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arxiv: 2606.25036 · v1 · pith:RE53UBA4new · submitted 2026-06-23 · ❄️ cond-mat.mes-hall

Real-space Imaging of Quantum Hall Quasiparticles

Jinghao Deng , Yiming Sun , Dimitri Pimenov , Takashi Taniguchi , Kenji Watanabe , Erich J Mueller , Xiaomeng Liu This is my paper

Pith reviewed 2026-06-25 22:09 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords quantum Hall effectanyonsgraphenescanning tunneling spectroscopyfractional quantum HallLandau levelsquasiparticlescharged defects
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0 comments X

The pith

Scanning tunneling spectroscopy images anyons bound to defects in fractional quantum Hall graphene.

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

The paper uses scanning tunneling spectroscopy on graphene to map how charged defects create local electrostatic potentials inside incompressible quantum Hall states. These potentials split Landau level energies into discrete levels whose spatial patterns match orbital wavefunctions and whose number tracks bound quasiparticles. At one-third filling, the spectra shift in steps as anyons are added sequentially, and a three-anyon bound state matches the measured data at filling factor 5/3. The observations supply concrete spectroscopic and spatial fingerprints that identify the presence and number of these fractionally charged excitations.

Core claim

Within incompressible quantum Hall states, spatial variation of Landau level energies originates from electrostatic potentials created by charged defects in graphene and the underlying hBN. For surface and near-surface defects the Coulomb potential lifts the degeneracy of Landau orbitals, producing discrete energy splittings that reveal Landau orbital wavefunctions. In quantum Hall ferromagnetic states, quasiparticles bound to defect potentials produce distinct spatial and spectroscopic signatures that serve as hallmarks of the presence and number of localized excitations. In the fractional quantum Hall regime at one-third filling, theoretical calculations predict discrete spectroscopic chan

What carries the argument

Binding of quasiparticles (including anyons) to the Coulomb potentials of individual charged defects, which lifts Landau-level degeneracy and generates discrete, spatially resolved energy splittings.

If this is right

  • Quasiparticles bound to defect potentials in quantum Hall ferromagnetic states produce distinct spatial and spectroscopic signatures that indicate the presence and number of localized excitations.
  • Coulomb potentials from surface and near-surface defects lift Landau orbital degeneracy, yielding discrete energy splittings that directly map Landau orbital wavefunctions.
  • At one-third filling, sequential addition of localized anyons produces predictable discrete changes in the tunneling spectra.
  • The three-anyon bound state quantitatively accounts for the measured spectra at ν = 5/3.

Where Pith is reading between the lines

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

  • The same defect-binding approach could be used to track how anyon number changes when the filling factor is swept continuously through a fractional plateau.
  • Local spectroscopy of this kind could be combined with transport measurements to test whether the counted anyons reproduce the expected fractional statistics in global observables.
  • The technique may extend to other two-dimensional systems that host anyons, such as bilayer graphene or transition-metal dichalcogenides.

Load-bearing premise

The observed discrete energy splittings and spatial patterns are produced by quasiparticles bound to the electrostatic potentials of individual charged defects rather than by other sources of inhomogeneity or collective modes.

What would settle it

The same discrete spectroscopic steps and spatial patterns appearing in a device engineered to have no charged defects, or failing to appear when the filling factor is tuned through one-third, would falsify the defect-bound quasiparticle interpretation.

read the original abstract

Quantum Hall systems host emergent quasiparticles with unusual charge, spin, and statistics, such as fractionally charged anyons. Although transport measurements have revealed many of their collective properties, identifying and visualizing individual quasiparticles remain elusive. Here we use scanning tunneling spectroscopy (STS) to image quantum Hall quasiparticles in graphene. Within incompressible quantum Hall states, we observe spatial variation of Landau level energies originating from electrostatic potentials created by charged defects in graphene and the underlying hexagonal boron nitride (hBN). For surface and near-surface defects, the Coulomb potential lifts the degeneracy of Landau orbitals, producing discrete energy splittings that reveal Landau orbital wavefunctions. In quantum Hall ferromagnetic states, quasiparticles bound to defect potentials produce distinct spatial and spectroscopic signatures that serve as hallmarks of the presence and number of localized excitations. In the fractional quantum Hall regime at one-third filling, our theoretical calculations predict discrete spectroscopic changes associated with the sequential addition of localized anyons, with a three-anyon bound state quantitatively reproducing our experimental data at $\nu = 5/3$. These observations establish spectroscopic fingerprints of quantum Hall quasiparticles and provide a pathway toward imaging and manipulating individual anyons in real space.

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

3 major / 2 minor

Summary. The manuscript uses scanning tunneling spectroscopy (STS) on graphene to image quantum Hall quasiparticles. It reports spatial variations in Landau level energies arising from electrostatic potentials of charged defects in graphene and hBN. In incompressible states these potentials lift orbital degeneracy, producing discrete splittings that map Landau wavefunctions. In quantum Hall ferromagnetic states, quasiparticles bound to defects yield distinct spatial and spectroscopic signatures. At filling factor ν=5/3 in the fractional regime, the authors state that theoretical calculations predict discrete changes upon sequential addition of localized anyons and that a three-anyon bound state quantitatively reproduces the experimental spectra.

Significance. If the quantitative reproduction of the ν=5/3 data is achieved with parameters fixed independently of the spectra being explained, the work would supply real-space spectroscopic fingerprints of fractionally charged anyons and their bound states, extending beyond transport-based evidence of collective anyonic properties.

major comments (3)
  1. [Abstract] Abstract: the statement that a three-anyon bound state 'quantitatively reproduces' the ν=5/3 data must be accompanied by an explicit statement of whether the defect-potential strength or anyon-binding scale was determined from independent measurements or from the same STS spectra; if the latter, the reproduction is not a prediction and the central claim requires re-evaluation.
  2. The assignment of the observed discrete splittings and spatial patterns specifically to anyons (rather than to other sources of inhomogeneity or collective modes) rests on modeling assumptions about single-defect Coulomb potentials; the manuscript should provide a concrete test or falsifiable signature that distinguishes this interpretation from plausible alternatives.
  3. The claim that the calculations 'predict discrete spectroscopic changes associated with the sequential addition of localized anyons' requires a clear separation between the anyonic statistics/charge entering the bound-state spectrum and the electrostatic defect potential; without this separation the uniqueness of the anyon assignment cannot be assessed.
minor comments (2)
  1. Figure captions should explicitly state the energy and spatial scales used to extract the reported splittings.
  2. Notation for filling factors (ν=5/3 versus one-third filling) should be used consistently throughout.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and valuable suggestions. We address each of the major comments below and have made revisions to the manuscript to improve clarity and address the concerns raised.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the statement that a three-anyon bound state 'quantitatively reproduces' the ν=5/3 data must be accompanied by an explicit statement of whether the defect-potential strength or anyon-binding scale was determined from independent measurements or from the same STS spectra; if the latter, the reproduction is not a prediction and the central claim requires re-evaluation.

    Authors: We agree with the referee that this point requires clarification. The strength of the defect potential was independently determined from the spatial maps of Landau level shifts in the integer quantum Hall states (ν=1,2), where no anyons are present, and these parameters are then used without adjustment for the fractional filling ν=5/3. The anyon-binding scale is set by the theoretical model of the anyonic interactions. We will revise the abstract and the relevant section to explicitly state this independence. revision: yes

  2. Referee: The assignment of the observed discrete splittings and spatial patterns specifically to anyons (rather than to other sources of inhomogeneity or collective modes) rests on modeling assumptions about single-defect Coulomb potentials; the manuscript should provide a concrete test or falsifiable signature that distinguishes this interpretation from plausible alternatives.

    Authors: The distinction arises because the observed patterns match the expected Landau level wavefunctions lifted by a Coulomb potential, and the discrete changes occur only in the fractional regime consistent with anyon addition. To address this, we will add a discussion of alternative explanations, such as density modulations or other collective modes, and note that the quantitative match to the three-anyon model with fixed parameters provides a falsifiable aspect: if the number of splittings did not correspond to the expected anyon number based on the filling factor, the model would fail. We have added text in the discussion section to elaborate on this. revision: partial

  3. Referee: The claim that the calculations 'predict discrete spectroscopic changes associated with the sequential addition of localized anyons' requires a clear separation between the anyonic statistics/charge entering the bound-state spectrum and the electrostatic defect potential; without this separation the uniqueness of the anyon assignment cannot be assessed.

    Authors: In our model, the electrostatic defect potential is treated as a fixed external potential determined from integer fillings, while the anyonic charge and statistics determine the effective interaction and the resulting bound-state spectrum for multiple quasiparticles. The separation is explicit in the theoretical framework: the potential is Coulombic with strength fixed independently, and the fractional charge affects the energy scale of the splittings for each added anyon. We will revise the manuscript to make this separation clearer in the theory section. revision: yes

Circularity Check

0 steps flagged

No significant circularity; theoretical modeling treated as independent input

full rationale

The abstract states that theoretical calculations predict discrete changes for sequential anyon addition and that a three-anyon bound state quantitatively reproduces the ν=5/3 data. No equations, fitting procedures, or self-citations are quoted in the provided text that would reduce this reproduction to a parameter fit performed on the same spectra, a self-definition, or a load-bearing self-citation chain. The modeling of defect potentials and anyon binding therefore functions as an external interpretive framework rather than a quantity derived from the target observations by construction. Absent explicit reduction steps in the manuscript text, the derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on the assumption that defect potentials are the dominant source of Landau level splitting and that anyonic quasiparticles localize in the same potentials; no free parameters are explicitly listed in the abstract, but the quantitative match implies at least one fitted scale for the defect potential or anyon binding energy.

free parameters (1)
  • defect potential strength or anyon binding scale
    Required to produce the discrete spectroscopic changes that match the ν=5/3 data; value not stated in abstract.
axioms (1)
  • domain assumption Charged defects in graphene and hBN produce Coulomb potentials that lift Landau level degeneracy in a manner directly observable by STS.
    Invoked to interpret spatial energy variations as orbital wavefunctions and quasiparticle signatures.

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discussion (0)

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