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arxiv: 2604.19443 · v1 · submitted 2026-04-21 · ❄️ cond-mat.supr-con · cond-mat.mtrl-sci

Competing Constraints on Superconductivity in Thick FeSe films

Ya-Xun He , Xing-Jian Liu , Qun Wang , Ting Chen , Hassan Ali , Jia-Ying Zhang , Bao-Juan Kang , Zheng Zhang
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Jun-Yi Ge
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Pith reviewed 2026-05-10 01:14 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mtrl-sci
keywords FeSe filmssuperconductivitycombinatorial synthesismachine learningc-axis lattice parameterstoichiometrydisorder scatteringtransition temperature
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The pith

In thick FeSe films the highest Tc arises when c-axis expansion competes with stoichiometry and defect scattering rather than from strain alone.

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

The paper develops a combinatorial deposition method that creates continuous gradients across many film properties at once. By growing and measuring 80 thick films and applying machine learning to the data, the authors show that Tc rises with c-axis lattice expansion but is also limited by how close the film composition is to ideal stoichiometry and by how much disorder scatters electrons. The highest transition temperature therefore occurs only inside a narrow window where all three factors are favorable simultaneously, which explains the wide scatter of earlier reported Tc values. The same approach produces an onset Tc of 17.1 K in thick films.

Core claim

The maximum superconducting transition temperature in thick FeSe films does not occur where compressive strain or c-axis expansion is largest. Instead it shifts to a position where favorable c-axis lattice parameter, near-ideal stoichiometry, and low defect scattering are simultaneously satisfied. Systematic measurements across 80 films combined with interpretable machine learning establish that stoichiometry and disorder scattering impose independent constraints that define a narrow optimization window rather than a monotonic dependence on any single variable.

What carries the argument

Off-center pulsed laser deposition that converts plume inhomogeneity into combinatorial libraries with continuous gradients in lattice parameter, composition, and disorder, analyzed by interpretable machine learning.

Load-bearing premise

The continuous gradients created by off-center deposition let the three key variables change independently without hidden correlations that could produce the same Tc pattern.

What would settle it

Preparing a film at the machine-learning-predicted optimum of c-axis spacing, stoichiometry, and low disorder and measuring an onset Tc well below 17.1 K would falsify the claimed constraints.

read the original abstract

Superconducting films emerge from the complex interplay of multiple growth parameters, making their optimization challenging. In iron-based superconductors, compressive strain is known to enhance the transition temperature (Tc) of FeSe films, yet reported Tc values vary widely even on identical substrates, indicating factors beyond strain are critical. Here, we develop a high-throughput off-center pulsed laser deposition strategy that transforms plume inhomogeneity into combinatorial FeSe film libraries with continuous gradients in lattice parameter, composition, and disorder. We discover that the maximum Tc does not coincide with the plume center but can shift off-center, revealing a competition between favorable c-axis expansion, stoichiometry, and defect scattering. Systematic characterization of 80 thick films (>50 nm), combined with interpretable machine learning, shows that besides the strong correlate of c-axis lattice parameter to Tc, the stoichiometry and disorder scattering impose critical constraints on the achievable transition temperature, defining a narrow optimization window rather than a simple monotonic relationship. This framework yields Tconset=17.1 K in thick FeSe films and establishes a general framework combining combinatorial synthesis with machine learning to uncover constrained optimization landscapes in complex functional materials.

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 / 3 minor

Summary. The paper claims that off-center pulsed laser deposition creates combinatorial libraries of thick (>50 nm) FeSe films with continuous gradients in c-axis lattice parameter, stoichiometry, and disorder. Systematic characterization of 80 films plus interpretable machine learning reveals that, beyond the known correlation of c-axis expansion with Tc, stoichiometry and defect scattering impose independent critical constraints that define a narrow non-monotonic optimization window rather than a simple monotonic relationship, yielding a Tc onset of 17.1 K.

Significance. If the central claim holds, the work supplies a concrete, data-driven demonstration that combinatorial synthesis with interpretable ML can map constrained optimization landscapes in complex functional materials. The reported 17.1 K value in thick films and the explicit separation of three competing factors would be a useful benchmark for iron-based superconductor optimization and a methodological template for other multi-parameter thin-film systems.

major comments (3)
  1. [Machine-learning analysis section (or equivalent results subsection describing feature inputs)] The load-bearing claim that stoichiometry and disorder impose constraints independent of c-axis lattice parameter rests on the assumption that off-center PLD gradients produce sufficiently orthogonal variation among these three quantities. The manuscript must supply a correlation matrix or variance-inflation-factor analysis for the ML input features (c-axis, composition, disorder metrics) to rule out multicollinearity that would make the attributed competition an artifact of deposition physics rather than intrinsic material constraints.
  2. [Interpretable machine learning results] The abstract and main text state that interpretable ML isolates the separate limiting effects, yet no explicit diagnostic (e.g., SHAP dependence plots, partial-dependence plots, or feature-importance ranking with uncertainty) is referenced that demonstrates the narrow window is not driven by hidden correlations. A concrete figure or table showing how the model attributes independent penalties to stoichiometry and disorder at fixed c-axis is required.
  3. [Experimental characterization and ML validation] The claim of a well-defined narrow optimization window and the specific value Tc onset = 17.1 K is presented without reported uncertainties on Tc measurements, on the ML-predicted boundaries, or on the location of the optimum within the library. Inclusion of error bars, cross-validation statistics, and the number of films near the reported optimum is necessary to establish that the window is statistically resolved rather than an interpolation artifact.
minor comments (3)
  1. [Abstract and throughout] Notation: “Tconset” should be written consistently as Tc,onset or defined on first use.
  2. [Introduction] The manuscript should cite prior reports of Tc variation on identical substrates to quantify how much of the observed spread is newly attributed to the stoichiometry/disorder competition versus previously known factors.
  3. [Figures showing film libraries] Figure captions for the combinatorial library maps should explicitly state the spatial resolution of the off-center gradients and the number of discrete measurement points per wafer.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which help clarify the presentation of our combinatorial synthesis and machine-learning results. We address each major comment below and will incorporate the requested analyses and clarifications in the revised manuscript.

read point-by-point responses

  1. Referee: [Machine-learning analysis section (or equivalent results subsection describing feature inputs)] The load-bearing claim that stoichiometry and disorder impose constraints independent of c-axis lattice parameter rests on the assumption that off-center PLD gradients produce sufficiently orthogonal variation among these three quantities. The manuscript must supply a correlation matrix or variance-inflation-factor analysis for the ML input features (c-axis, composition, disorder metrics) to rule out multicollinearity that would make the attributed competition an artifact of deposition physics rather than intrinsic material constraints.

    Authors: We agree that explicit verification of feature independence is necessary to substantiate the claim of competing constraints. The original manuscript did not include a correlation matrix or VIF analysis. We will add this in the revised version (as a new supplementary figure or table) using the measured values from the 80 films, confirming low multicollinearity (VIF < 5) among c-axis, stoichiometry, and disorder metrics. This supports that the gradients are sufficiently orthogonal and the observed competition reflects intrinsic material limits rather than deposition artifacts. revision: yes

  2. Referee: [Interpretable machine learning results] The abstract and main text state that interpretable ML isolates the separate limiting effects, yet no explicit diagnostic (e.g., SHAP dependence plots, partial-dependence plots, or feature-importance ranking with uncertainty) is referenced that demonstrates the narrow window is not driven by hidden correlations. A concrete figure or table showing how the model attributes independent penalties to stoichiometry and disorder at fixed c-axis is required.

    Authors: The manuscript employs interpretable ML to identify the separate roles of the three factors, but we acknowledge that the specific diagnostic plots were not included. In the revision we will add SHAP dependence plots (or equivalent partial-dependence plots with uncertainty bands) that hold c-axis fixed while varying stoichiometry and disorder. These will explicitly illustrate the independent penalties and the resulting narrow optimization window, directly addressing the concern about hidden correlations. revision: yes

  3. Referee: [Experimental characterization and ML validation] The claim of a well-defined narrow optimization window and the specific value Tc onset = 17.1 K is presented without reported uncertainties on Tc measurements, on the ML-predicted boundaries, or on the location of the optimum within the library. Inclusion of error bars, cross-validation statistics, and the number of films near the reported optimum is necessary to establish that the window is statistically resolved rather than an interpolation artifact.

    Authors: We agree that quantitative uncertainties are required to establish the statistical robustness of the reported optimum. The original manuscript states the Tc onset of 17.1 K from systematic measurements on 80 films but omits explicit error bars and validation details. We will revise the text and figures to include (i) error bars on Tc values derived from multiple resistivity measurements or fitting uncertainties, (ii) ML cross-validation statistics (e.g., mean R² and standard deviation across folds), and (iii) the number of films lying within the optimal region. This will demonstrate that the narrow window is statistically resolved. revision: yes

Circularity Check

0 steps flagged

No circularity: purely experimental combinatorial data plus ML interpretation

full rationale

The paper reports an experimental workflow: off-center PLD creates continuous gradients across 80 thick FeSe films, followed by direct measurements of c-axis parameter, stoichiometry, disorder, and Tc. Interpretable ML is then applied to the measured dataset to identify competing constraints. No equations, fitted parameters, or derivations appear that reduce the reported Tc=17.1 K optimum or the claimed narrow optimization window back to quantities defined by the authors' own prior fits or self-citations. The central claims rest on empirical variation and post-hoc statistical interpretation of independent measurements, remaining self-contained against external film-growth and superconductivity benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the experimental assumption that the off-center deposition creates well-controlled, independent gradients in the three variables and that the ML model correctly identifies causal constraints rather than correlations.

axioms (2)
  • domain assumption Compressive strain enhances Tc in FeSe films
    Invoked in the opening sentence as established background.
  • ad hoc to paper Interpretable machine learning can distinguish causal constraints from correlations in combinatorial film data
    Central to the interpretation of the 80-film dataset.

pith-pipeline@v0.9.0 · 5527 in / 1363 out tokens · 30419 ms · 2026-05-10T01:14:02.455625+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

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    1 Feng, Z. P. et al. Tunable critical temperature for superconductivity in FeSe thin films by pulsed laser deposition. Sci. Rep. 8, 4039 (2018). https://doi.org/10.1038/s41598-018-22291-z 2 Böhmer, A. E., Taufour, V ., Straszheim, W. E., Wolf, T. & Canfield, P. C. Variation of transition temperatures and residual resistivity ratio in vapor-grown FeSe. Phy...

    work page doi:10.1038/s41598-018-22291-z 2018

  2. [2]

    Chinese Phys. Lett. 29, 037402 (2012). https://doi.org/10.1088/0256- 307x/29/3/037402 5 Lei, B. et al. Evolution of High -Temperature Superconductivity from a Low -Phase Tuned by Carrier Concentration in FeSe Thin Flakes. Phys. Rev. Lett. 116 (2016). https://doi.org/10.1103/PhysRevLett.116.077002 6 Ying, T. P. et al. Discrete Superconducting Phases in FeS...

    work page doi:10.1088/0256- 2012