 3] The derivation of the modulation-gate periodicity is difficult to follow; the relation ΔVMG×nb×B=Φ0×P should be defined more carefully, with every symbol (including the parameter P) introduced and its physical meaning stated.
[Fig. 1 and main text] The term 'pajama' is used for the AB interference pattern without definition; a brief explanation would make the paper more accessible to readers outside the immediate group.
[Methods / device parameters] In the sentence 'the top gates radia are 0.5 µm (OMZI1) and 0.35µm (OMZI2)', 'radia' should be 'radii'.
[Supp. S6] The note that 'the noise of the entire interferometer does not follow a simple relationship to the QP charge' is an important caveat and should be stated in the main text rather than only in the supplement.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the interference periodicity and the Fano factor are independent measurements connected by the standard AB relation, not by a fitted input.

full rationale

The paper's central claims rest on two independent measurements: (i) the AB interference period in the B-VMG plane, converted to a flux period via the fabricated area A=3 µm2, and (ii) the shot-noise Fano factor F measured at a single QPC. The inference of a bunched quasiparticle charge e_b=νe uses the standard Aharonov-Bohm relation ΔΦ=Φ0/q, which is not an input fitted to the data; the Fano factor independently gives F=ν. No equation in the paper defines the bunch charge in terms of the observed period or vice versa beyond the standard physical relation. The dissociation claim is based on a measured change of the magnetic-field periodicity when the top gate is charged, and the paper openly reports that the corresponding modulation-gate periodicities at ν=3/5 and 4/7 are not understood, which is an unresolved consistency issue rather than a circular step. The paper cites prior work by the same group (Ref. 16 for the OMZI architecture and particle-state baseline, Ref. 30 for neutral-mode shot-noise theory), but these are independent published results on different fillings or a separate theoretical model; the load-bearing observations in this paper are newly measured data, and no uniqueness theorem or ansatz is imported from those citations to force the conclusion. The admitted limitation that neutral-mode contributions were not established (Supp. S6) and the unexplained modulation-gate anomaly weaken the interpretation but do not make the derivation equivalent to its inputs. Accordingly, no circular step is identified.

Assumptions & free parameters 3 free parameters · 5 assumptions · 1 invented entities

The central claim depends on the standard AB-to-charge mapping and on the identification of the measured Fano factor with the tunneling charge. The first is conventional, the second is explicitly uncertain in the dissociated regime. The modulation-gate capacitance constancy is the least supported premise, and the data themselves show it fails in one regime.

free parameters (3)

Fano factor F = 2/3, 3/5, 4/7 (one per bulk filling)
Extracted by fitting the excess noise versus current (Fig. 2); used as an independent charge meter to support the bunching interpretation.
Electron temperature T = 13 ± 2 mK (calibrated; also a fit parameter in noise curves)
Entered in the shot-noise fitting formula alongside F; uncertainty in T affects the Fano factor extraction.
Modulation-gate capacitance C = Inferred from ΔVMG and B periodicity, not stated independently
Assumed independent of bulk filling and top-gate voltage when converting ΔVMG to ΔΦ; the dissociated-regime data at ν=3/5 and 4/7 violate the expected scaling, so this parameter's constancy is load-bearing and unverified.

assumptions (5)

domain assumption AB flux period is set by the charge q of the interfering quasiparticle via ΔΦ=Φ0/(q/e).
Invoked throughout to convert measured B or VMG periodicities into quasiparticle charge; this is the standard working assumption for these interferometers and is not independently calibrated here.
domain assumption The elementary quasiparticle charge at bulk filling ν is e*=e/3 for ν=2/3, e/5 for ν=3/5, e/7 for ν=4/7.
Used to define the conventional period that the dissociated regime recovers; standard fractional quantum Hall hierarchy result.
domain assumption The Fano factor measured at a QPC equals the partitioned charge when neutral modes do not contribute.
Needed for F=ν to support charge νe. The paper cites Ref. 30 to argue this can fail and explicitly states the neutral-mode contribution was not established in these measurements.
domain assumption The modulation-gate capacitance C is independent of bulk filling and top-gate voltage.
Used to derive expected ΔVMG periodicity; the observed dissociated-regime behavior at ν=3/5 and 4/7 is inconsistent with this assumption and is left unexplained in the text.
standard math K-matrix edge formalism correctly describes which quasiparticles excite neutral modes.
Used in Supp. S12 to argue Laughlin quasiparticles (charge νe) do not excite neutral modes, supporting the neutral-mode explanation for the Fano factor.

invented entities (1)

Coherently bunched quasiparticle (pair, triplet, or quadruplet of elementary QPs with total charge νe) independent evidence
purpose: Explains the AB flux period ΔΦ=Φ0/ν and the Fano factor F=ν at VTG=0 in particle-hole conjugated states.
The paper predicts the same bunching should appear in particle-like Jain states at lower temperatures, a falsifiable consequence outside the current measurements. Within this paper, the entity is inferred from the periodicity and noise rather than directly detected.

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Pith. "Pith review of Coherent Bunching of Anyons and their Dissociation in Interference Experiments." pith.science (2026). https://pith.science/paper/VM4NYVOQ

@misc{pith2026241216316,
  author       = {Pith},
  title        = {Pith review of: Coherent Bunching of Anyons and their Dissociation in Interference Experiments},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VM4NYVOQ}},
  note         = {Machine review of arXiv:2412.16316}
}

abstract

Aharonov-Bohm (AB) interference of fractional quasiparticles in the quantum Hall Effect generally reveals their elementary charge ($e^*$)[1-15]. Recently, our interferometry experiments with several particle states reported flux periods of ${\Delta}{\Phi}=(e/e^*){\Phi}_0$ the flux quantum) at moderate temperatures[16]. Here, we report interference measurements of particle-hole conjugated states at filling factor ${\nu}=2/3, 3/5, 4/7$, revealing unexpected flux periodicities of ${\Delta}{\Phi}={\Phi}_0/{\nu}$. The measured shot noise Fano factor (F) of the partitioned quasiparticles in each of the interferometers quantum point contacts (QPCs), was found to be, $F={\nu}$[17], and not that of the elementary charge, $F=e^*/e$[18,19]. These observations point to interference of bunched (clustered) elementary quasiparticles as coherent pairs, triples, and quadruplets, respectively. A small metallic gate (top gate, TG), deposited in the center of the interferometer bulk, forming an antidot (or a dot) when charged, thus introducing local quasiparticles at the (anti)dots perimeter. Surprisingly, such charging led to a dissociation of the bunched quasiparticles and thus recovered the conventional flux periodicity set by the elementary quasiparticles charge. However, the shot noise Fano factor (of each QPC) consistently remained at $F={\nu}$, possibly due to the neutral modes accompanied the conjugated states. The two observations - bunching and debunching (or dissociation) - are not expected by current theories. Similar effects may likely arise in Jains particle states (at lower temperatures) and at even denominator FQH states[20]

Figures

Figures reproduced from arXiv: 2412.16316 by the authors.

**Figure 1.** Device structure of an optical Mach-Zehnder interferometer (OMZI). (a) Schematic representation of the OMZI. Its structure is based on three regions, each tuned to a different filling factor. The central region (the bulk, dark gray) is tuned by the magnetic field B to the filling nb. It is flanked by two boundary regions, each tuned to different filling via the applied voltage to two wide metallic gates. The upper g… view at source ↗

**Figure 2.** Shot noise measured in a single QPC of the OMZI. Noise measured at three ‘particle-hole conjugated’ states with bulk fillings: (a) n=2/3, (b) n=3/5, (c) n=4/7. Top panels: Nonlinear transmissions of the QPC. Bottom panels: Excess noise as a function of the sourced current. The blue lines represent the fitted curves and the Fano factor, F. The pink lines correspond to F=nb, and the purple lines correspond to F=e*/e … view at source ↗

**Figure 3.** Evidence of coherent bunching of anyons in particle-hole conjugated states. Aharonov-Bohm (AB) interference (pajamas) of the measured three states, plotted as a function of magnetic field B and modulation gate voltage VMG. Each of the two QPCs is tuned to transmission, t1=t2=0.8, while the top gate (TG) is not charged. The pajamas and the corresponding 2D Fast Fourier Transforms (FFTs) relate to the states: (a, b) n… view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Evidence of coherent dissociation of bunched anyons in ‘particle-hole conjugated’ states. Activating the top gate with VTG=-(100-120)mV forms an antidot that harbors isolated quasiparticles. An apparent dissociation of the bunched anyons takes place. Figures (a), (c), …

**Figure 5.** Figure 5: Evolution of the dissociated anyons with charging the top gate at nb=2/3 and 3/5. The top gate (TG) was incrementally charged within different VTG ranges. For nb=2/3, VTG was varied from -150 mV to +60 mV, while for nb=3/5, the VTG incremented in steps of DVTG=5mV with…

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Entropy of Non-Abelian Anyons from Slow Quasiparticle Dynamics in Quantum Hall Interferometers
cond-mat.mes-hall 2026-07 unverdicted novelty 6.5 of 10

Proposes using time-dependent phase switching in quantum Hall interferometers to perform non-local charge measurements that extract the O(1) entropy of non-Abelian anyons at intermediate temperatures.

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages · cited by 1 Pith paper

[1]

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

work page 1994
[2]

Quantum Field Theory of Many-body Systems, Xiao-Gang Wen (Oxford Graduate, 2004)

work page 2004
[5]

239−"23/0.1!:. Here, I is the impinging current, t is the transmission (ra,o between the transmibed and impinging currents) of the QPC, 𝑅4 =!5

Evolution of the dissociated anyons with charging the top gate at nb=2/3 and 3/5. The top gate (TG) was incrementally charged within different VTG ranges. For nb=2/3, VTG was varied from -150 mV to +60 mV, while for nb=3/5, the VTG incremented in steps of DVTG=5mV within the range (0-70)mV and the AB pajamas in the B-VMG plane were recorded at each step. ...

work page
[20]

Firstly, we expect the flux periodicity to change at low temperatures. Secondly, tracking the previously observed phase slips in the low-temperature regime may provide additional vital insights into bunching, dissociation, and how they are influenced by adding localized QPs (at will) into the bulk of the interferometer. Control over the interfering quasip...

work page arXiv 2009

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Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

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

work page 1994

[2] [2]

Quantum Field Theory of Many-body Systems, Xiao-Gang Wen (Oxford Graduate, 2004)

work page 2004

[3] [5]

239−"23/0.1!:. Here, I is the impinging current, t is the transmission (ra,o between the transmibed and impinging currents) of the QPC, 𝑅4 =!5

Evolution of the dissociated anyons with charging the top gate at nb=2/3 and 3/5. The top gate (TG) was incrementally charged within different VTG ranges. For nb=2/3, VTG was varied from -150 mV to +60 mV, while for nb=3/5, the VTG incremented in steps of DVTG=5mV within the range (0-70)mV and the AB pajamas in the B-VMG plane were recorded at each step. ...

work page

[4] [20]

Firstly, we expect the flux periodicity to change at low temperatures. Secondly, tracking the previously observed phase slips in the low-temperature regime may provide additional vital insights into bunching, dissociation, and how they are influenced by adding localized QPs (at will) into the bulk of the interferometer. Control over the interfering quasip...

work page arXiv 2009