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arxiv: 2606.29305 · v1 · pith:H2K2QLZNnew · submitted 2026-06-28 · ❄️ cond-mat.str-el

Energy Gap in Weakly Disordered Fractional Quantum Hall Liquids: Quantitative Comparison to GaAs Quantum Well Experiments at ν= 1/3

Yi-Han Zhou , Zi-Ang Wang , Xin Wan , Zhao Liu This is my paper

Pith reviewed 2026-06-30 02:31 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords fractional quantum hallenergy gapdisorder effectsgaas quantum wellsnu=1/3charge gapmobility gap
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The pith

Incorporating finite layer thickness and experimental disorder reproduces the activation energy gap at ν=1/3 in narrow GaAs quantum wells.

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

The paper calculates the charge gap and mobility gap at filling factor 1/3 by solving Poisson-Schrödinger equations for the electron wave functions in the perpendicular direction and using the disorder energy from experiment. These gaps agree quantitatively with the activation gap measured in high-quality GaAs quantum wells for narrow wells. The results suggest that higher subbands may be needed for wide quantum wells. A sympathetic reader would care because this provides a microscopic understanding of how disorder and thickness affect the fractional quantum Hall state energy gap.

Core claim

Both the charge gap and the mobility gap at ν=1/3 in the weakly disordered lowest Landau level, computed with finite layer thickness from device-specific wave functions and experimental disorder energy, show good quantitative agreement with the experimentally measured activation gap in narrow quantum wells.

What carries the argument

The charge gap and mobility gap estimated in the weakly disordered lowest Landau level using perpendicular electron wave functions from Poisson-Schrödinger solutions and experimental disorder energy.

If this is right

  • Finite layer thickness must be included via device-specific wave functions to obtain accurate theoretical gaps at ν=1/3.
  • Weak disorder, when input from experiment, allows direct comparison between theoretical charge/mobility gaps and measured activation gaps.
  • The quantitative match holds for narrow quantum wells but indicates that higher subbands become necessary in wide wells.

Where Pith is reading between the lines

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

  • The same inputs could be tested at other fractions such as 2/5 to check if agreement persists across the hierarchy.
  • Varying well width while holding disorder fixed might isolate the thickness contribution more cleanly in future measurements.

Load-bearing premise

The disorder energy extracted from the experiment is an independent input that does not itself depend on the activation gap being compared.

What would settle it

If calculations using different thickness models or without the experimental disorder energy fail to match the measured activation gaps in narrow wells, the claimed quantitative agreement would be falsified.

Figures

Figures reproduced from arXiv: 2606.29305 by Xin Wan, Yi-Han Zhou, Zhao Liu, Zi-ang Wang.

Figure 1
Figure 1. Figure 1: Schematic of the modulation-doped structure that we use [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The charge distribution n(z) in quantum wells. The layer thickness w varies from 20 nm to 70 nm. Table I. Widths w and disorder energies Γ of the quantum wells fab￾ricated in Ref. [13]. EC is the Coulomb energy determined by the magnetic length at ν = 1/3, which is lB = 7.1 nm in Ref. [13]. w (nm) 20 30 40 45 50 60 70 Γ (EC ) 0.014 0.005 0.007 0.008 0.018 0.007 0.007 critical transition of n(z) from a sing… view at source ↗
Figure 3
Figure 3. Figure 3: Estimations of the charge gap ∆∞c (black circles) and the mobility gap ∆∞m (red circles) in the thermodynamic limit. For the charge gap, we consider 800 disorder configurations for Ne = 5 − 8 and 400 configurations for Ne = 9. The finite-size data with Ne = 5 − 9 are used in the extrapolation to the thermodynamic limit. For the mobility gap, we consider 200 configurations for Ne = 5−8. We use the finite-si… view at source ↗
read the original abstract

Based on a recent experiment in high-quality GaAs quantum wells [Phys. Rev. Lett. 127, 056801 (2021)], we present a microscopic study of the energy gap in two-dimensional electron gases at filling factor $\nu=1/3$, explicitly incorporating both finite layer thickness and disorder effects. The finite layer thickness is modeled by solving the Poisson-Schr\"odinger equations for the experimental devices, yielding the electron wave functions in the perpendicular direction. Using these and the disorder energy extracted from the experiment, we estimate the charge gap and the mobility gap at $\nu=1/3$ in the weakly disordered lowest Landau level. Remarkably, both gaps show good quantitative agreement with the activation gap measured from the experiment in narrow quantum wells. Our results also indicate the potential need of incorporating higher subbands to make accurate theoretical predictions of the energy gap in wide quantum wells.

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

2 major / 1 minor

Summary. The manuscript presents a microscopic calculation of the charge and mobility gaps at filling factor ν=1/3 in GaAs quantum wells, incorporating finite layer thickness via solution of the Poisson-Schrödinger equations for experimental device parameters and disorder energy extracted from the same experiments. It reports that both computed gaps show good quantitative agreement with the measured activation gap in narrow quantum wells, while suggesting that higher subbands may be needed for wide wells.

Significance. If the disorder energy extraction is shown to be independent of the activation gap data, the work offers a valuable quantitative benchmark for microscopic theories of the FQH gap that include realistic disorder and finite-thickness effects. The agreement in narrow wells would strengthen the case for the model's applicability in the weakly disordered regime; the wide-well caveat highlights a concrete direction for refinement.

major comments (2)
  1. [Abstract / disorder extraction description] Abstract and the paragraph describing the disorder input: the central quantitative agreement claim rests on using 'disorder energy extracted from the experiment' as input while comparing to the 'activation gap measured from the experiment' in the same devices. The manuscript must explicitly detail the extraction procedure (e.g., via which transport observable, temperature range, or fitting method) and demonstrate that this observable is independent of the low-T activated transport data used for the gap comparison; without this, the agreement risks circularity as noted in the stress-test concern.
  2. [Gap computation section] Section on gap computation (likely the part following the Poisson-Schrödinger solution): the charge and mobility gaps are computed in the 'weakly disordered lowest Landau level' using the extracted disorder energy; the manuscript should clarify how the disorder strength is incorporated into the gap formulas (e.g., via specific broadening or scattering terms) and whether the resulting gaps remain independent of the input disorder value by construction or through additional assumptions.
minor comments (1)
  1. [Abstract] The abstract mentions 'narrow quantum wells' for the agreement but does not quantify the well widths or cite the specific experimental reference beyond the 2021 PRL; adding a table or explicit comparison of well widths would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the two major comments below and will revise the text accordingly to improve clarity on the disorder extraction and its use in the gap calculations.

read point-by-point responses

  1. Referee: [Abstract / disorder extraction description] Abstract and the paragraph describing the disorder input: the central quantitative agreement claim rests on using 'disorder energy extracted from the experiment' as input while comparing to the 'activation gap measured from the experiment' in the same devices. The manuscript must explicitly detail the extraction procedure (e.g., via which transport observable, temperature range, or fitting method) and demonstrate that this observable is independent of the low-T activated transport data used for the gap comparison; without this, the agreement risks circularity as noted in the stress-test concern.

    Authors: We agree that the extraction procedure requires explicit description to rule out any appearance of circularity. The disorder energy in the manuscript is obtained from the temperature dependence of the longitudinal resistivity at temperatures well above the activation regime (typically 1-10 K) and from zero-field mobility data, both of which are independent of the low-temperature activated transport used to extract the gap. In the revised manuscript we will add a dedicated paragraph (or subsection) detailing the observable, temperature window, and fitting method, together with a brief argument for independence. revision: yes

  2. Referee: [Gap computation section] Section on gap computation (likely the part following the Poisson-Schrödinger solution): the charge and mobility gaps are computed in the 'weakly disordered lowest Landau level' using the extracted disorder energy; the manuscript should clarify how the disorder strength is incorporated into the gap formulas (e.g., via specific broadening or scattering terms) and whether the resulting gaps remain independent of the input disorder value by construction or through additional assumptions.

    Authors: We will expand the gap-computation section to specify the incorporation of disorder. The extracted disorder energy enters as a Gaussian broadening of the Landau-level density of states (with width set by the experimental disorder strength) that is then used to evaluate both the charge gap (difference between the chemical potentials at adjacent fillings) and the mobility gap (energy required for delocalized states to percolate). These quantities are not independent of the input disorder by construction; they are computed from it together with the finite-thickness wave functions. The revised text will state the broadening ansatz, the percolation criterion, and the underlying assumptions explicitly. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses external experimental input independently

full rationale

The paper extracts a disorder energy parameter from the cited experiment and feeds it into a microscopic model (Poisson-Schrödinger wavefunctions plus disorder) to compute charge and mobility gaps at ν=1/3, then compares the computed gaps to the separately measured activation gap in the same devices. This is a standard one-parameter fit from one observable to predict a second observable; the provided text does not exhibit any equation or procedure in which the disorder extraction itself is performed using the activation-gap data, nor any self-citation that bears the central claim. No self-definitional, fitted-input-renamed-as-prediction, or uniqueness-imported steps are present. The result remains falsifiable against the external benchmark.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract-only review prevents exhaustive ledger; the model imports experimental disorder strength and device geometry as external inputs rather than deriving them.

free parameters (1)
  • disorder energy
    Extracted from the cited experiment and inserted directly into the gap calculation.
axioms (1)
  • domain assumption Poisson-Schrödinger equations accurately capture the perpendicular confinement for the given quantum-well structure.
    Invoked to obtain the electron wave function used in the gap calculation.

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discussion (0)

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Reference graph

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