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REVIEW 4 major objections 4 minor 47 references

Tunable Inter-Edge Interactions in a Bilayer Graphene Quantum Hall Antidot

T0 review · 4 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A bilayer graphene quantum Hall antidot can be tuned from single-dot to paired-edge double-dot behavior, with a measured tunneling charge of about 2e at even fillings.

desk verdict Promising gate-defined antidot with a real tunable inter-edge crossover, but the 2e pairing claim is arithmetically inconsistent with the paper's own equations and period data. read the letter →

arxiv 2504.16750 v1 pith:EGF3QPMJ submitted 2025-04-23 cond-mat.mes-hall

Mario Di Luca , Emily Hajigeorgiou , Zekang Zhou , Tengyan Feng , Kenji Watanabe , Takashi Taniguchi , Ferdinand Kuemmeth , Mitali Banerjee This is my paper · ORCID
classification cond-mat.mes-hall
keywords bilayergraphenequantumHallantidotinter-edgeinteractionsCoulombblockadeoscillationsedge-statepairingLandauleveldegeneracyAharonov-Bohminterferencetunnelingcharge
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 a fully gate-defined antidot in bilayer graphene—a potential hill circled by chiral quantum Hall edge states—can be tuned by voltage between two regimes. In the weakly coupled regime the antidot shows ordinary Coulomb-blockade oscillations at integer filling factors, with a gate period set by one electron and a magnetic-field period set by $\phi_0/\nu$. At even fillings, once the antidot couples more strongly to the extended edge, the two innermost Landau-level edges pair up: the tunneling charge doubles to about $2e$ and the flux period follows $1/(\nu(\nu-1))$. The authors interpret this as capacitive inter-edge coupling that can dominate the device response, and they argue the same antidot geometry can be used to study inter-edge interactions in the fractional quantum Hall regime.

What carries the argument

The central object is a capacitive-coupling model for the two innermost chiral edges around the antidot. The energy is $E = \tfrac{1}{2}K_1\delta Q_1^2 + \tfrac{1}{2}K_2\delta Q_2^2 + K_{12}\delta Q_1\delta Q_2$, where $\delta Q_i$ is the charge imbalance on edge $i$, $K_i$ the edge stiffness, and $K_{12}$ the inter-edge coupling, with stability requiring $K_1K_2 > K_{12}^2$. A nonzero $K_{12}$ lengthens both the field and gate periods relative to the single-dot values, giving $q\approx 2e$ and $\Delta B_s = \Delta B/(1 - (K_{12}/K_1)(\nu_1/\nu_2))$. From the measured period enhancement the authors extract $K_{12}/K_1 = 0.72 \pm 0.03$ at $\nu=2$ and $0.54 \pm 0.05$ at $\nu=4$; the flux-period law $\phi_\nu/\phi_0 = 1/(\nu(\nu-1))$ is the paired-edge signature that distinguishes this regime from ordinary Aharonov-Bohm oscillations.

What would settle it

Measure the magnetic-field period of the strong-coupling oscillations at $\nu=6$ in a similar device. The paired-edge model predicts $\phi/\phi_0 = 1/30$; observing the single-dot value $1/6$ (or any period inconsistent with $1/(\nu(\nu-1))$) would falsify the claim. A complementary check is a shot-noise measurement of the effective charge in the $\nu=2$ strong-coupling regime, which should read $2e$ rather than $e$.

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Extended reading notes

Core claim

The central claim is that strong coupling between the two innermost edge states of a bilayer graphene quantum Hall antidot produces a double-dot regime with a measurable doubling of the tunneling charge. In the weakly coupled case, oscillations at $\nu = 1$–$4$ follow the single-edge prescription $\Delta B = \phi_0/(\nu_{\mathrm{int}} A)$ and a gate period corresponding to one electron. In the strongly coupled case at even fillings, the gate period yields $q_{\nu=2}/e = 1.98 \pm 0.18$ and $q_{\nu=4}/e = 2.55 \pm 0.35$, close to two electrons per period, and the flux periods $\phi_{\nu}/\phi_0 = 1.78 \pm 0.56$ ($\nu=2$) and $0.80 \pm 0.11$ ($\nu=4$) agree with $\phi_{\nu}/\phi_0 = 1/(\nu(\nu-1))$. Aharonov-Bohm interference is ruled out because the extracted diameter is too small and because the oscillations are density-driven Coulomb diamonds; the phase slips in the data are instead attributed to two capacitively coupled edge states, analogous to coupled islands seen in earlier scanning-tunneling experiments.

Load-bearing premise

The paired-edge interpretation relies on the underived flux-period law $\phi_\nu/\phi_0 = 1/(\nu(\nu-1))$ and on the assumption that the top gate couples mainly to the inner edge; if either premise fails, the measured periods no longer demonstrate a doubled tunneling charge.

Editorial extensions

If this is right

  • At even integer filling factors, bilayer graphene antidots provide a tunable double-dot system in which the two innermost edges behave as a single correlated object with effective tunneling charge $2e$.
  • Because the inter-edge coupling is controlled by the antidot potential, the same device can be swept continuously from single-dot to double-dot behavior, with a coexistence region where both oscillation modes appear.
  • Inter-edge interactions, not just Aharonov-Bohm phase, can dominate a quantum Hall interferometer's response; measurements in this regime must account for the paired-edge dynamics before extracting interference information.
  • The gate-defined antidot geometry extends naturally to the fractional quantum Hall regime, where interactions between multiple edges are expected to be the central physics that any quasiparticle interferometer must handle.

Reading between the lines

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

  • A sharp test of the paired-edge picture would be to measure the strong-coupling flux period at $\nu=6$: the model predicts $\phi/\phi_0 = 1/30$, an order of magnitude below the single-edge value $1/6$.
  • The double-dot regime may act as a parity detector: if the tunneling charge is truly $2e$, a conductance measurement counts whether an even or odd number of electrons has been added to the coupled pair.
  • A shot-noise measurement of the effective charge in the strongly coupled regime would independently confirm the $2e$ value without relying on the capacitive model's gate-coupling assumptions.
  • Comparing the coupling ratio $K_{12}/K_1$ as a function of displacement field would separate the role of the $N=0/N=1$ orbital degeneracy from purely electrostatic coupling; the model predicts the pairing weakens when the degeneracy is lifted.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper reports a dual gate-defined bilayer graphene antidot operated in the Coulomb-dominated quantum Hall regime. In the weakly coupled regime, the authors observe Coulomb oscillations at integer filling factors ν = 1−4 and extract the expected single-electron tunneling charge and φ0/ν magnetic-field periods. When the antidot potential is tuned deeper, new oscillations with larger periods appear at even filling factors ν = 2 and ν = 4. These are interpreted as a crossover to a strongly coupled double-dot regime in which the two innermost edge states are capacitively coupled. Using Eq. (1) the authors extract an apparent tunneling charge close to 2e, and they propose a flux-period law φνint/φ0 = 1/(νint(νint−1)) that they claim agrees with measured flux periods of 1.78 and 0.80 at ν = 2 and ν = 4. A capacitive model with two coupled edges is presented in the supplementary material, and coupling ratios K12/K1 are extracted from the measured period increases. The qualitative crossover is supported by conductance maps, 2D-FFTs, and Coulomb diamonds, but the quantitative claims of edge-state pairing and the 2e charge contain internal inconsistencies and rely on an underived formula.

Significance. If substantiated, the tunable crossover from single-dot to double-dot behavior in a graphene antidot would be a useful contribution, both as a platform for studying inter-edge interactions and as a step toward fractional quantum Hall interferometry. The experimental work is careful: the device is well characterized, the weakly coupled oscillations are clean, the Coulombs diamonds are shown for multiple filling factors, and the supplementary material contains complementary bottom-gate and area-sweep measurements. The qualitative observation that even filling factors develop larger-period oscillations with phase slips is interesting and consistent with earlier STM studies. However, the central quantitative claims—the doubling of the tunneling charge and the specific flux-period law—are the load-bearing evidence for the double-dot interpretation, and these claims are not internally consistent as presented. The paper's significance would be substantially improved if the model were used to derive the period modifications and the charge, rather than applying the single-edge formula Eq. (1) to the coupled regime.

major comments (4)
  1. [Inter-Edge Coupling, Eq. (1) and Supplementary S4] The reported tunneling charges qν=2/e = 1.98±0.18 and qν=4/e = 2.55±0.35 are inconsistent with Eq. (1) when the stated period increases are inserted. The strong-coupling flux periods are larger than the weak-coupling ones by factors of about 3.6 (ν=2) and 3.2 (ν=4), while the supplementary material (S4) states that the density-oscillation gate period increase is close to 2. Under Eq. (1), q_s/q_w = (ΔV_s/ΔV_w)/(ΔB_s/ΔB_w), which gives roughly 2/3.6 ≈ 0.6 and 2/3.2 ≈ 0.6, not the reported doubling. The authors must state explicitly which ΔB and ΔV values were used in Eq. (1) for the strong-coupling data, and justify why a single-edge formula can be applied at all in the coupled regime. As written, the three reported numbers (ΔV ratio, ΔB ratio, and q) cannot all be correct under Eq. (1).
  2. [Inter-Edge Coupling, flux-period formula] The claimed relation φνint/φ0 = 1/(νint(νint−1)) is arithmetically inconsistent with the values it is said to predict: for νint = 2 it gives 1/2 = 0.5, not 1.5, and for νint = 4 it gives 1/12 ≈ 0.083, not 0.58. The quoted predicted values instead match 1/νint + 1/(νint−1). This formula is stated without derivation in the main text, and the supplementary capacitive model (Eqs. 5−8) does not derive it either; Eq. (7) gives a modified ΔB but no explicit flux-period law. Since this formula is the main quantitative support for identifying the new oscillations with the two innermost coupled edges, the authors need to correct the formula, provide a derivation, and recompute the comparison with the measured flux periods.
  3. [Supplementary 'Theoretical Model for the strongly coupled regime'] The extraction of K12/K1 from the measured period increase via Eq. (7), together with the application of Eq. (1) to the same period data to claim a 2e charge, makes the 'doubling of the tunneling charge' a re-expression of the period increase rather than an independent measurement. The model itself predicts a modified gate period through Eq. (8), with an unknown ratio of capacitances C1/C2, but the authors state that the computation was not developed for the density-modulation case. Therefore the 2e charge claim currently has no model-based derivation. Please derive the tunneling charge in the coupled two-edge model and show explicitly that the data are consistent with q ≈ 2e, or soften the claim accordingly.
  4. [Inter-Edge Coupling, qν=4 value] The extracted charge at ν = 4 is q = (2.55 ± 0.35)e, which is more than 1.5 standard deviations above 2e and about 27% higher than the nominal doubling value. The abstract's statement of a 'measured doubling of the tunneling charge' is therefore an overstatement for ν = 4. A quantitative treatment should either account for the systematic area-induced increase (as done in the weakly coupled regime) or report the discrepancy explicitly.
minor comments (4)
  1. [Eq. (2) and Supplementary Eq. (5)] The capacitive energy is written with linear terms (1/2)K1δQ1 and (1/2)K2δQ2, but it should be quadratic in the charge imbalances, e.g., (1/2)K1δQ1² + (1/2)K2δQ2² + K12δQ1δQ2. As printed, the expression is dimensionally inconsistent with the physics it is meant to describe.
  2. [Supplementary 'Theoretical Model'] The sentence 'Using ν2 = ν1−ν2 we get the values extracted from the 2D-FFT...' is unclear and appears to contain a typo; presumably one of the ν2 symbols should be Δν2 or a different label. Please rewrite this passage to show how the quoted K12/K1 values follow from the measured period ratios.
  3. [Main text and Supplementary S4] The statement that the density-oscillation period increase 'is close to 2' appears only in the supplementary material, but it is a crucial numerical input for the 2e charge claim. This ratio should be stated and explicitly linked to the charge extraction in the main text.
  4. [Supplementary S4 caption] The last sentence of the S4 caption attributes the discrepancy between area- and density-oscillation period ratios to 'different capacitive coupling ... which differs for different edges.' This is a plausible but unquantified statement; a brief justification or reference would help.

Circularity Check

1 steps flagged · score 6.0 of 10

The reported 2e tunneling charge is the strong-coupling period ratio re-expressed through Eq. 1, and the model's coupling parameter is fitted to the same periods, so the central pairing claim is partially circular.

  1. fitted input called prediction [Main text, 'INTER-EDGE COUPLING' (application of Eq. 1); Supplementary 'Theoretical Model for the strongly coupled regime' (Eqs. 5-8)]
    "Assuming a small variation in the interfering diameter, we can calculate the charge using Eq. 1. We obtain qν=2/e = 1.98±0.18 and qν=4/e = 2.55±0.35, both of which are close to two electrons per period. ... Using ν2 = ν1−ν2 we get the values extracted from the 2D-FFT we get K12/K1|ν=2 = 0.72±0.03 and K12/K1|ν=4 = 0.54±0.05."

    Eq. 1 defines q = CΔVφ0/(ΔBνint) from the same gate and magnetic periods whose increase defines the strong-coupling regime. The 'measured doubling of the tunneling charge' is therefore the period ratio re-expressed as a charge, not an independent confirmation of edge-state pairing. In addition, the capacitive model's parameter K12/K1 is extracted from those same 2D-FFT periods through Eq. 7, and the paper explicitly declines to compute the density-oscillation period for the coupled system ('we have not further developed the computations'). Thus the central quantitative evidence for pairing reduces to the input periods, with the model parameter calibrated to the data it is invoked to explain.

full rationale

The paper contains one significant circular step: the claim of a measured 2e tunneling charge is obtained by inserting the strong-coupling ΔV and ΔB periods into Eq. 1, which was derived for a single uncoupled edge. That makes the 'doubling' a re-expression of the very period increase that defines the strong-coupling regime, rather than an independent observable, and the coupling ratio K12/K1 used to support the model is fitted from the same periods. Some independent content remains: the even-odd filling-factor asymmetry, the phase slips, and the Coulomb-diamond character of the oscillations are qualitative features not simply equivalent to Eq. 1. Separately, the printed flux-period law φ/φ0 = 1/(ν(ν−1)) is arithmetically inconsistent with the quoted values (1.5 and 0.58), and the supplementary capacitive model does not derive that law; these are correctness and derivation-gap concerns rather than circularity. Because the central 'doubling' claim is substantially constructed from the input periods and the model parameter is fitted to the same data, a partial-circularity score of 6 is appropriate.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central interpretation rests on the capacitive coupling model with fitted coupling ratios, an underived flux-period formula, the bilayer graphene Landau level structure from prior literature, and a COMSOL-derived effective diameter. No new physical entities are introduced.

free parameters (2)
  • K12/K1 at ν=2 = 0.72 ± 0.03
    Extracted from the measured increase of the gate-voltage period relative to the weakly coupled regime, using the capacitive model in the supplementary (Eqs. 7-8). The period increase is attributed entirely to inter-edge coupling.
  • K12/K1 at ν=4 = 0.54 ± 0.05
    Same extraction procedure at filling factor 4, also from the supplementary model.
assumptions (5)
  • domain assumption Bilayer graphene Landau level structure: at low displacement field, the N=0 and N=1 orbital levels are degenerate, so at even filling factors the two innermost edges share spin and valley but differ in orbital index, leading to a smaller gap and stronger inter-edge coupling.
    Cited from prior BLG Landau level studies [37,38,45]; used to explain why the strong-coupling oscillations appear only at even ν.
  • ad hoc to paper Capacitive coupling model with two edges and energy E = 1/2 K1 δQ1^2 + 1/2 K2 δQ2^2 + K12 δQ1 δQ2 describes the coupled edge system.
    Introduced in this paper to interpret the larger-period oscillations. Parameters K1, K2, K12 are not derived from microscopic theory.
  • ad hoc to paper The flux period of two coupled inner edges follows ϕνint/ϕ0 = 1/(νint(νint-1)).
    Stated without derivation in the main text (Inter-edge coupling section); not explicitly derived in the supplementary model either.
  • domain assumption The effective antidot diameter of about 290 nm from COMSOL simulations at zero field is representative of the electrostatic diameter in the measurement regime.
    Used to compare extracted oscillation diameters and to rule out Aharonov-Bohm interference; the comparison depends on this simulation value.
  • domain assumption Oscillations are Coulomb-dominated rather than Aharonov-Bohm in both regimes.
    Supported by Coulomb diamonds and density-driven slopes, but the interpretation depends on excluding the AB mechanism.

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Cite this review

Pith. "Pith review of Tunable Inter-Edge Interactions in a Bilayer Graphene Quantum Hall Antidot." pith.science (2026). https://pith.science/paper/EGF3QPMJ

@misc{pith2026250416750,
  author       = {Pith},
  title        = {Pith review of: Tunable Inter-Edge Interactions in a Bilayer Graphene Quantum Hall Antidot},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EGF3QPMJ}},
  note         = {Machine review of arXiv:2504.16750}
}
read the original abstract

Electronic interferometers in the quantum Hall regime are one of the best tools to study the statistical properties of localized quasiparticles in the topologically protected bulk. However, since their behavior is probed via chiral edge modes, bulk-to-edge and inter-edge interactions are two important effects that affect the observations. Moreover, almost all kinds of interferometers heavily rely on a pair of high-quality quantum point contacts where the presence of impurities significantly modifies the behavior of such constrictions, which in turn can alter the outcome of the measurements. Antidots, potential hills in the quantum Hall regime, are particularly valuable in this context, as they overcome the geometric limitations of conventional geometries and act as controlled impurities within a quantum point contact. Furthermore, antidots allow for quasiparticle charge detection through simple conductance measurements, replacing the need for complex techniques such as shot noise. Here, we use a gate-defined bilayer graphene antidot, operated in the Coulomb-dominated regime. By varying the antidot potential, we can tune inter-edge interactions, enabling a crossover from a single-dot to a double-dot behavior. In the latter, strong coupling between the two edge states leads to edge-state pairing, resulting in a measured doubling of the tunneling charge. We find that in certain regimes, the inter-edge coupling completely dominates over other energy scales of the system, overshadowing the interference effects these devices are mainly designed to probe. These results highlight the significant role of inter-edge interactions and establish antidots as a versatile platform for exploring quantum Hall interferometry.

Figures

Figures reproduced from arXiv: 2504.16750 by the authors.

Figure 1
Figure 1. FIG. 1: Gate-defined antidot in bilayer graphene. a [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Coulomb dominated oscillations for integer filling factor. a-d [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Inter-Edge coupling in even filling factors a [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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Reference graph

Works this paper leans on

47 extracted references · 34 canonical work pages

  1. [1]

    B. I. Halperin, A. Stern, I. Neder, and B. Rosenow, The- ory of the Fabry-P \’erot quantum Hall interferometer, Phys. Rev. B 83, 155440 (2011)

    work page 2011

  2. [2]

    D. T. McClure, Y. Zhang, B. Rosenow, E. M. Levenson- Falk, C. M. Marcus, L. N. Pfeiffer, and K. W. West, Edge- State Velocity and Coherence in a Quantum Hall Fabry- P\’erot Interferometer, Phys. Rev. Lett. 103, 206806 (2009). 7

    work page 2009

  3. [3]

    N. Ofek, A. Bid, M. Heiblum, A. Stern, V. Umansky, and D. Mahalu, Role of interactions in an electronic Fabry–Perot interferometer operating in the quantum Hall effect regime, Proc. Natl. Acad. Sci. U.S.A. 107, 5276 (2010)

    work page 2010

  4. [4]

    D´ eprez, L

    C. D´ eprez, L. Veyrat, H. Vignaud, G. Nayak, K. Watan- abe, T. Taniguchi, F. Gay, H. Sellier, and B. Sac´ ep´ e, A tunable Fabry–P´ erot quantum Hall interferometer in graphene, Nat. Nanotechnol. 16, 555 (2021)

    work page 2021

  5. [5]

    Ronen, T

    Y. Ronen, T. Werkmeister, D. Haie Najafabadi, A. T. Pierce, L. E. Anderson, Y. J. Shin, S. Y. Lee, Y. H. Lee, B. Johnson, K. Watanabe, T. Taniguchi, A. Ya- coby, and P. Kim, Aharonov–Bohm effect in graphene- based Fabry–P´ erot quantum Hall interferometers, Nat. Nanotechnol. 16, 563 (2021)

    work page 2021

  6. [6]

    H. Fu, K. Huang, K. Watanabe, T. Taniguchi, M. Kayyalha, and J. Zhu, Aharonov–Bohm Oscilla- tions in Bilayer Graphene Quantum Hall Edge State Fabry–P´ erot Interferometers, Nano Lett.23, 718 (2023)

    work page 2023

  7. [7]

    Nakamura, S

    J. Nakamura, S. Fallahi, H. Sahasrabudhe, R. Rah- man, S. Liang, G. C. Gardner, and M. J. Manfra, Aharonov–Bohm interference of fractional quantum Hall edge modes, Nat. Phys. 15, 563 (2019)

    work page 2019

  8. [8]

    Nakamura, S

    J. Nakamura, S. Liang, G. C. Gardner, and M. J. Man- fra, Direct observation of anyonic braiding statistics, Nat. Phys. 16, 931 (2020)

    work page 2020

Show all 47 references
  1. [9]

    N. L. Samuelson, L. A. Cohen, W. Wang, S. Blanch, T. Taniguchi, K. Watanabe, M. P. Zaletel, and A. F. Young, Anyonic statistics and slow quasiparticle dynam- ics in a graphene fractional quantum Hall interferometer, arXiv 10.48550/arXiv.2403.19628 (2024), 2403.19628

    2024 doi arXiv

  2. [10]

    Werkmeister, J

    T. Werkmeister, J. R. Ehrets, Y. Ronen, M. E. Wes- son, D. Najafabadi, Z. Wei, K. Watanabe, T. Taniguchi, D. E. Feldman, B. I. Halperin, A. Yacoby, and P. Kim, Strongly coupled edge states in a graphene quantum Hall interferometer, Nat. Commun. 15, 1 (2024)

    2024

  3. [11]

    J. Kim, H. Dev, R. Kumar, A. Ilin, A. Haug, V. Bhard- waj, C. Hong, K. Watanabe, T. Taniguchi, A. Stern, and Y. Ronen, Aharonov–Bohm interference and statistical phase-jump evolution in fractional quantum Hall states in bilayer graphene, Nat. Nanotechnol. , 1 (2024)

    2024

  4. [12]

    Y. Ji, Y. Chung, D. Sprinzak, M. Heiblum, D. Mahalu, and H. Shtrikman, An electronic Mach–Zehnder interfer- ometer, Nature 422, 415 (2003)

    2003

  5. [13]

    Neder, N

    I. Neder, N. Ofek, Y. Chung, M. Heiblum, D. Mahalu, and V. Umansky, Interference between two indistinguish- able electrons from independent sources, Nature448, 333 (2007)

    2007

  6. [14]

    H. K. Kundu, S. Biswas, N. Ofek, V. Umansky, and M. Heiblum, Anyonic interference and braiding phase in a Mach-Zehnder interferometer, Nat. Phys.19, 515 (2023)

    2023

  7. [15]

    Deviatov, S

    V. Deviatov, S. V. Egorov, G. Biasiol, and L. Sorba, Quantum Hall Mach-Zehnder interferometer at fractional filling factors, Europhysics Letters 100, 10.1209/0295- 5075/100/67009 (2012)

    2012 doi

  8. [16]

    Ghosh, M

    B. Ghosh, M. Labendik, L. Musina, V. Uman- sky, M. Heiblum, and D. F. Mross, Anyonic Braid- ing in a Chiral Mach-Zehnder Interferometer, arXiv 10.48550/arXiv.2410.16488 (2024), 2410.16488

    2024 doi arXiv

  9. [17]

    Levy Schreier, A

    S. Levy Schreier, A. Stern, B. Rosenow, and B. I. Halperin, Reprint of : Thermodynamic properties of a quantum Hall anti-dot interferometer, Physica E 82, 145 (2016)

    2016

  10. [18]

    H.-S. Sim, M. Kataoka, and C. J. B. Ford, Electron inter- actions in an antidot in the integer quantum Hall regime, Phys. Rep. 456, 127 (2008)

    2008

  11. [19]

    Ihnatsenka, I

    S. Ihnatsenka, I. V. Zozoulenko, and G. Kir- czenow, Electron-electron interactions in antidot-based Aharonov-Bohm interferometers, Phys. Rev. B 80, 115303 (2009)

    2009

  12. [20]

    S. W. Hwang, J. A. Simmons, D. C. Tsui, and M. Shayegan, Quantum interference in two indepen- dently tunable parallel point contacts, Phys. Rev. B 44, 13497 (1991)

    1991

  13. [21]

    C. J. B. Ford, P. J. Simpson, I. Zailer, D. R. Mace, M. Yosefin, M. Pepper, D. A. Ritchie, J. E. F. Frost, M. P. Grimshaw, and G. A. C. Jones, Charging and double-frequency Aharonov-Bohm effects in an open sys- tem, Phys. Rev. B 49, 17456 (1994)

    1994

  14. [22]

    Kataoka, C

    M. Kataoka, C. J. B. Ford, G. Faini, D. Mailly, M. Y. Simmons, D. R. Mace, C.-T. Liang, and D. A. Ritchie, Detection of Coulomb Charging around an Antidot in the Quantum Hall Regime, Phys. Rev. Lett. 83, 160 (1999)

    1999

  15. [23]

    H.-S. Sim, M. Kataoka, H. Yi, N. Y. Hwang, M.-S. Choi, and S.-R. E. Yang, Coulomb Blockade and Kondo Effect in a Quantum Hall Antidot, Phys. Rev. Lett. 91, 266801 (2003)

    2003

  16. [24]

    V. J. Goldman and B. Su, Resonant Tunneling in the Quantum Hall Regime: Measurement of Fractional Charge, Science 267, 1010 (1995)

    1995

  17. [25]

    V. J. Goldman, J. Liu, and A. Zaslavsky, Fractional statistics of Laughlin quasiparticles in quantum antidots, Phys. Rev. B 71, 153303 (2005)

    2005

  18. [26]

    A. Kou, C. M. Marcus, L. N. Pfeiffer, and K. W. West, Coulomb Oscillations in Antidots in the Integer and Frac- tional Quantum Hall Regimes, Phys. Rev. Lett. 108, 256803 (2012)

    2012

  19. [27]

    Das Sarma, M

    S. Das Sarma, M. Freedman, and C. Nayak, Topologically Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State, Phys. Rev. Lett.94, 166802 (2005)

    2005

  20. [28]

    Nayak, S

    C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-Abelian anyons and topological quan- tum computation, Rev. Mod. Phys. 80, 1083 (2008)

    2008

  21. [29]

    S. H. Simon, Proposal for a quantum Hall pump, Phys. Rev. B 61, R16327 (2000)

    2000

  22. [30]

    K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Nature 438, 197 (2005)

    2005

  23. [31]

    Zhang, Y.-W

    Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Ex- perimental observation of the quantum Hall effect and Berry’s phase in graphene, Nature 438, 201 (2005)

    2005

  24. [32]

    S. Jung, G. M. Rutter, N. N. Klimov, D. B. Newell, I. Calizo, A. R. Hight-Walker, N. B. Zhitenev, and J. A. Stroscio, Evolution of microscopic localization in graphene in a magnetic field from scattering resonances to quantum dots, Nat. Phys. 7, 245 (2011)

    2011

  25. [33]

    Guti´ errez, D

    C. Guti´ errez, D. Walkup, F. Ghahari, C. Lewandowski, J. F. Rodriguez-Nieva, K. Watanabe, T. Taniguchi, L. S. Levitov, N. B. Zhitenev, and J. A. Stroscio, Interaction- driven quantum Hall wedding cake–like structures in graphene quantum dots, Science 361, 789 (2018)

    2018

  26. [34]

    Walkup, F

    D. Walkup, F. Ghahari, C. Guti´ errez, K. Watanabe, T. Taniguchi, N. B. Zhitenev, and J. A. Stroscio, Tuning single-electron charging and interactions between com- pressible Landau level islands in graphene, Phys. Rev. B 101, 035428 (2020)

    2020

  27. [35]

    S. M. Mills, A. Gura, K. Watanabe, T. Taniguchi, 8 M. Dawber, D. V. Averin, and X. Du, Dirac fermion quantum Hall antidot in graphene, Phys. Rev. B 100, 245130 (2019)

    2019

  28. [36]

    S. M. Mills, D. V. Averin, and X. Du, Localizing Frac- tional Quasiparticles on Graphene Quantum Hall Anti- dots, Phys. Rev. Lett. 125, 227701 (2020)

    2020

  29. [37]

    B. M. Hunt, J. I. A. Li, A. A. Zibrov, L. Wang, T. Taniguchi, K. Watanabe, J. Hone, C. R. Dean, M. Za- letel, R. C. Ashoori, and A. F. Young, Direct measure- ment of discrete valley and orbital quantum numbers in bilayer graphene, Nat. Commun. 8, 1 (2017)

    2017

  30. [38]

    J. Li, Y. Tupikov, K. Watanabe, T. Taniguchi, and J. Zhu, Effective Landau Level Diagram of Bilayer Graphene, Phys. Rev. Lett. 120, 047701 (2018)

    2018

  31. [39]

    V. J. Goldman, J. Liu, and A. Zaslavsky, Electron tun- neling spectroscopy of a quantum antidot in the integer quantum Hall regime, Phys. Rev. B 77, 115328 (2008)

    2008

  32. [40]

    Werkmeister, J

    T. Werkmeister, J. R. Ehrets, M. E. Wesson, D. H. Na- jafabadi, K. Watanabe, T. Taniguchi, B. I. Halperin, A. Yacoby, and P. Kim, Anyon braiding and tele- graph noise in a graphene interferometer, arXiv 10.48550/arXiv.2403.18983 (2024), 2403.18983

    2024 doi arXiv

  33. [41]

    J. Kim, H. Dev, R. Kumar, A. Ilin, A. Haug, V. Bhard- waj, C. Hong, K. Watanabe, T. Taniguchi, A. Stern, and Y. Ronen, Aharonov–Bohm interference and statistical phase-jump evolution in fractional quantum Hall states in bilayer graphene, Nat. Nanotechnol. 19, 1619 (2024)

    2024

  34. [42]

    M. P. R¨ o¨ osli, L. Brem, B. Kratochwil, G. Nicol´ ı, B. A. Braem, S. Hennel, P. M¨ arki, M. Berl, C. Reichl, W. Wegscheider, K. Ensslin, T. Ihn, and B. Rosenow, Observation of quantum Hall interferometer phase jumps due to a change in the number of bulk quasiparticles, Phys....

    2020

  35. [43]

    M. P. R¨ o¨ osli, M. Hug, G. Nicol´ ı, P. M¨ arki, C. Reichl, B. Rosenow, W. Wegscheider, K. Ensslin, and T. Ihn, Fractional Coulomb blockade for quasi-particle tunnel- ing between edge channels, Sci. Adv. 7, 10.1126/sci- adv.abf5547 (2021)

    2021 doi

  36. [44]

    W. Yang, D. Perconte, C. D´ eprez, K. Watanabe, T. Taniguchi, S. Dumont, E. Wagner, F. Gay, I. Safi, H. Sellier, and B. Sac´ ep´ e, Evidence for correlated elec- tron pairs and triplets in quantum Hall interferometers, arXiv 10.48550/arXiv.2312.14767 (2023), 2312.14767

    2023 doi arXiv

  37. [45]

    Barlas, R

    Y. Barlas, R. Cˆ ot´ e, K. Nomura, and A. H. MacDon- ald, Intra-Landau-Level Cyclotron Resonance in Bilayer Graphene, Phys. Rev. Lett. 101, 097601 (2008)

    2008

  38. [46]

    Martin, B

    J. Martin, B. E. Feldman, R. T. Weitz, M. T. Allen, and A. Yacoby, Local Compressibility Measurements of Correlated States in Suspended Bilayer Graphene, Phys. Rev. Lett. 105, 256806 (2010). METHODS A. Sample fabrication The device was fabricated using a standard van der Waals...

    2010

  39. [47]

    Since the oscillations are gate-induced, we cannot directly extract the interfering charge

    This corresponds to a flux period of ϕ0 and an antidot diameter of D = 269± 18 nm. Since the oscillations are gate-induced, we cannot directly extract the interfering charge. Source-drain measurements, shown in figure S5- c, still display a Coulomb-dominated pattern with a cha...

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