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Impurity effect and vortex cluster phase in mesoscopic type-1.5 superconductors

by Tian-Yi Han, Guo Wang, Jie Li, Hai Huang

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Submission summary

Authors (as registered SciPost users): Guo Wang
Submission information
Preprint Link: scipost_202411_00012v2  (pdf)
Date submitted: July 24, 2025, 6:06 a.m.
Submitted by: Guo Wang
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Experiment
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Phenomenological

Abstract

Based on two-band time-dependent Ginzburg-Landau theory, we study the electromagnetic properties of two-band mesoscopic superconductors. We perform the numerical simulations with the finite element method, and determine the minimum sample size Lc for the existence of the type-1.5 superconductivity from the obtained phase diagram in the absence of impurity. Meanwhile in the presence of an isotropic impurity, our numerical results reveal that the vortex cluster state induced by the attractive defect potential will gradually appear in the mesoscopic system with the sample size L<Lc, and the critical defect strength is about 0.2 in the Tc disorder model. In addition, we also investigate the effect of anisotropic defect structures and multiple correlated disorders on the patterns of magnetic vortex distributions. Our theoretical study thus indicates that the diversity of impurity depositions has a significant influence on the semi-Meissner state in mesoscopic type-1.5 superconductors.

Author indications on fulfilling journal expectations

  • Provide a novel and synergetic link between different research areas.
  • Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
  • Detail a groundbreaking theoretical/experimental/computational discovery
  • Present a breakthrough on a previously-identified and long-standing research stumbling block

List of changes

We would like to thank the editor and anonymous referees for very inspiring suggestions. We have provided the point-by-point responses to comments from the reviewers, see file attachments "Type-1.5-response-1.pdf", "Type-1.5-response-2.pdf" and "Type-1.5-response-3.pdf" for detail.
Current status:
Has been resubmitted

Reports on this Submission

Report #2 by Anonymous (Referee 1) on 2025-9-20 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202411_00012v2, delivered 2025-09-20, doi: 10.21468/SciPost.Report.11972

Strengths

While the morphology of vortex clusters in clean type-1.5 superconductors was studied in many works, the effects of pinning and defects have not been well investigated. This study explored a subject that is experimentally relevant and timely. It is especially timely because of the 2023 Science paper by Kathryn Molel and Yusuke Iguchi as well as works from Hong Ding's and Yihua Wang's groups that explicitly demonstrated the composite nature of vortices in multiband systems, directly related to the type-1.5 concept.

Weaknesses

In a long-term perspective, it would be interesting to expand that study and explore the effects as a function of interband Josephson coupling. Also, it would be interesting to see the modelling of larger-scale disorder, but that is beyond the scope of the current work.

Report

The authors study the effects in magnetically-coupled condensates. While other couplings are also interesting, that is the most generic coupling, which makes this study a clear exploration of the well-defined problem; many of the results will also qualitatively apply to the cases where fractional vortices are confined not only electromagnetically but also by Josephson coupling. Hence I recommend acceptance of this study.

Recommendation

Publish (meets expectations and criteria for this Journal)

  • validity: high
  • significance: good
  • originality: high
  • clarity: good
  • formatting: good
  • grammar: good

Author:  Wang Guo  on 2025-10-27  [id 5951]

(in reply to Report 2 on 2025-09-20)
Category:
answer to question
suggestion for further work

We would like to thank the editor and the anonymous referee for the comments and suggestions on the manuscript. We would also like to appreciate the reviewer's recognition of our research work and the decision to recommend our manuscript for publication. According to the referee's suggestion, we will investigate the effects of interband Josephson coupling and try to develop a larger-scale disorder model for two-band mesoscopic superconductors in the future studies.

Report #1 by Anonymous (Referee 2) on 2025-8-26 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202411_00012v2, delivered 2025-08-26, doi: 10.21468/SciPost.Report.11806

Report

The authors significantly improved the manuscript, providing the requested results for systems with different sizes and impurity strengths. In the updated text, the $L-\kappa_1$ phase diagram shows how the vortex cluster formation depends on the system size in the absence of impurity. The $g-\kappa_1$ phase diagram demonstrates how the presence of the impurities and their strength modify the cluster formation.
However, it should be clarified how these diagrams were obtained, and, specifically, which criteria were used to distinguish the vortex lattice and cluster phases. The studied systems have only 10-15 vortices, and the authors should motivate how they distinguish the phases while working with such a small number of vortices.
In addition to that, the current version of the text does not provide any details about the method used to draw the phase separation lines. I recommend that the authors specify which points they check in the parameter space and explain how they extrapolate the results.

Finally, I kindly ask the authors to increase the image resolution and the font size for Fig. 2 and Figs. 4-11.

Requested changes

1 - formally specify the difference between the vortex lattice phase and the vortex cluster phase
2 - describe the method used for the calculation of the phase diagrams
3 - increase the image resolution and the font size for Fig. 2 and Figs. 4-11

Recommendation

Ask for minor revision

  • validity: ok
  • significance: ok
  • originality: ok
  • clarity: good
  • formatting: good
  • grammar: -

Author:  Wang Guo  on 2025-10-27  [id 5952]

(in reply to Report 1 on 2025-08-26)
Category:
answer to question

We would like to thank the anonymous referee for very helpful suggestions. We have provided the point-by-point response to comments from Reviewer 2, see file attachment "Type-1.5-response-2.pdf" for detail.

Attachment:

Type-1.5-response-2.pdf

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