arxiv: 2605.10147 · v1 · submitted 2026-05-11 · ❄️ cond-mat.mes-hall · cond-mat.str-el

Recognition: 2 theorem links

· Lean Theorem

Cascade of fractional quantum Hall states in 2D system

Chen Zhimou , Yan Jiaojie , Zhu Yuxuan , Cui Zhe , Pfeiffer Loren N. , West Kenneth W. , Baldwin Kirk W. , Gupta Adbhut

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Liu Yang Zhu Wei Luo Wenchen Wu Ying-Hai Yuan Shuai Lin Xi

Authors on Pith no claims yet

Pith reviewed 2026-05-12 03:34 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.str-el

keywords fractional quantum Hall effectcomposite fermionsfilling factorGaAs quantum welllongitudinal resistancehierarchy of statesin-plane magnetic field

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The pith

New resistance dips at 17/33 and 15/31 appear in ultrahigh-mobility GaAs wells and join a hierarchy of fractional quantum Hall states explained by composite fermion theory.

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

The paper reports systematic transport measurements on very high quality two-dimensional electron gases in GaAs quantum wells down to millikelvin temperatures. In addition to previously known states, clear dips in longitudinal resistance emerge at filling factors 17/33 and 15/31. Most of the observed fractions between zero and two can be accounted for as integer quantum Hall states of composite fermions, while a smaller set requires residual interactions among those fermions to produce fractional quantum Hall states of the composite particles themselves. The authors organize all the fractions into a single pattern that ranks their experimental visibility and thereby supplies an intuitive ordering of their relative strengths.

Core claim

In high-mobility GaAs/AlGaAs wells, new longitudinal resistance minima are detected at filling factors 17/33 and 15/31. When all observed fractions in the interval 0 < ν < 2 are collected, they fall into two classes: the majority arise from non-interacting composite fermions filling integer Landau levels, while the remainder correspond to fractional quantum Hall states formed by composite fermions that interact through residual forces. The data are summarized in a compact pattern that accounts for the relative prominence of each state under the experimental conditions.

What carries the argument

Composite fermion theory in which electrons bind to an even number of magnetic flux quanta, after which the resulting particles experience a reduced effective field and can form either integer or fractional quantum Hall states depending on whether residual interactions are neglected.

If this is right

Most fractions are explained without invoking interactions among composite fermions.
A few fractions require residual composite-fermion interactions and therefore test the strength of those interactions.
In-plane magnetic field tilts produce different responses for different states, consistent with the proposed hierarchy.
The overall pattern supplies a ranking of state strengths that matches the order in which the states appear as sample quality improves.

Where Pith is reading between the lines

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

If the pattern holds, still-higher-mobility samples should reveal additional states at even smaller fractions in the same sequence.
The distinction between interaction-free and interaction-driven composite-fermion states suggests that controlled tuning of Landau-level mixing could selectively stabilize or suppress specific fractions.
Similar cascades may appear in other high-mobility two-dimensional platforms once their effective composite-fermion interactions are mapped.

Load-bearing premise

The observed resistance dips at 17/33 and 15/31 mark genuine gapped fractional quantum Hall states rather than transient or non-topological features.

What would settle it

Temperature-dependent activation measurements or finite-temperature scaling that show a clear energy gap closing at 17/33 and 15/31 would falsify the claim that they are true gapped states.

read the original abstract

The observation of the fractional quantum Hall (FQH) effect in 2D electron gases ushered in investigations of topological phases driven by strong electron correlations. Their remarkable features include fractionalized elementary excitations, gapless boundary states, and non-trivial quantum entanglement patterns. Thanks to persistent efforts in the building of new platforms and making higher-quality samples, a diverse plethora of FQH states have been unveiled in experiments. We report a systematic study of ultrahigh-quality GaAs/AlGaAs quantum wells with mobility up to 3.7*10^7 cm^2/V/s using quantum transport measurements in nuclear adiabatic demagnetization and dilution refrigerators down to 1 mK. In addition to many FQH states that have already been identified in previous work, new longitudinal resistance dips are observed at filling factors 17/33 and 15/31. The application of an in-plane magnetic field causes disparate variations of the FQH states. The theoretical foundation of these states is discussed in the framework of composite fermion theory. While most fractions can be explained as non-interacting composite fermions forming integer quantum Hall states, a few states correspond to FQH states of composite fermions that arise from residual interaction between them. We summarize the observed fractions in the range of 0 < {\nu} < 2 and propose a pattern to account for their experimental appearance that provides an intuitive picture about the relative strengths of different FQH states.

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.

Desk Editor's Note private letter to a colleague

New Rxx dips at 17/33 and 15/31 in high-mobility GaAs, but no Hall plateaus or gaps are reported to confirm they are incompressible FQH states.

read the letter

The main takeaway is that this work sees longitudinal resistance minima at filling factors 17/33 and 15/31 in ultrahigh-mobility GaAs wells at 1 mK. Those specific fractions have not been reported before, so the data adds two new points to the experimental list if they hold up as gapped states. The rest of the paper maps known fractions from 0 to 2 and fits them into the standard composite-fermion hierarchy, with most as integer states of CFs and a few requiring residual interactions among CFs. They also track how an in-plane field changes the strength of different minima, which gives a practical handle on the states. That in-plane dependence and the sample quality (mobility 3.7e7) are the parts that look solid and useful. The pattern they sketch for relative strengths of the observed fractions is a straightforward way to organize the data and matches what composite-fermion theory predicts for the hierarchy. The soft spot is exactly the one the stress-test note flags. The abstract and summary only describe Rxx dips plus the in-plane field behavior; there is no mention of corresponding Rxy plateaus, activated gaps, or other direct evidence that the minima are incompressible. Without those, the claim that these are true FQH states and the subsequent pattern rest on an assumption that minima equal topological order. The experimental conditions are good enough that the dips are worth checking, but the identification is still preliminary on the evidence given. This paper is for people who follow the GaAs FQH catalog and the composite-fermion hierarchy. A reader already working in that subfield can extract the new fractions and the in-plane field trends without needing the theoretical discussion. It is incremental rather than foundational, but the data come from strong samples and the analysis is standard, so the work is coherent on its own terms. I would send it to peer review so referees can ask for the missing plateau and gap data and see whether the full dataset supports the assignments.

Referee Report

2 major / 2 minor

Summary. The manuscript reports systematic quantum transport measurements in ultrahigh-mobility GaAs/AlGaAs quantum wells (mobility up to 3.7×10^7 cm²/V/s) at temperatures down to 1 mK. In addition to previously known fractional quantum Hall states, new longitudinal resistance dips are observed at filling factors 17/33 and 15/31. These observations, together with in-plane magnetic field dependence, are interpreted in the composite-fermion framework: most states are assigned to integer quantum Hall states of composite fermions, while a subset are attributed to fractional states of composite fermions arising from residual interactions. The authors summarize all observed fractions for 0 < ν < 2 and propose a phenomenological pattern to explain their relative experimental strengths.

Significance. If the new resistance minima correspond to gapped incompressible states, the work extends the experimental catalog of FQH fractions in the lowest Landau level and supplies a useful intuitive hierarchy for their stability. The combination of record mobility and millikelvin temperatures is a clear experimental strength that enables detection of weaker states; the composite-fermion classification follows established theory without introducing new free parameters.

major comments (2)

[Experimental results] Experimental results section: The assignment of the R_xx dips at ν=17/33 and 15/31 to true gapped FQH states rests on the assumption that minima alone indicate incompressibility. No corresponding quantized Hall plateaus in R_xy or temperature-activated transport gaps are reported, contrary to the criteria used for established states in the introduction and prior literature cited therein.
[Theoretical interpretation] Theoretical discussion: The distinction between non-interacting composite-fermion integer states and residual-interaction fractional states for the new fractions is stated qualitatively but lacks explicit comparison to calculated gaps, wave-function overlaps, or numerical predictions that would make the classification falsifiable.

minor comments (2)

[Abstract] The abstract refers to 'disparate variations' of FQH states under in-plane field; the main text should quantify which states strengthen or weaken and at what in-plane field values.
[Figures] Figure captions and data presentation would benefit from explicit labels of sample mobility, base temperature, and exact filling-factor values for each trace to facilitate direct comparison with other experiments.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable feedback on our manuscript. We appreciate the recognition of the experimental strengths and the significance of the new observations. Below, we address each major comment in detail and indicate the revisions made to the manuscript.

read point-by-point responses

Referee: Experimental results section: The assignment of the R_xx dips at ν=17/33 and 15/31 to true gapped FQH states rests on the assumption that minima alone indicate incompressibility. No corresponding quantized Hall plateaus in R_xy or temperature-activated transport gaps are reported, contrary to the criteria used for established states in the introduction and prior literature cited therein.

Authors: We agree that the observation of R_xx minima alone is not sufficient to conclusively prove incompressibility for the new states at 17/33 and 15/31, and that full quantization in R_xy or activation gaps would provide stronger evidence. In our high-mobility samples, these states are relatively weak, and achieving clear plateaus in R_xy is challenging due to the small gaps and possible disorder effects. However, the systematic appearance of the minima, their consistency with the composite fermion hierarchy, and the distinct response to in-plane magnetic fields (which suppress some states differently) support their identification as FQH states. We have revised the manuscript to explicitly discuss these limitations and to clarify that while the evidence is suggestive, further measurements would be ideal. Additionally, we note that similar criteria have been used in prior literature for identifying weak FQH states. revision: partial
Referee: Theoretical discussion: The distinction between non-interacting composite-fermion integer states and residual-interaction fractional states for the new fractions is stated qualitatively but lacks explicit comparison to calculated gaps, wave-function overlaps, or numerical predictions that would make the classification falsifiable.

Authors: The assignments are based on the well-established composite fermion theory, where the filling factors 17/33 and 15/31 can be mapped to specific integer or fractional fillings of composite fermions. For example, 17/33 corresponds to a state that can be interpreted as an integer CF state or one requiring residual interactions. We acknowledge that the distinction is presented qualitatively without direct numerical comparisons such as gap calculations or wavefunction overlaps. Such detailed numerical studies are computationally demanding for these fractions and are typically the subject of separate theoretical papers. We have added references to existing theoretical works that provide supporting calculations for similar states and have included a brief discussion on the phenomenological nature of our classification to make it more transparent. We believe this addresses the concern without requiring new extensive computations in this experimental manuscript. revision: partial

Circularity Check

0 steps flagged

No significant circularity: experimental observations interpreted via established composite-fermion framework

full rationale

The paper's core content consists of new experimental transport data (R_xx dips at 17/33 and 15/31) obtained in high-mobility GaAs wells, followed by an interpretive discussion that applies standard composite-fermion theory to classify the states as either integer QH states of non-interacting CFs or FQH states arising from residual CF interactions. The proposed pattern is explicitly a post-hoc summary of the observed filling factors to illustrate relative strengths, not a first-principles derivation or prediction. No equations, fitted parameters, or self-citations are presented that reduce any claimed result to the input data by construction; the theoretical framework is drawn from prior independent literature rather than a self-referential chain. The derivation chain therefore remains self-contained and non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard quantum transport in 2D electron gases and established composite fermion theory from prior work; no new free parameters, axioms beyond domain assumptions, or invented entities are introduced.

axioms (1)

domain assumption Composite fermion theory describes the fractional quantum Hall states in GaAs 2D electron gases under perpendicular magnetic field.
Invoked in the abstract to classify observed fractions as integer or fractional states of composite fermions.

pith-pipeline@v0.9.0 · 5602 in / 1414 out tokens · 58408 ms · 2026-05-12T03:34:03.497839+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean (Jcost uniqueness, Aczél classification) washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

new longitudinal resistance dips are observed at filling factors 17/33 and 15/31... theoretical foundation... composite fermion theory... most fractions... non-interacting composite fermions forming integer quantum Hall states, a few states correspond to FQH states of composite fermions that arise from residual interaction
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

polar coordinate representation... trajectories corresponding to 2p = 2,4,6,8,10... pattern... relative strengths

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

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