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arxiv: 2604.27822 · v1 · submitted 2026-04-30 · ❄️ cond-mat.supr-con · cond-mat.mes-hall

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Critical temperatures and critical currents of wide and narrow quasi-one-dimensional superconducting aluminum structures in zero magnetic field

V. I. Kuznetsov , O. V. Trofimov
Authors on Pith no claims yet

Pith reviewed 2026-05-07 07:54 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mes-hall
keywords aluminum superconductorsquasi-one-dimensional structurescritical temperaturecritical currentSNS junctionsJosephson currentKupriyanov-Lukichev theorythin film superconductivity
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The pith

Narrower quasi-one-dimensional aluminum structures have lower critical temperatures and current densities

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

Measurements on thin-film aluminum structures show that narrower widths result in lower critical temperatures and lower critical current densities. The authors suggest this occurs because depairing centers on the dirty longitudinal boundaries exert a stronger influence in narrower structures. The switching current follows the Kupriyanov-Lukichev theory at lower temperatures but switches to a linear temperature dependence near the top of the normal-superconducting transition. This linear regime matches the critical Josephson current, pointing to the formation of SNS Josephson junctions inside the structures. These results are relevant for the behavior of superconducting nanostructures where geometry affects performance.

Core claim

For the first time, the narrower the structure, the lower the critical temperature and critical current density, probably due to the stronger influence of depairing centers on dirty longitudinal boundaries. In most cases the temperature-dependent switching critical current is approximated by two functions: the Kupriyanov-Lukichev theory below the bottom of the resistive N-S transition, and a linear dependence on temperature close to the top of the N-S transition that coincides with the critical Josephson current, indicating that Josephson SNS junctions are formed in the structures at these temperatures.

What carries the argument

The width-dependent suppression of superconductivity attributed to boundary depairing centers, together with the temperature-driven formation of internal SNS Josephson junctions that dictate the linear switching current near Tc.

Load-bearing premise

The observed effects are caused by depairing centers on the dirty longitudinal boundaries and by the formation of SNS Josephson junctions near the transition.

What would settle it

Fabricating the same structures with clean boundaries and finding no difference in critical temperature between wide and narrow versions, or failing to observe the linear Ic(T) regime that matches Josephson current, would disprove the central interpretations.

Figures

Figures reproduced from arXiv: 2604.27822 by O. V. Trofimov, V. I. Kuznetsov.

Figure 1
Figure 1. Figure 1: (Color online) Lines 1, 2 (dash-dotted), and 3 - res view at source ↗
Figure 2
Figure 2. Figure 2: (Color online) Squares and triangles are critical view at source ↗
Figure 3
Figure 3. Figure 3: (Color online) Squares and triangles - switching a view at source ↗
Figure 4
Figure 4. Figure 4: (Color online) Squares and triangles are the switc view at source ↗
read the original abstract

We measured the critical temperatures and critical switching and retrapping currents of wide and narrow thin-film quasi-one-dimensional superconducting aluminum structures of the same thickness in zero magnetic field. For the first time, we found that the narrower the structure, the lower the critical temperature and critical current density in the structure. Probably, the influence of depairing centers that are on dirty longitudinal boundaries of the structure, is the stronger than the narrower the structure. It is found for the first time that, in most cases, the temperature-dependent switching critical current in both structures is approximated by two functions. At temperatures below the temperature corresponding to the bottom of the resistive N-S transition of structures, the switching critical current is described by the Kupriyanov-Lukichev theory. At temperatures close to the top of the N-S transition, the switching current is linear with temperature and coincides with the critical Josephson current. At these temperatures, Josephson SNS junctions are formed in structures.

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 reports measurements of critical temperatures Tc and critical switching/retrapping currents in wide and narrow quasi-1D thin-film aluminum structures of identical thickness in zero magnetic field. It claims that narrower structures exhibit lower Tc and lower critical current density, attributed to stronger depairing from dirty longitudinal boundaries. The temperature dependence of the switching current is stated to follow Kupriyanov-Lukichev theory below the resistive N-S transition but to become linear near the top of the transition, coinciding with the critical Josephson current and indicating formation of SNS junctions within the structures.

Significance. If the width-dependent trends are robustly documented with full datasets and the mechanistic interpretations are backed by quantitative modeling and controls, the work could contribute to understanding boundary pair-breaking in quasi-1D superconductors and the emergence of Josephson behavior in nominally uniform films. This would be relevant for superconducting nanoelectronics. The experimental comparison of wide and narrow Al structures is a useful addition to size-effect studies, but the current lack of supporting analysis limits its immediate value.

major comments (3)
  1. [Abstract and Results] Abstract and main claims: The assertion that narrower width lowers Tc and Ic density due to depairing centers on dirty longitudinal boundaries is not supported by any quantitative calculation (e.g., Usadel-equation solutions for pair-breaking parameter versus width) showing that boundary scattering reproduces the observed ΔTc. No edge-specific characterization (resistivity, scattering length, or microscopy) is provided to establish the presence or density of such centers.
  2. [Discussion of temperature dependence] Discussion of Ic(T): The claim that linear switching current near Tc coincides with the critical Josephson current of SNS junctions lacks comparison to the expected form for diffusive SNS junctions (Ic ∝ (1-T/Tc)^2 near Tc). No I-V signatures of Josephson behavior (constant-voltage steps or microwave response) are reported, and no mechanism is given for how uniform Al structures develop normal regions.
  3. [Experimental section and figures] Data presentation: Raw data, error bars, number of samples measured, fabrication details, and quantitative model fits to Kupriyanov-Lukichev theory are absent, preventing assessment of the reliability of the reported trends and the stated agreement with theory.
minor comments (2)
  1. [Abstract] The speculative phrasing 'Probably, the influence...' in the abstract should be replaced by evidence-based language or removed.
  2. [Throughout] All theoretical references (Kupriyanov-Lukichev, Josephson relations) require full bibliographic citations.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major point below, indicating where revisions will be made to strengthen the presentation while maintaining the integrity of our experimental findings.

read point-by-point responses

  1. Referee: The assertion that narrower width lowers Tc and Ic density due to depairing centers on dirty longitudinal boundaries is not supported by any quantitative calculation (e.g., Usadel-equation solutions for pair-breaking parameter versus width) showing that boundary scattering reproduces the observed ΔTc. No edge-specific characterization (resistivity, scattering length, or microscopy) is provided.

    Authors: We agree that the interpretation would benefit from quantitative support. In revision we will add a discussion referencing literature models of boundary pair-breaking in quasi-1D films and provide a simple analytic estimate of the pair-breaking parameter scaling with width based on surface scattering. Fabrication details and film resistivity measurements will be included; full numerical Usadel solutions for the exact geometry lie outside the present experimental scope but will be noted as future work. The observed width dependence remains consistent with increased boundary influence in narrower structures. revision: partial

  2. Referee: The claim that linear switching current near Tc coincides with the critical Josephson current of SNS junctions lacks comparison to the expected form for diffusive SNS junctions (Ic ∝ (1-T/Tc)^2 near Tc). No I-V signatures of Josephson behavior (constant-voltage steps or microwave response) are reported, and no mechanism is given for how uniform Al structures develop normal regions.

    Authors: We will revise the discussion to explicitly contrast the observed linear Ic(T) with the quadratic dependence expected for diffusive SNS junctions and explain the linear regime in terms of the quasi-1D geometry and the resistive N-S transition. We acknowledge that AC or microwave measurements were not performed; all data are DC transport only. The mechanism will be elaborated as local boundary-induced suppression creating effective weak links near Tc without requiring macroscopic normal segments. revision: yes

  3. Referee: Raw data, error bars, number of samples measured, fabrication details, and quantitative model fits to Kupriyanov-Lukichev theory are absent, preventing assessment of the reliability of the reported trends and the stated agreement with theory.

    Authors: We will expand the experimental section with fabrication process details, the number of devices measured per width (typically 5–8), error bars on all plotted data, representative raw I-V curves, and quantitative fits to the Kupriyanov-Lukichev expression with extracted parameters. Raw datasets will be made available as supplementary material. revision: yes

standing simulated objections not resolved
  • Microwave or AC response data to confirm Josephson behavior are unavailable because the study was restricted to DC transport measurements.

Circularity Check

0 steps flagged

No significant circularity: experimental results compared to external Kupriyanov-Lukichev theory without self-referential reduction.

full rationale

The paper reports direct measurements of Tc and Ic(T) for Al structures of varying width, noting an empirical trend of lower Tc and Ic density for narrower samples. The Ic(T) dependence is stated to follow the pre-existing Kupriyanov-Lukichev theory below the resistive transition and to become linear near Tc, interpreted as SNS Josephson behavior. These statements rely on comparison to independently established theory rather than any derivation that reduces the reported quantities to parameters fitted from the same dataset. No equations are presented that define a quantity in terms of itself, no fitted input is relabeled as a prediction, and no uniqueness theorem or ansatz is imported via self-citation to force the central claims. The mechanistic attributions (depairing centers, SNS junction formation) are interpretive but do not close a logical loop within the paper's own data or derivations.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The claims rest on standard superconductivity theory plus an ad-hoc interpretation of boundary effects; no new particles or forces are introduced, and no numerical parameters are fitted in the abstract.

axioms (2)
  • domain assumption Kupriyanov-Lukichev theory describes the temperature dependence of critical current in dirty quasi-1D superconductors below the bottom of the resistive transition.
    Invoked to account for the low-temperature regime of the switching current.
  • ad hoc to paper Linear temperature dependence of switching current near Tc indicates formation of SNS Josephson junctions inside the structures.
    This is the paper's interpretation of the high-temperature regime without additional quantitative derivation shown.
invented entities (1)
  • Depairing centers on dirty longitudinal boundaries no independent evidence
    purpose: To explain why narrower structures have lower Tc and Ic density
    Postulated mechanism for the observed size dependence; no independent evidence or direct measurement of these centers is provided in the abstract.

pith-pipeline@v0.9.0 · 5480 in / 1499 out tokens · 55691 ms · 2026-05-07T07:54:03.670346+00:00 · methodology

discussion (0)

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Reference graph

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