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arxiv: 2606.25024 · v1 · pith:OB6EJDYZnew · submitted 2026-06-23 · ❄️ cond-mat.mes-hall · cond-mat.str-el

Local spectroscopy of anyons bound to charge traps

Jeong Min Park , Cristian Voinea , Yen-Chen Tsui , Songyang Pu , Kenji Watanabe , Takashi Taniguchi , Nigel R. Cooper , Michael P. Zaletel
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Zlatko Papi\'c Ali Yazdani
This is my paper

Pith reviewed 2026-06-25 22:12 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.str-el
keywords anyonsfractional quantum Hall effectscanning tunneling spectroscopygraphenecharge trapsanyon bound statesquantum Hall spectroscopy
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The pith

STM spectroscopy near charged impurities in graphene reveals an extra energy splitting in fractional quantum Hall states only inside the gap, linked to trapped anyon configurations that require anisotropic confinement.

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

The paper examines local excitation spectra near individual charged impurities in monolayer graphene using scanning tunneling spectroscopy across integer and fractional quantum Hall regimes. In integer states the spectra show discrete levels from lifted orbital degeneracy, while in the fractional states at filling 1/3 and 2/5 an additional splitting of the lowest feature appears exclusively when the chemical potential lies inside a fractional gap. The authors attribute the splitting to distinct many-body arrangements of anyons bound by the impurity potential. Numerical modeling shows the splitting occurs only for anisotropic traps and disappears for rotationally symmetric ones, because the competing states differ in how charge is redistributed outside the core while keeping nearly identical core charge. This positions local tunneling as a probe of confined anyon states relevant to braiding and fusion.

Core claim

In the fractional quantum Hall states at ν=1/3 and 2/5, scanning tunneling spectra near charged impurities exhibit an additional energy splitting of the lowest-energy spectral feature that occurs only when the chemical potential lies within a fractional gap and is absent in compressible or integer regimes. Numerical calculations demonstrate that this splitting requires an anisotropic confining potential and vanishes for a rotationally symmetric trap. The competing multi-anyon states carry nearly identical charge within the core of the potential but differ in how that charge is redistributed at larger radius.

What carries the argument

Many-body configurations of anyons trapped by an anisotropic impurity potential, which produce distinct energies through different outer-radius charge redistributions while sharing nearly identical core charge.

If this is right

  • Local tunneling spectroscopy acts as a direct probe of anyon bound states in confined geometries.
  • The splitting is absent in integer quantum Hall states and compressible regimes.
  • Competing multi-anyon states can be distinguished by outer charge distribution despite similar core charge.
  • Anisotropic confinement is required to make the splitting observable.

Where Pith is reading between the lines

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

  • The technique could be used to test whether specific anyon configurations can be selected by tuning trap anisotropy.
  • Similar local signatures may appear when anyons are confined in other fractional states or in different host materials.
  • Engineering controlled anisotropy around impurities might allow local manipulation of anyon positions or fusion outcomes.

Load-bearing premise

The splitting is produced by many-body anyon configurations rather than single-particle orbital effects or disorder, which rests on the numerical result that the splitting vanishes for rotationally symmetric traps together with the assumption that the experimental potential is sufficiently anisotropic.

What would settle it

Observation of the same splitting in a rotationally symmetric confining potential, or its complete absence when the chemical potential sits inside a fractional gap, would contradict the attribution to anisotropic anyon bound states.

Figures

Figures reproduced from arXiv: 2606.25024 by Ali Yazdani, Cristian Voinea, Jeong Min Park, Kenji Watanabe, Michael P. Zaletel, Nigel R. Cooper, Songyang Pu, Takashi Taniguchi, Yen-Chen Tsui, Zlatko Papi\'c.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. Model geometry. The hBN layer with dielectric constants ( [PITH_FULL_IMAGE:figures/full_fig_p019_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a),(b): LDOS for IQH state with [PITH_FULL_IMAGE:figures/full_fig_p020_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Energy spectrum of the [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Energy spectra resolved by [PITH_FULL_IMAGE:figures/full_fig_p022_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Spatial LDOS maps for the electron removal from a [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The evolution of the LDOS peak intensity at [PITH_FULL_IMAGE:figures/full_fig_p023_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The evolution of energy spectra as a function of gradient ∆ [PITH_FULL_IMAGE:figures/full_fig_p024_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Finite-size linear extrapolation of ∆ [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Susceptibility diagnostic, Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p025_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: shows the excess charge for states in different Lz sectors which include the ground state and lowest-lying excited states. Here, we focus on Ne = 8 electrons, where the complete LDOS calculation is not accessible in numerics, but the larger system size allows for a better visualization of the charge profile, and directly applies to smaller systems as well. From [PITH_FULL_IMAGE:figures/full_fig_p026_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. STM topography of a pristine monolayer graphene surface, showing atomically clean regions without defects. [PITH_FULL_IMAGE:figures/full_fig_p027_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Full gate voltage range spanning the quantum Hall gaps from [PITH_FULL_IMAGE:figures/full_fig_p027_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Zoom-in of the LL sector between [PITH_FULL_IMAGE:figures/full_fig_p027_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Zoom-in of the LL sector between [PITH_FULL_IMAGE:figures/full_fig_p028_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Energy level splitting at the [PITH_FULL_IMAGE:figures/full_fig_p028_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Energy level splitting at the [PITH_FULL_IMAGE:figures/full_fig_p029_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Comparison of different impurity potentials. (a-c) Linecut spectra at [PITH_FULL_IMAGE:figures/full_fig_p029_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Impurity with shallow/neutral potential. (a) Linecut spectrum at [PITH_FULL_IMAGE:figures/full_fig_p030_18.png] view at source ↗
read the original abstract

Fractional quantum Hall states host anyons, emergent quasiparticles with fractional charge and nontrivial exchange statistics. Controlling, trapping, and braiding anyons are central goals for both fundamental physics and topological quantum computation. A key step toward such control is understanding how anyons behave when confined in local potentials, where their internal structure can become relevant. Here, we use the scanning tunneling microscopy/spectroscopy (STM/STS) to study the excitation spectrum in integer and fractional quantum Hall states of monolayer graphene near individual charged impurities. In the integer quantum Hall states, the STS spectra show lifting of orbital degeneracy near defects, appearing as a band of discrete energy levels. In fractional states, (v=1/3 and 2/5), however, we observe an additional energy splitting of the lowest-energy spectral feature that occurs only when the chemical potential lies within a fractional gap and is absent in compressible or integer regimes. We attribute this to many-body configurations of anyons trapped by an impurity potential. Strikingly, numerical calculations show that the splitting requires an anisotropic confining potential, vanishing for a rotationally symmetric trap. The competing multi-anyon states carry nearly identical charge within the core of the potential but differ in how that charge is redistributed at larger radius. Our results establish local tunneling spectroscopy as a direct probe of anyon bound states, providing a key step toward understanding and controlling their behavior in confined geometries relevant for braiding and fusion.

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 reports STM/STS measurements near charged impurities in monolayer graphene under integer and fractional quantum Hall conditions. In integer states, spectra exhibit discrete levels from lifted orbital degeneracy. In fractional states (ν=1/3 and 2/5), an additional splitting of the lowest-energy feature appears exclusively when the chemical potential lies inside a fractional gap and is absent in compressible or integer regimes. The authors attribute this splitting to many-body anyon configurations bound by the impurity potential. Numerical calculations are presented showing that the splitting requires an anisotropic confining potential and vanishes for rotationally symmetric traps; the competing multi-anyon states carry nearly identical core charge but differ in radial redistribution.

Significance. If the central attribution is sustained, the work supplies a local spectroscopic signature of confined anyons and demonstrates that potential anisotropy is essential for the observed splitting. The explicit numerical demonstration that the effect disappears under rotational symmetry constitutes a concrete, falsifiable control that strengthens the interpretation. This constitutes a useful step toward local probes of anyon fusion and braiding in engineered potentials.

major comments (1)
  1. [STS spectra and numerical calculations section] The section describing the STS spectra and the numerical calculations: the attribution of the splitting to anyon bound states rests on the numerical result that the splitting vanishes for rotationally symmetric traps. The experimental analysis does not report an independent quantification or fit of the impurity potential anisotropy (via topography, electrostatic modeling, or otherwise). Without such a measurement, it remains possible that the real potential lies below the anisotropy threshold used in the simulations, allowing single-particle orbital effects or other many-body states to produce the observed splitting.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of the manuscript's significance and for the detailed comment. We respond point-by-point below.

read point-by-point responses

  1. Referee: [STS spectra and numerical calculations section] The section describing the STS spectra and the numerical calculations: the attribution of the splitting to anyon bound states rests on the numerical result that the splitting vanishes for rotationally symmetric traps. The experimental analysis does not report an independent quantification or fit of the impurity potential anisotropy (via topography, electrostatic modeling, or otherwise). Without such a measurement, it remains possible that the real potential lies below the anisotropy threshold used in the simulations, allowing single-particle orbital effects or other many-body states to produce the observed splitting.

    Authors: The additional splitting appears exclusively inside the fractional gaps (ν=1/3, 2/5) and is absent both in the integer quantum Hall regime and in compressible regions. In the integer regime the same impurities produce only the expected discrete levels from orbital-degeneracy lifting, without the further splitting. This regime selectivity already excludes generic single-particle orbital effects from the impurity potential. The numerical calculations establish that anyonic multi-particle states produce the observed splitting only when the confining potential is anisotropic and that the splitting vanishes under rotational symmetry; the competing states differ in radial charge redistribution while carrying nearly identical core charge. Because the experimental feature is tied to the fractional regime, the anisotropy threshold relevant for anyons is the one that matters, and the absence of the feature outside fractional gaps supplies the necessary control. We therefore maintain that the attribution is supported without requiring an independent experimental fit of the anisotropy. revision: no

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central claim rests on direct experimental STS observations of an energy splitting that appears exclusively inside fractional gaps (ν=1/3, 2/5) and is absent in integer or compressible regimes, together with separate numerical calculations showing that the splitting vanishes for rotationally symmetric traps. No step in the reported chain reduces by the paper's own equations to a fitted parameter, a self-definition, or a self-citation whose content is itself the target result. The numerics are presented as an independent computational check rather than a renaming or tautological fit, and the experimental attribution does not invoke any load-bearing self-citation or ansatz smuggled from prior work. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The claim rests on the standard domain assumption that fractional quantum Hall states host anyons, plus the interpretive step that the extra spectral feature arises from multi-anyon configurations whose charge redistribution is sensitive to trap anisotropy. No free parameters or new invented entities are explicitly introduced in the abstract.

axioms (1)
  • domain assumption Fractional quantum Hall states host anyons with fractional charge and nontrivial exchange statistics.
    Invoked to interpret the additional splitting as many-body anyon configurations.
invented entities (1)
  • anyon bound states in anisotropic impurity traps no independent evidence
    purpose: To account for the extra energy splitting observed only in fractional gaps.
    Postulated on the basis of the STS feature and the numerical result that splitting requires anisotropy; no independent falsifiable signature outside the present experiment is stated.

pith-pipeline@v0.9.1-grok · 5830 in / 1480 out tokens · 36165 ms · 2026-06-25T22:12:40.725559+00:00 · methodology

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Reference graph

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    The breaking of rotational symmetry The spectra in Figure 4 include the impurity and tip effects (placed directly above the impurity), but no gradient potential, hence there is exact rotational symmetry about thez-axis. In this scenario, the LDOS spectrum for the electron removal from a 3-quasiparticle ground state in the strong-impurity regime shows a si...

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