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arxiv: 2606.10754 · v1 · pith:M57WOB4Pnew · submitted 2026-06-09 · ❄️ cond-mat.mes-hall

Spin polarisation signatures of Fractionally Charged Skyrmions in Fractional Quantum Hall states

Odysseas Williams , Stefan Faelt , Christian Reichl , Werner Wegscheider This is my paper

Pith reviewed 2026-06-27 12:06 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords fractional quantum hallskyrmionsspin polarisationcavity polariton spectroscopygaas quantum wellscomposite fermionsquasiparticles
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The pith

Minimal fractionally charged skyrmions form in fractional quantum Hall states, shown by symmetric spin depolarisation.

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

The paper measures spin polarisation across fractional quantum Hall fillings from 1/3 to 1 using cavity-polariton spectroscopy on GaAs quantum wells. It reports complete suppression of the lowest excitation oscillator strength at quantised fillings, confirming fully polarised states. At high magnetic fields, symmetric depolarisation occurs away from these fillings and follows the empirical relation S equals nu star, where S counts spin flips per added flux quantum. The authors interpret the pattern as direct evidence that minimal fractionally charged skyrmions arise from bound spin-flip and quasiparticle excitations. A reader would care because this identifies a concrete low-energy excitation that organises spin response in these strongly interacting regimes.

Core claim

Cavity-polariton spectroscopy extracts the spin polarisation of the electron system as a function of filling factor. Complete suppression of the oscillator strength of the lowest energy excitation occurs, characteristic of singlet trion formation in fully polarised systems. At large magnetic fields, fully polarised fractional quantum Hall states exhibit symmetric depolarisation away from quantised fillings that follows the empirical law S equals nu star. This behaviour is interpreted as evidence for minimal fractionally charged skyrmions formed from bound spin-flip and quasiparticle excitations.

What carries the argument

Minimal Fractionally Charged Skyrmions (MFCS), bound states of spin-flip and quasiparticle excitations that produce the observed symmetric depolarisation law S equals nu star.

Load-bearing premise

The observed symmetric depolarisation away from quantised fillings is caused by the formation of minimal fractionally charged skyrmions rather than other spin-relaxation mechanisms.

What would settle it

High-field measurements that find either asymmetric depolarisation or a dependence on filling factor other than S equals nu star would contradict the minimal fractionally charged skyrmion interpretation.

Figures

Figures reproduced from arXiv: 2606.10754 by Christian Reichl, Odysseas Williams, Stefan Faelt, Werner Wegscheider.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Optical transfer-matrix simulations used to design devices 2 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Lowest polariton energy in sample 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: The magnetic-field axes are scaled such that a [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Three lowest excitation energies [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Coupling energies Ω [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Spin polarisation [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: shows the same spin-polarisation data replot￾ted as a function of the effective CF filling factor ν ∗ , obtained from Eq. 1. The ν+ = 1/3, 2/5, 3/7, 4/9, and 5/11 states (B = 6.48, 5.40, 5.04, 4.86, and 4.75 T) are shown for sample 3λ (red), while the ν− = 1, 2/3, 3/5, 4/7, and 5/9 states (B = 4.32, 6.48, 7.20, 7.56, and 7.78 T) are shown for sample 2λ (blue). The full polarisation of these FQH states is c… view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. CF representation of the fully polarised [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
read the original abstract

We investigate spin polarisation and low-energy excitations in fractional quantum Hall (FQH) states using cavity-polariton spectroscopy of high-mobility GaAs quantum wells. By measuring the optical coupling strength of interband Landau-level excitations over the range $1/3 \le \nu \le 1$, we extract the spin polarisation of the electron system as a function of filling factor. Complete suppression of the oscillator strength of the lowest energy excitation, characteristic of singlet trion formation in fully polarised systems, is reported for the first time in this regime. At large magnetic fields, fully polarised FQH states exhibit symmetric depolarisation away from their quantised fillings, analogous to Skyrmionic behaviour near $\nu=1$. The depolarisation follows an empirical law $S=\nu^*$, where $S$ is the number of spin flips per added magnetic flux quantum and $\nu^*$ the effective Composite Fermion filling factor. We interpret this behaviour as evidence for Minimal Fractionally Charged Skyrmions (MFCS) formed from bound spin-flip and quasiparticle excitations.

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 / 1 minor

Summary. The manuscript reports cavity-polariton spectroscopy measurements of spin polarisation in fractional quantum Hall states (1/3 ≤ ν ≤ 1) in high-mobility GaAs quantum wells. It claims complete suppression of the oscillator strength of the lowest-energy interband excitation (indicating singlet trion formation) at fully polarised FQH states, and symmetric depolarisation away from quantised fillings that follows an empirical law S=ν* (S = number of spin flips per added flux quantum, ν* = effective composite-fermion filling factor). This behaviour is interpreted as evidence for Minimal Fractionally Charged Skyrmions (MFCS) formed from bound spin-flip and quasiparticle excitations, analogous to integer-QH skyrmions.

Significance. If the data and interpretation are substantiated with quantitative analysis, the result would extend skyrmion physics into the fractional regime and demonstrate cavity-polariton spectroscopy as a probe of spin textures in FQH systems. This could impact understanding of low-energy excitations and spin-charge coupling in strongly correlated 2D electrons.

major comments (3)
  1. The central claim that symmetric depolarisation constitutes evidence for MFCS relies on the empirical law S=ν* being both observed and then used to support the MFCS interpretation; no independent derivation of this law from an MFCS model or quantitative contrast with alternative spin-relaxation mechanisms (e.g., unbound composite-fermion spin textures) is provided.
  2. No data plots, error bars, sample details, quantitative fits, or oscillator-strength extraction procedures are described, so the claimed support for the MFCS interpretation cannot be assessed; the abstract states the law and the interpretation without visible verification.
  3. The assumption that the cavity-polariton signal arises specifically from bound MFCS states rather than other low-energy spin-flip excitations is load-bearing but untested against alternatives in the presented material.
minor comments (1)
  1. The definition and range of the effective filling factor ν* should be stated explicitly with reference to composite-fermion theory.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below and will revise the manuscript accordingly to improve clarity, add discussion of alternatives, and ensure the data analysis is fully documented.

read point-by-point responses

  1. Referee: The central claim that symmetric depolarisation constitutes evidence for MFCS relies on the empirical law S=ν* being both observed and then used to support the MFCS interpretation; no independent derivation of this law from an MFCS model or quantitative contrast with alternative spin-relaxation mechanisms (e.g., unbound composite-fermion spin textures) is provided.

    Authors: We agree the S=ν* law is empirical, observed directly in the data, and the MFCS interpretation is proposed by analogy to integer-QH skyrmions together with the observed symmetry. A microscopic derivation lies outside the scope of this primarily experimental study. In revision we will add a dedicated discussion section contrasting the MFCS picture with unbound composite-fermion spin textures, noting that the latter do not naturally produce the linear S=ν* dependence or the symmetric depolarisation around both integer and fractional fillings. Relevant theoretical literature on fractional skyrmions will be cited. revision: partial

  2. Referee: No data plots, error bars, sample details, quantitative fits, or oscillator-strength extraction procedures are described, so the claimed support for the MFCS interpretation cannot be assessed; the abstract states the law and the interpretation without visible verification.

    Authors: The full manuscript contains figures with the measured spectra, extracted spin polarisation versus filling factor (including error bars), sample parameters (mobility >10^7 cm²/Vs, density), and the fitting procedure used to obtain oscillator strengths from the polariton lineshapes. We will revise the main text to reference these elements more explicitly and add a concise methods paragraph detailing the oscillator-strength extraction and error analysis. revision: yes

  3. Referee: The assumption that the cavity-polariton signal arises specifically from bound MFCS states rather than other low-energy spin-flip excitations is load-bearing but untested against alternatives in the presented material.

    Authors: We acknowledge that the assignment to bound MFCS is interpretive. The complete suppression of the lowest-energy excitation at the quantised fillings and the symmetric recovery away from them are the key observations. In the revision we will expand the discussion to compare the expected signatures of alternative spin-flip excitations (e.g., unbound CF spin waves) with the data and explain why the observed S=ν* scaling favors the bound MFCS scenario. We note that future theoretical calculations of the polariton response for different excitations would be valuable. revision: partial

Circularity Check

0 steps flagged

No circularity in derivation chain; purely observational interpretation

full rationale

The paper reports cavity-polariton spectroscopy measurements of spin polarisation in FQH states and states that depolarisation away from quantised fillings 'follows an empirical law S=ν*'. It then offers an interpretation of this observed behaviour as evidence for MFCS. No first-principles derivation, model prediction, or equation is presented that reduces to the input data by construction. The law is explicitly labeled empirical (i.e., extracted from the measurements), and the MFCS claim is framed as an interpretation rather than a closed-loop result. No self-citations, ansatzes, or fitted parameters renamed as predictions appear in the text. The analysis is self-contained as an experimental observation plus post-hoc naming, with no load-bearing step that equates output to input by definition.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on the assumption that optical coupling strength directly reports spin polarisation and that the empirical depolarisation pattern uniquely indicates MFCS; the MFCS entity is introduced without independent falsifiable evidence outside the presented data.

free parameters (1)
  • empirical depolarisation law S=ν*
    The relation between number of spin flips and effective composite-fermion filling factor is presented as an empirical law fitted to the observed depolarisation.
axioms (1)
  • domain assumption Optical coupling strength of interband Landau-level excitations measures the spin polarisation of the electron system
    This mapping is invoked to extract spin polarisation from the measured oscillator strengths.
invented entities (1)
  • Minimal Fractionally Charged Skyrmions (MFCS) no independent evidence
    purpose: To account for the symmetric depolarisation away from quantised fillings as bound spin-flip plus quasiparticle excitations
    The entity is postulated to interpret the data; the abstract provides no independent falsifiable prediction or external evidence for its existence.

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Reference graph

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