Peer Review History

Original SubmissionMarch 31, 2023
Decision Letter - Boris Malomed, Editor

PONE-D-23-09741Temperature effects on the calculation of the functional derivative of Tc with respect to α2F(ω)PLOS ONE

Dear Dr. Mesa,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Jun 22 2023 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

  • A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
  • A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
  • An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.
If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Boris Malomed

Academic Editor

PLOS ONE

Journal Requirements:

When submitting your revision, we need you to address these additional requirements.

1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and 

https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf

2. Please update your submission to use the PLOS LaTeX template. The template and more information on our requirements for LaTeX submissions can be found at http://journals.plos.org/plosone/s/latex

Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: 1. I cannot agree with the sentence: "The function α2F(ω) is obtained from the solution of the Eliashberg equations" (page 3, line 62).

It is generally known that the function α2F(ω) is an input parameter (together with the Coulomb pseudopotential) to the Eliashberg equations.

Eliashberg spectral function can be obtained theoretically (DFT calculations) or experimentally (tunneling experiment).

2. Paper is very interesting but more technical information is needed. Did Authors use their codes and are they widely available?

It would be great to can verify their correct operation.

3. It is possible to calculate the functional derivative of Tc on the base of the Allen-Dynes equation? Tc calculated using the Allen-Dynes equation depends on the a2F function.

After addressing this topics, I would recommend this paper for publication in PLOS ONE

Reviewer #2: The paper discusses the behavior of δTc/δα2 F(ω) as a function of frequency calculated for H3S at different pressures and temperatures. The authors present their findings in Figs. 2-4 and discuss the implications of their results.

Overall, the paper is well-written and the results are presented clearly. The figures are of good quality and support the conclusions drawn by the authors. However, some points should be addressed:

It would be helpful to provide more context about the significance of the results for non-experts in the field. While the authors briefly mention the importance of the behavior of δTc/δα2 F(ω) for determining optimal physical conditions of the superconducting state and estimating Tc, more information could be provided about why this is important and how it relates to current research in the field.

The authors mention in the abstract that their findings support the hypothesis that H3S under 155 GPa pressure achieves the highest experimental Tc. However, this is not discussed in detail in the main text. It would be helpful to explain how the results in Figs. 2-4 support this hypothesis, and to relate this to the broader literature on high-temperature superconductivity.

The authors mention that μ* shows an almost linear correlation with temperature in Fig. 4, but it is unclear from the figure whether this is true for all pressures or only for certain ones. It would be helpful to clarify this point in the caption or main text

**********

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

**********

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

https://doi.org/10.1371/journal.pone.0286855.r001
Revision 1
Author Response

Bogotá - Colombia, 18 de May 2023

PLOS ONE

Editorial Board

Dear Sirs,

The authors wish to acknowledge all the suggestions and comments given to this work by the reviewers. The ideas proposed by reviewers are very interesting and consistent with our work. The corrections made considerably improved the manuscript.

We present point-by-point responses to the comments from reviewers:

For Reviewer 1:

(1) I cannot agree with the sentence: "The function α2F(ω) is obtained from the solution of the Eliashberg equations" (page 3, line 62). It is generally known that the function α2F(ω) is an input parameter (together with the Coulomb pseudopotential) to the Eliashberg equations. Eliashberg spectral function can be obtained theoretically (DFT calculations) or experimentally (tunneling experiment).

Answer: We recognize the error in the mentioned sentence. So, the last part of the paragraph that contains the mentioned sentence was adjusted as follows:

“All that information is gathered in a function, the Eliashberg spectral function, or electron-phonon coupling function α2F(ω) (see Fig.1a), which can be obtained both theoretically (DFT calculations) and experimentally (tunneling experiment). The Eliashberg spectral function is obtained from the calculated phonon spectrum and the calculated electron–phonon matrix elements [cites]. The Coulombic repulsion between electrons was included through a parameter μ”

As can be seen in the manuscript:

(2) Paper is very interesting but more technical information is needed. Did Authors use their codes and are they widely available? It would be great to can verify their correct operation.

Answer: This work is based on a2F(w) calculations obtained by us in previous works, which were developed using Quantum ESPRESSO code. The functional derivatives were determined with the procedure widely used by Carbotte et al., which is based on the work of G. Bergmann and D. Rainer.

So, the Materials and Methods section was adjusted with the following clarification:

Here, the functional derivatives were obtained with the procedure widely used by Carbotte et al. [cites] which is based on the work of G. Bergmann and D. Rainer [cite].

As can be seen in the manuscript:

(3) It is possible to calculate the functional derivative of Tc on the base of the Allen-Dynes equation? Tc calculated using the Allen-Dynes equation depends on the a2F function.

Answer: The critical temperature formula proposed by Allen-Dynes could be understood as a result of the adjustment of the Eliashberg model with a tendency to the BCS limit. The Allen-Dynes equation depends indirectly on the function α2F(ω) through the electron-phonon coupling parameter (λ). This implies the possibly that δTc/δα2F(ω) could be obtained from it. We infer that this possible procedure would not achieve the generality of the one proposed by G. Bergmann and D. Rainer, since the Allen-Dynes equation contains physical considerations (phonon contributions simplified) that limit its scope. So, obtaining the functional derivative of Tc from Allen-Dynes equation would leave the phonon-detailed contribution incomplete.

In a recent work1 an improved analytical correction to the Allen-Dynes equation (which eliminates the systematic underprediction of Tc at higher temperatures) was reported, through a symbolic regression to a curated dataset of α2F(ω) spectral functions. Possibly through this new formulation of Tc formula a δTc/δα2F(ω) could be obtained, with relatively consistent results.

1https://www.nature.com/articles/s41524-021-00666-7

This subject is interesting, but we think that it must be analyzed in greater detail before making any proposal. For this reason, this idea will not be included in this manuscript.

For Reviewer 2:

(1) It would be helpful to provide more context about the significance of the results for non-experts in the field. While the authors briefly mention the importance of the behavior of δTc/δα2 F(ω) for determining optimal physical conditions of the superconducting state and estimating Tc, more information could be provided about why this is important and how it relates to current research in the field.

Answer: The following contextualization paragraph is included in the manuscript (introduction section)

“One of the possible contributions of theoretical physics in superconductivity is to clearly establish the fundamental physical foundations of the superconducting phenomenon in order to suggest with certainty, the line of experimental process to obtain superconductivity at room temperature in viable conditions for its application to large-scale. An example of the predictive effect of the theoretical approach on superconductivity was observed in the idea proposed by Ashcroft (cita), who stated that hydrogen-rich systems would be viable candidates to be high critical temperature (Tc) superconductors. This proposal gave rise to experimentation in this field with the discovery of new high-Tc superconductors, as H3S (Tc of 203 K at 155 GPa) or LaH10 (Tc of 260 K at 180 GPa), called hydride superconductors. This discovery gave a new impetus to this field of study, which had been stuck with the superconducting cuprates (Tc of 150 K) since 1995. The current difficulty with the hydride superconductors is in their high-pressure conditions of formation.

In this sense, evaluating possible new ways to predict Tc values in terms of well-defined physical conditions (such as pressure, doping, etc.) is an interesting line of work. Here, the study of the derivative seeks to establish the possible existence of patterns that lead to the determination of an optimum temperature of the system (superconducting critical temperature), which would also avoid the use of test or experimental Tc in first-principles calculations.”

As can be seen in the manuscript:

(2) The authors mention in the abstract that their findings support the hypothesis that H3S under 155 GPa pressure achieves the highest experimental Tc. However, this is not discussed in detail in the main text. It would be helpful to explain how the results in Figs. 2-4 support this hypothesis, and to relate this to the broader literature on high-temperature superconductivity.

Answer: The authors clarify that no mention was made in the abstract of the submitted manuscript that our results support “the hypothesis that H3S under 155 GPa pressure achieves the highest experimental Tc”. However, in the main text, the following affirmation was made: “These patterns seem to point to the system under 155 GPa pressure as the distinctive or particular condition of H3S, which is consistent with the fact that at this pressure, H3S achieves the highest experimental Tc”. We do not have the necessary results that allow us to support with certainty the validity of said assumption, remaining only as a coincidence. For this reason, the wording is adjusted to avoid any misinterpretation, remaining as follows:

The patterns of the derivative vs. Tc in the H3S reveal that these seem to have a characteristic behavior at a specific pressure (155 GPa).

As can be seen in the manuscript:

(3) The authors mention that μ* shows an almost linear correlation with temperature in Fig. 4, but it is unclear from the figure whether this is true for all pressures or only for certain ones. It would be helpful to clarify this point in the caption or main text.

Answer: The wording of the sentence was improved to make the idea clearer.

It is observed in Fig.4 that μ* vs T has a comparable trend between pressures. This could be assumed to be quasi-linear in a first approximation. However, this quasi-linearity is much more evident at higher pressure.

As can be seen in the manuscript:

The final version of the manuscript is attached (LaTeX format), in which all the adjustments made have been highlighted.

We hope that we have been clear in each answer.

Thank you for your consideration of our work,

Yours,

The Authors (José Camargo, Ivan Gonzalez, and Fredy Mesa).

Attachments
Attachment
Submitted filename: Response to Reviewers.pdf
https://doi.org/10.1371/journal.pone.0286855.r002
Decision Letter - Boris Malomed, Editor

Temperature effects on the calculation of the functional derivative of Tc with respect to α2F(ω)

PONE-D-23-09741R1

Dear Dr. Mesa,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Boris Malomed

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

https://doi.org/10.1371/journal.pone.0286855.r003
Formally Accepted
Acceptance Letter - Boris Malomed, Editor

PONE-D-23-09741R1

Temperature effects on the calculation of the functional derivative of Tc with respect to α2F(ω) 

Dear Dr. Mesa:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

If we can help with anything else, please email us at plosone@plos.org.

Thank you for submitting your work to PLOS ONE and supporting open access.

Kind regards,

PLOS ONE Editorial Office Staff

on behalf of

Prof. Boris Malomed

Academic Editor

PLOS ONE

https://doi.org/10.1371/journal.pone.0286855.r004

Open letter on the publication of peer review reports

PLOS recognizes the benefits of transparency in the peer review process. Therefore, we enable the publication of all of the content of peer review and author responses alongside final, published articles. Reviewers remain anonymous, unless they choose to reveal their names.

We encourage other journals to join us in this initiative. We hope that our action inspires the community, including researchers, research funders, and research institutions, to recognize the benefits of published peer review reports for all parts of the research system.

Learn more at ASAPbio .