Possible Superconductivity in Very Thin Magnesium Films

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

 The study utilizes a modified Eliashberg framework to analyze the dependence of superconducting critical temperature (Tc) on film thickness, predicting that magnesium can exhibit superconductivity under very specific conditions. The text is clear, and the objectives are straightforward and effectively conveyed through the equations. However, it is not explicitly explained why only magnesium is predicted to show this phenomenon. If another pure element possesses a similar Eliashberg electron-phonon function, could it also exhibit superconductivity? I noticed that the answers to this question are in the paper by the same authors, which was submitted to arXiv on February 17. This article is a case study, a specific instance of what is presented in the other paper. The authors should clarify this to the readers and, most importantly, this journal. With this, the article becomes original only from Section 3 onward. The article has merit, but it needs to be restructured to ensure transparency.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This theoretical paper is devoted to a very interesting topic of possible emergence of a superconducting state in materials that initially in their bulk state cannot be superconducting. From the formal point of view, this manuscript is a continuation of the authors' recent publication Quantitative Eliashberg theory of the superconductivity of thin films in Journal of Physics: Condensed Matter. 
In general, I have positive impressions of the manuscript, but the authors need to clarify a number of details and answer questions, after which I will be able to decise about the probable publication.

1) The authors should mention the role of fluctuations in predicting the critical temperature of very thin films and how significant can the Ginzburg-Levanyuk number be in this case?

2) Since the authors are actually considering the case of a rectangular potential well, how many real energy levels can it have in the context of this problem? Only one?

3) What exactly do the authors mean by the change in the shape of the Fermi surface? Is it a topological Lifshitz transition?

4) Will there be a geometric dependence of the coherence length, i.e., a dependence on the film thickness?

I also have a number of technical comments. 
1) The angstrom unit is spelled and labeled differently than in Figures 1-3.
2) Why is \omega_c not equal to the Debye frequency for magnesium in this case?
3) Does changing the cutoff frequency greatly affect the final results, since as seen in equation (1) the series is not convergent? Or did the authors use the standard BCS trick of adding and subtracting series by Matsubara frequencies?

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors clearly indicate that this is their original work and now correctly cite the article.

Reviewer 2 Report

Comments and Suggestions for Authors

I am grateful to the authors for clarification. I recommend this interesting manuscript for publication.