Designing Large Two-Dimensional Arrays of Josephson Junctions for RF Magnetic Field Detection

Round 1

Reviewer 1 Report

In this paper, the authors propose a new geometry for parallel Josephson junction array in view of  applications such as magnetic field sensing. Based on their simulations, the new geometry improves the uniformity of the bias current across the width of the array and as a consequence the performance of the Josephson junctions array.

The work is certainly interesting for the community of researchers and technologists who deal with superconducting electronics; therefore it is recommended the publication in Electronics Journal after the following minor revisions.

1)    Add more recent SQUID references:    J. Clarke, A.I. Braginski (Eds.), The SQUID Handbook Vol. I: Fundamentals and Technology of SQUIDs and SQUID Systems, Wiley-VCH Verlag GmbH & Co. KgaA, Weinheim, 2004;  P. Seidel (Ed.), Applied Superconductivity: Handbook on Devices and Applications,Wiley, Weinheim, 2015; A.Vettoliere, P. Silvestrini and C. Granata, Superconducting quantum magnetic sensing in Quantum Materials, Devices, and Applications, Eds  Mohamed Henini and Marcelo Oliveira Rodrigues, Elsevier 2023. https://doi.org/10.1016/C2019-0-01977-2

2)    I would suggest deleting the points on page 2 and write them normally in the text (pag 2, lines 68-75).

3)    Scales in figures 2a, 2b and 4b are not very clear. Eliminate some intermediate values.

4)    In the conclusions, please comment more on the last sentence regarding the inapplicability of the model to short, long and nano junctions.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The authors reported their findings in two simulations on the magnetic field and current distributions in both micrometer-size and sub-micrometer-size Josephson arrays. The topic could be interesting if the simulations were designed properly. However, in the current manuscript, I cannot find that excitement in either science or technology advancement. The overall simulation design was incomplete, and the results were poorly presented. I am sorry that I cannot recommend the publication of this manuscript.

1.       The design of the simulations lacks justification. Everything seems to be simply a course assignment, where students just plug in the professor’s requirements into an open-source software to get the results. There is no scientific justification for using 7 and/or 11 branches? What can be learned from these simulations?

2.       What is the superconducting material used in these simulations? How do the material properties, such as superconducting coherence length and field penetration depth, affect the simulation results?

3.       What is the Josephson junction in this study? Is it formed by two large superconducting pads connected by a narrow region with the same superconducting materials? It is not clear in either the main text or the figure captions.

4.       When simulating the vector potential, what is the gauge used here? For the vector potential, only Ax is non-zero, while all other components are 0?

5.        Many terms were randomly used in the manuscript without definition. For example, it seems “grid”, “arrays”, and “branches” were all used to represent the same thing. What is the “barrier” in line 96? “quasi-periodic”, “non-periodic grid”, “Fourier components”, etc. were never mentioned when described the results. However, they just randomly appeared in “Discussion”. If those features were not shown in your results, how can you discuss them?

6.       A lot of key information was missing. For example, “these initial values” mentioned in line 104 never shown in the manuscript. For the iteration, what is the convergence criterion? X, y, z directions in Figures 2 and 4 were missing.

7.       Units of physical quantities were missing. For example, quantities reported in Table 1 and 2, lines 156-157.

8.       There could be some other scientific errors as well. For example, the \Delta A_x in equation (2) should be spatial differential instead of difference. (d/dj)^2 in line 96 is meaningless. If d is a variable (or magnetic thickness of the junction barrier?), then it can be simplified to j^{-2}; if d is the differential operator, then which quantity this operator should act on?

Many incomplete sentences in this manuscript, which greatly hinder the understanding of the manuscript. For example, "a nearly ideal share of 1/11 in the next pair of branches; and an excess of about 0.08...0.12% in the inner branches." (lines 117-118).

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

This work studies an improved design of 2D Josephson junctions (JJ) arrays for better magnetic field detection. The authors numerically calculate the current distribution of several models including high temperature superconductor nanostructures with misalignment considered. They find that this geometry can enhance the uniformity of the current distribution in the array. Before this paper can be considered for publication, I would like the authors to address the following questions and comments.

1.     In general, although authors introduce the background in the introduction section as well as a brief summary of their work, I feel they should add one paragraph to highlight the motivation and importance of their work before summarizing their results. Adding more details can help general readers to better understand the motivation/scope of this paper.

2.     While authors show the numerical results for a parallel array of N JJ (such as figure 1), they don’t really show the calculations for long JJ or long JJ arrays. Although they claim that “the same is expected for long JJ and long JJ arrays”, they need to at least show the numerical results similar to figure 1 for these cases.

3.     In the abstract, the authors suggest that this new design can potentially push the magnetic field detectors to a large scale and “larger sensitivity”. However, they don’t really explain how this design could lead to better sensitivity in the main text. would be great if the authors can explain this.

4.     In the conclusion, the authors summarize the main findings of the work, claiming that this 2-layer structure design has several advantages. It would be good if they can specifically mention these advantages in the conclusions and also compare this with current designs (either here or in the introduction) to highlight the importance their work.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors have made a thorough edits on the main text, which greatly increases the readability of the manuscript. I'd like to suggest a publication of this manuscript after some minor English improvement.

Minor English editing is required. Some unconventional notions, such as "4 ... 5 iterations", can be replaced by normal texts.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

i am satisfied with the current version and can now recommend it for publication. 

Author Response

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Author Response File: Author Response.pdf