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arxiv: 2604.09440 · v1 · submitted 2026-04-10 · ❄️ cond-mat.supr-con

Realistic Pearl vortices in thin film superconductors

Aur\'elien Balzli , Louk Rademaker , Giulia Venditti This is my paper

Pith reviewed 2026-05-10 16:17 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords thin film superconductorsvortex magnetic fieldPearl vortexGinzburg-Landaumagnetic screeninguniversal curvetwo-dimensional superconductivity
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The pith

In sufficiently thin superconducting films with κ = 1/√2, the magnetic screening around a vortex follows a universal curve that scales with the film thickness rather than exponential or Pearl power-law decay.

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

The paper examines the magnetic field profiles of vortices in thin-film superconductors using the Ginzburg-Landau framework. It demonstrates that for realistic values of the Ginzburg-Landau parameter κ equal to one over the square root of two in sufficiently thin films, the screening is neither the exponential decay expected in bulk materials nor the power-law decay predicted by Pearl. Instead, a universal curve emerges that scales with the sample thickness, consistent with the Pearl length but indicating reduced magnetic screening in two-dimensional superconductors. This finding helps quantify the crossover from bulk-like to thin-film behavior and provides better length scales for analyzing experimental data.

Core claim

In thin films with the Ginzburg-Landau parameter set to κ = 1/√2, the magnetic field variation around a vortex core is captured by a universal function of distance scaled by the film thickness, revealing a screening behavior that differs from both three-dimensional bulk superconductors and the two-dimensional Pearl model.

What carries the argument

Numerical solution of the thin-film Ginzburg-Landau equations for the vector potential around a vortex, with κ fixed at 1/√2, to obtain the thickness-dependent universal magnetic field profile.

If this is right

  • The thickness dependence is consistent with the seminal Pearl length and indicates reduced magnetic field screening in two-dimensional superconductors.
  • The crossover from bulk-like to thin superconductors can be quantified with different screening length-scales.
  • These length-scales become relevant for analyzing experimental data on vortices in thin films.

Where Pith is reading between the lines

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

  • The universal curve may require reanalysis of existing STM or magneto-optical measurements of vortex fields in atomically thin superconductors.
  • The model could be tested by varying film thickness in a single material to map the predicted scaling collapse.
  • Extensions to include finite lateral size or weak disorder would show how the universal profile breaks down.

Load-bearing premise

The Ginzburg-Landau framework with fixed κ=1/√2 and the thin-film limit accurately capture the screening without additional effects such as disorder, finite lateral size, or non-local corrections that could alter the field profile.

What would settle it

A direct measurement of the magnetic field as a function of radial distance from an isolated vortex in a thin film with κ close to 0.707 that fails to collapse onto a single universal curve when distances are scaled by film thickness.

Figures

Figures reproduced from arXiv: 2604.09440 by Aur\'elien Balzli, Giulia Venditti, Louk Rademaker.

Figure 1
Figure 1. Figure 1: FIG. 1. Magnetic field profiles for different sample thick [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Magnetic field profiles in the center of films of [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Magnetic screening lengths. The values of [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
read the original abstract

We analyze magnetic field profiles of vortices in thin-film superconductors, shedding new light on this old and presumed settled problem. In sufficiently thin films with realistic Ginzburg-Landau parameter $\kappa = 1/\sqrt{2}$, the magnetic screening around a vortex core is neither exponential -- as is expected in bulk -- nor the power-law that was predicted by Pearl. Instead, a universal curve for the magnetic field variation appears that scales with the sample thickness. The thickness dependence is consistent with the seminal Pearl length, and serves as an indication of the reduced magnetic field screening present in two-dimensional superconductor. Finally, we quantify the crossover from bulk-like to thin superconductors, and establish different screening length-scales relevant for the analysis of experimental data.

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 / 2 minor

Summary. The manuscript analyzes magnetic field profiles of vortices in thin-film superconductors using the Ginzburg-Landau framework at fixed κ = 1/√2. It claims that in sufficiently thin films the screening is neither the exponential decay of bulk superconductors nor the power-law decay of the Pearl solution; instead a universal curve for B(r) emerges that scales with film thickness, consistent with the Pearl length and indicative of reduced screening in 2D. The work also quantifies the crossover from bulk-like to thin-film regimes and identifies relevant screening length scales for experimental data analysis.

Significance. If the central claim holds, the identification of a thickness-scaled universal curve would provide a practical, parameter-light description for interpreting vortex imaging and magnetometry data in thin superconducting films, directly relevant to 2D superconductivity and device applications. The choice of realistic κ = 1/√2 and the explicit crossover quantification are strengths that enhance applicability beyond idealized models. The result could serve as a benchmark for future work on vortex dynamics in reduced dimensions.

major comments (2)
  1. [§3, Eq. (7)] §3, Eq. (7): The derivation of the universal curve assumes the local London/GL screening equations remain valid in the thin-film limit; the manuscript does not test or bound the effect of non-local corrections (Pippard kernel or finite-coherence-length terms) on the claimed functional form, which is load-bearing for the assertion that the profile is neither exponential nor Pearl-like.
  2. [§4.1 and Figure 4] §4.1 and Figure 4: The quantification of the bulk-to-thin crossover and the different screening length scales lacks reported numerical methods, mesh convergence, or error estimates; without these it is unclear whether the extracted universal scaling is robust to discretization or to small deviations from exactly κ = 1/√2.
minor comments (2)
  1. [Abstract] The abstract states the central claim clearly but supplies no derivation outline or numerical approach; a one-sentence summary of the method in the abstract would improve accessibility.
  2. [Figure 2] Figure 2 would benefit from overlaying the bulk exponential and classic Pearl profiles on the same axes as the new universal curve to make the claimed distinction visually immediate.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our work's significance and for the detailed, constructive comments. We address each major comment point by point below, providing our response and indicating the revisions we will implement in the next version of the manuscript.

read point-by-point responses

  1. Referee: [§3, Eq. (7)] §3, Eq. (7): The derivation of the universal curve assumes the local London/GL screening equations remain valid in the thin-film limit; the manuscript does not test or bound the effect of non-local corrections (Pippard kernel or finite-coherence-length terms) on the claimed functional form, which is load-bearing for the assertion that the profile is neither exponential nor Pearl-like.

    Authors: We thank the referee for this observation on the local approximation underlying Eq. (7). Our analysis employs the standard Ginzburg-Landau framework, which is formulated as a local theory and is the conventional approach for vortex studies at κ = 1/√2. Non-local corrections (via the Pippard kernel or finite-ξ terms) are expected to be small when the film thickness d is the dominant scale and the mean free path is not excessively long. Nevertheless, we acknowledge that the manuscript does not explicitly bound these effects. In the revised manuscript we will add a paragraph following Eq. (7) that estimates the regime of validity by comparing ξ, λ, and d, and that references prior work on non-local modifications to Pearl vortices. This will clarify the conditions under which the reported universal curve remains robust. revision: yes

  2. Referee: [§4.1 and Figure 4] §4.1 and Figure 4: The quantification of the bulk-to-thin crossover and the different screening length scales lacks reported numerical methods, mesh convergence, or error estimates; without these it is unclear whether the extracted universal scaling is robust to discretization or to small deviations from exactly κ = 1/√2.

    Authors: We agree that explicit documentation of the numerical procedures is required to substantiate the robustness of the crossover quantification and the universal scaling. In the revised manuscript we will expand §4.1 with a new subsection that details the numerical methods (discretization scheme, mesh density, convergence criteria) together with quantitative error estimates for the extracted screening lengths. We will also include a short supplementary analysis demonstrating that small deviations from κ = 1/√2 leave the functional form of the universal curve and the location of the bulk-to-thin crossover unchanged within the reported precision. revision: yes

Circularity Check

0 steps flagged

No circularity: universal curve emerges from thin-film GL equations

full rationale

The paper solves the Ginzburg-Landau equations in the thin-film limit at fixed κ=1/√2 to obtain the magnetic field profile B(r). The claimed universal curve that scales with thickness and deviates from both bulk exponential and Pearl power-law forms is presented as a direct numerical or analytical consequence of those equations, not as a fitted parameter renamed as a prediction or as a self-citation load-bearing step. No load-bearing premise reduces by construction to the input data or to prior self-citations; the derivation remains self-contained against the model assumptions. The skeptic concern about local electrodynamics validity is a question of model applicability, not circularity in the derivation chain.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The claim rests on the standard Ginzburg-Landau theory as the modeling framework and on the choice of κ=1/√2 as a representative value; no new entities are introduced.

free parameters (1)
  • κ = 1/√2
    Selected as the realistic Ginzburg-Landau parameter for the thin-film analysis.
axioms (1)
  • domain assumption Ginzburg-Landau theory governs the superconducting order parameter and magnetic screening in the thin-film geometry
    Invoked throughout the abstract as the basis for calculating vortex field profiles.

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