Charging of Superconducting Layers in Arrays of Coupled Josephson Junctions for Overcritical Currents
Round 1
Reviewer 1 Report
The authors presented some results on IV-characteristics and charging of superconducting layeres for the stack of coupled Josephson junctions. The results are important for understanding the physics of coupled overdamped Josephson junctions.
There are some comments:
Line 47: There is no diffusion current in the sum below! The authors should describe the model clearly .
Line 92: Can the authors explain their statement?
Section 3.3: Results in this section are not explained well. Are there any difference between charge traveling waves at periodic and nonperiodic bounday conditions?
I could not find references to the paper [37]. It should be appear in the Introduction.
There are some misprints:
Line 49: This system... Which system?
Line 55: Extra "the".
Line 97: Should be amplitude of charge oscillations instead of charge.
The authors do reference to the experimental papers [29] and [30]. Can they arrange some comparison of their theoretical results?
To my mind the paper might be published after serious revision.
Author Response
Response to Reviewer 1
We would like to thank the reviewer for the careful and thorough reading of this manuscript and for the thoughtful comments and constructive suggestions, which help to improve its quality. Our response follows (the reviewer comments are in italic)
Comment:The authors presented some results on IV-characteristics and charging of superconducting layeres for the stack of coupled Josephson junctions. The results are important for understanding the physics of coupled overdamped Josephson junctions.
Reply:We appreciate the positive feedback from the reviewer, and are eager to make changes to make this manuscript better.
Comment:There are some comments:
Line 47: There is no diffusion current in the sum below! The authors should describe the model clearly .
Reply:We completed the description of the model. The presented formula (eq. 5) was obtained after the summation of superconducting, quasiparticle, displacement anddiffusion currents(p. 3, line 65 – 66).
Comment:Line 92: Can the authors explain their statement?
Reply:Significant voltage reduction in the stack can occur due to the modification of charge transport mechanism to a less dissipative one. We proposed to study the appearance of charging of superconducting layers and generation of charge traveling waves in order to identify it. (p.4 line 93 – 95).
Comment:Section 3.3: Results in this section are not explained well. Are there any difference between charge traveling waves at periodic and nonperiodic bounday conditions?
Reply:In case of nonperiodic boundary conditions the traveling wave is less stable, and the the average charge accumulated on the superconducting layers has a nonzero value. (p.7, line 172 – 175).
Comment:I could not find references to the paper [37]. It should be appear in the Introduction.
Reply:We introduced the work [29] ([37] in previous article version) in the Introduction. (p.2 line 35).
Comment:There are some misprints:
Line 49: This system... Which system?
Reply:We reformulated the sentence.
Comment:Line 55: Extra "the".
Reply: Corrected
Comment:Line
97: Should be amplitude of charge oscillations instead of charge.
Reply: Corrected
Comment:The authors do reference to the experimental papers [29] and [30]. Can they arrange some comparison of their theoretical results?
Reply: The existence of an additional branching for currents greater than the critical one was clearly identified by M. Liatty and al. [30]. From the Figure 4 of the mentioned article [30]can be clearly seen the voltage jumps similar to the transitions BC and DA from the Figure 1 of our article. Because points A and B correspond to different, currents hysteresis appears. In accordance to our hypothesis about the necessity of strong coupling and high values of dissipation parameter, M Lyatty et. al. observed additional branch on the IV characteristic of the YBCO nanowires (YBCO is characterized by the lowest distance and the strong coupling between the superconducting lyers) and the study was implemented for higher temperatures which is in correspondence with high values of dissipation parameter. Small differences between the form of simulated and experimental IV characteristics result from the finite width of YBCO nanowires and its imperfect crystalline structure.
(p. 4 – 5, line 97 -106).
Comment:To
my mind the paper might be published after serious revision.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This article presents simulations and theoretical analysis of Josephson junction array, considering the capacitive effects of each junction. The basic concept of the article is good and interesting, but unfortunately, I cannot recommend this manuscript for publication in Crystals journal. This manuscript relies strongly on the article "Charging of superconducting layers and resonance-related hysteresis in the current-voltage characteristics of coupled Josephson junctions" (ref. [25]). [25] displays mathematical analysis (Exactly the same as that presented in the proposed manuscript!) and experimental results of up to N=9 junctions. Indeed article [25] does not provide simulation results, so I guess that the novelty of the proposed article is to present simulations that support the [25] experimental results. Well, here's exactly the problem, I would expect the simulation to test cases where N is greater than 9 (Or at least equal to this value). It is not clear at all why it was decided to check the case (and only the case) of N=3? It could be more interesting to present graphs for a different number of junctions and test the hysteresis variability relative to that number.
Beyond that, there are a few other things that I recommend to the authors to modify before they try to resubmit this article for publication again:
1. The English level of the proposed manuscript is pretty poor and there are quite a few problems of grammar, I encourage you to get professional help on this issue.
2. It is very difficult to understand from the abstract what the article is actually about. In addition, it should be noted in the abstract that the article includes simulation results only.
3. Since the proposed manuscript relies heavily on article [25], I highly recommend explaining in the introduction that the simulations presented in the manuscript are based on the [25] experiment.
4. line 37 – " framework of capacitively coupled Josephson.." , what it is the framework? You should elaborate.
5. It is unclear how you came from the first equation to the second one, a qualitative explanation could help.
6. line 57 - I'm not sure that the expression you wrote for the coupling parameter (α) is accurate, please check.
7. chapter 3: The connection between the simulation and the experiment is not clear enough, it would have been appropriate to elaborate on the subject at the beginning of this chapter.
8. What software did you use to perform the simulations? It's worth mentioning.
9. Fig 1: Is the leap from point B to point C observed in any experiment that supports the simulation results? worth mentioning.
10. Fig 2: The same question as in 9, did this hysteresis observed in any experiment that supports the simulation results?
11. Fig 4: What is the "ellipse"?
12. Conclusions: the sentence - "The origin of branching consists in the generation of charging of the superconducting layers, which is due to the absence of screening in them." How one can understand this sentence from the proposed manuscript? I think it's misleading.
13. Conclusions: the sentence - "Charge traveling waves form an efficient mechanism for charge transport through the stack, which leads to voltage reduction for the traveling wave branch." This sentence makes no sense!
14. Conclusions: the sentence – "Presence of a large range of currents for which the charging appears makes such systems attractive for technological applications" - how does this sentence relate at all?
15. Conclusions: the sentence – "We observe the charging for arrays with different number of junctions (N ≥ 2), including large stacks" – for different number of junctions? You just checked the case which N = 3.
Author Response
Response to Reviewer 2
We would like to thank the reviewer for the careful and thorough reading of this manuscript and for the thoughtful comments and constructive suggestions, which help to improve its quality. Our response follows (the reviewer comments are in italic)
Comment:This article presents simulations and theoretical analysis of Josephson junction array, considering the capacitive effects of each junction. The basic concept of the article is good and interesting, but unfortunately, I cannot recommend this manuscript for publication in Crystals journal.
This manuscript relies strongly on the article "Charging of superconducting layers and resonance-related hysteresis in the current-voltage characteristics of coupled Josephson junctions" (ref. [25]). [25] displays mathematical analysis (Exactly the same as that presented in the proposed manuscript!) and experimental results of up to N=9 junctions. Indeed article [25] does not provide simulation results, so I guess that the novelty of the proposed article is to present simulations that support the [25] experimental results.
Reply:In the article [25] Yu. M. Shukrinov and M. A. Gaafar studied the resonance related hysteresis in a stack of Josephson junctions for small dissipation parameter values (from 0.05 to 0.3). The resonance related hysteresis consists of traveling wave branch and outermost branch and is situated in the current interval between the break point current and the critical current.
In our paper we extended the study of behavior of Josephson junctions arrays presented in the study} [25] \hl{for high values of dissipation parameters. We focused on the JJ arrays behavior for the currents grater than the critical one, where the novel features appear. We show that for highly dissipative systems the charging of the superconducting layers is generated for a wide range of currents. As a result, branching appears for overcritical currents in the IV-characteristic.
Comment:Well, here's exactly the problem, I would expect the simulation to test cases where N is greater than 9 (Or at least equal to this value). It is not clear at all why it was decided to check the case (and only the case) of N=3? It could be more interesting to present graphs for a different number of junctions and test the hysteresis variability relative to that number.
Reply:We completed our article with aplot of IV characteristics for arrays with different number of junctions (Fig. 4, p. 6). We mention that we effectuated simulations for alarge stack (up to 20 junctions), but did notinclude the results in the article for the following reasons: there are not any qualitative changes in the form of IV characteristic with increase of number of junctions, the voltage for large stacks is much higher than for stack with few junctions, that makes the graphical representation of the results less clear.
Comment:Beyond that, there are a few other things that I recommend to the authors to modify before they try to resubmit this article for publication again:
1. The English level of the proposed manuscript is pretty poor and there are quite a few problems of grammar, I encourage you to get professional help on this issue.
Reply:We have shown our article to a native English speaker for proofreading.
Comment:2. It is very difficult to understand from the abstract what the article is actually about. In addition, it should be noted in the abstract that the article includes simulation results only.
Reply:We have completed the abstract.
“In this work we effectuated the numerical simulations of phase dynamics of an array of Josephson junctions taking into account capacitive coupling between the neighboring junctions and diffusion current in the stack. We observed that, if we increase the coupling and the dissipation parameters, the IV characteristic changes qualitatively from the IV characteristics studied before [1]. For currents greater than the critical one, we obtained an additional branch in the IV characteristics. This branch is characterized by a lower voltage than the outermost one. Moreover, we obtained an additional charging of the superconducting layers in IV region for currents greater than the critical one. We studied the time evolution of this charging by the means of Fast Fourier Transform. We proved that the charge density wave associated with this charging has a complex spectral structure. In addition, we analyzed the behavior of the system for different boundary conditions, appropriate to different experimental setups.”Comment:3. Since the proposed manuscript relies heavily on article [25], I highly recommend explaining in the introduction that the simulations presented in the manuscript are based on the [25] experiment.
Reply:Wehaveexplained the connection between our article and the work [25]. Particularly, we put in evidence the difference in simulation parameters (low dissipation in work [25] and high dissipation in our article) and the ranges of currentsfor which the hysteresis appears (less than critical current in work [25]and overcritical currents in our work).(p.2, line 34 – 44).
Comment:4. line 37 – " framework of capacitively coupled Josephson.." , what it is the framework? You should elaborate.
Reply:The models framework is described in the section 2. (p.2 – 3, line 50 – 73).
Comment:5. It is unclear how you came from the first equation to the second one, a qualitative explanation could help.
Reply:We presented complete deduction of the equation (6) (p. 2 – 3, line 56 – 67).
Comment:6. line 57 - I'm not sure that the expression you wrote for the coupling parameter (α) is accurate, please check.
Reply:We checked the expression and provided the references. (p. 3, line 60 – 63).
Comment:7. chapter 3: The connection between the simulation and the experiment is not clear enough, it would have been appropriate to elaborate on the subject at the beginning of this chapter.
Reply:We have presented the comparison of the simulation results with the experiment effectuated by M. Lyatti at al. [30] (p. 4 – 5, line 94 – 106).
Comment:8. What software did you use to perform the simulations? It's worth mentioning.
Reply:We used a special program implemented in C++, the previous version of this program was published in [36], and the simulation algorithm was described in [20,25]. (p. 3 – 4, l. 73 – 76).
Comment:9. Fig 1: Is the leap from point B to point C observed in any experiment that supports the simulation results? worth mentioning.
Reply: The similar transition was presented in Fig.4 of reference [30] (M. Liatty et. al., 2018).
Comment:10. Fig 2: The same question as in 9, did this hysteresis observed in any experiment that supports the simulation results?
Reply: The similar transition was presented in Fig.4 of reference [30] (M. Liatty et. al., 2018).
Comment: 11. Fig 4: What is the "ellipse"?
Reply: We used an ellipse to mark the selected current region (1.36 I_c – 1.48 I_c). (p. 7, Fig 5.)
Comment: 12. Conclusions: the sentence - "The origin of branching consists in the generation of charging of the superconducting layers, which is due to the absence of screening in them." How one can understand this sentence from the proposed manuscript? I think it's misleading.
Reply: We explained more carefully the obtained results. (p.8 line 177 – 182).
Comment: 13. Conclusions: the sentence - "Charge traveling waves form an efficient mechanism for charge transport through the stack, which leads to voltage reduction for the traveling wave branch." This sentence makes no sense!
Reply: We explained more carefully the obtained results. (p.8 line 177 – 182).
Comment: 14. Conclusions: the sentence – "Presence of a large range of currents for which the charging appears makes such systems attractive for technological applications" - how does this sentence relate at all?
Reply: Wedelitedthis sentence.
Comment: 15. Conclusions: the sentence – "We observe the charging for arrays with different number of junctions (N ≥ 2), including large stacks" – for different number of junctions? You just checked the case which N = 3.
Reply: We checked the behavior of Jjs arrays with different number of junctions, and completed the article with the results (p. 6 – 7, line 144– 150and Fig. 4)
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
No comments
Author Response
Thank you very much for the previous comments. It helped a lot to improve our manuscript.
Reviewer 2 Report
Your answers and corrections are quite satisfay, unfortunately, the article is still not written properly.
1. I will recommend it for publication only with serious English-editing, few examples for sentences that you must re-edit:
a. "To modulate behavior of JJs arrays was proposed LC shunting of the JJs arrays" (Page 1 - lines 25-26)
b. "in the superconducting layers appears charging" (Page 1 - lines 30)
c. "Previously was studied charging for currents lower than the critical one." (Page 1 - line 31).
d. "Particularly, due to the charge oscillations appears resonant related hysteresis, and occurs significant voltage step in the breakpoint region." (Page 2 - lines 33-34).
e. "To implement simulations was used method described in the studies" (Page 3 - straight after line 73)
f. "with step in current dI up and then down. "(Page 3 - after line 73). Maybe to- "with current steps dI".
g. "With arrows are shown the directions of current next to the IV-characteristics " (Page 4 – Fig. 1).
h. The sentence: "Because points A and B correspond to different, currents hysteresis appears." (Page 5 – lines 99-100). Did you mean: "Because points A and B correspond to different currents, hysteresis appears."?
There are quite a few more comments on this subject. Please make sure this time that the article goes through serious proofreading.
2. Fig 3, d: the x axis is ω/(2 π ωp), ω should be the angular frequency (frequency in Hz multiplied by 2 π) so the ratio ω/(2 π ωp) should be an irrational number. So how does the integer number in the graph make sense? Apparently the answer to this is that the units of ωp is in Hz, please fix it.
3. Your method is based heavily on the following article and it also strengthens your claims, I recommend you to quote it:
https://doi.10.1103/PhysRevB.60.3666 ("Simulation of I − V hysteresis branches in an intrinsic stack of Josephson junctions in high- T c superconductors")
Beyond that, your equation 6 is an approximation of Equation 13 in this article, it is worth checking out your simulations results for the more general case rather than the approximation.
4. Page 1 - line 23: "which can play an important role in some technological applications". At the end of this sentence it is worth quoting articles about applications that can use the presented method, I recommend on the following two:
- https://doi.org/10.1080/09205071.2018.1535333 ("High sensitivity high Tc superconducting Josephson junction antenna for 200 GHz detection")
- https://doi.org/10.1088/0953-2048/26/11/115012 ("Towards large scale HTS Josephson detector arrays for THz imaging")
Good luck
Author Response
Response to Reviewer 2
We would like to thank the reviewer for the positive feedback and careful reading of this manuscript and for the thoughtful comments and constructive suggestions, which help to improve its quality. Our response follows (the reviewer comments are in italic)
Comment: our answers and corrections are quite satisfay, unfortunately, the article is still not written properly.
1. I will recommend it for publication only with serious English-editing, few examples for sentences that you must re-edit:
Reply: We corrected the sentences mentioned by the reviewer and other sentences, where the mistakes were observed.
Comment: a. "To modulate behavior of JJs arrays was proposed LC shunting of the JJs arrays" (Page 1 - lines 25-26)
Reply: The LC shunting of the JJ was proposed to modulate the its behaviour. (p.1 lines 27 -28)
Comment: b. "in the superconducting layers appears charging" (Page 1 - lines 30)
Reply: the charging appears in the superconducting layers (p.1 line 32)
Comment: c. "Previously was studied charging for currents lower than the critical one." (Page 1 - line 31).
Reply: The charging for currents lower than the critical one was studied previously. (p. 2 line 33)
Comment: d. "Particularly, due to the charge oscillations appears resonant related hysteresis, and occurs significant voltage step in the breakpoint region." (Page 2 - lines 33-34).
Reply: Particularly, the resonance related hysteresis [27] appears in the IV-characteristic due to the charge oscillations, and a significant voltage step occurs in the breakpoint region[30]. (p. 2 lines 35 – 37).
Comment: e. "To implement simulations was used method described in the studies" (Page 3 - straight after line 73)
Reply: We used the method described in the studies to implement simulations (p. 3 after line 75)
Comment: f. "with step in current dI up and then down. "(Page 3 - after line 73). Maybe to- "with current steps dI".
Reply: To calculate the voltages on each insulating layer, we ran the current from I min to I max with current steps δI up and then down. (p. 3 after line 75)
Comment: g. "With arrows are shown the directions of current next to the IV-characteristics " (Page 4 – Fig. 1).
Reply: The directions of current are shown with arrows next to the IV-characteristics. (p. 4 fig 1)
Comment: h. The sentence: "Because points A and B correspond to different, currents hysteresis appears." (Page 5 – lines 99-100). Did you mean: "Because points A and B correspond to different currents, hysteresis appears."?
Reply: Because points A and B correspond to different currents, hysteresis appears. (p. 5 lines 101 - 102)
Comment: There are quite a few more comments on this subject. Please make sure this time that the article goes through serious proofreading.
Reply:
Artificial JJs arrays can be replaced by thin films of layered high-Tc superconductors in technological applications (p. 1 lines 17 - 18) The breakpoint region (corresponding to transition of some junction in the array from resistive to superconducting state) was observed in that zone. (p. 1, lines 20 - 23) Moreover, the total current after the summation has the form (p. 3, after line 68) Only one branch exists for currents greater then the critical one (p. 4, lines 84 -85) M Lyatty et. al. observed an additional branch on the IV characteristic of the YBCO nanowires (where YBCO is characterized by the lowest distance and the strong coupling between the superconducting lyers) and the study was implemented for higher temperatures which is in correspondence with high values of dissipation parameter and is in agreement with our hypothesis about the necessity of strong coupling and high values of the dissipation parameter. (p. 5, lines 101 -107) In the system branching appears in the overcritical currents region for a number of junctions greater or equal to two. (p. 7, lines 147 – 149). The IV-characteristics are presented in the Fig. 4 only for selected values of the numbers of junctions. (p. 7, lines 151 - 152) The IV-characteristics for distinct junctions are shown in the inset of the figure 4. (p. 7 lines 160 - 161) The IV-characteristics for the corresponding direction of currents are presented with dark lines. (p. 8 fig 6) And some other minor corrections were made.Comment: 2. Fig 3, d: the x axis is ω/(2 π ωp), ω should be the angular frequency (frequency in Hz multiplied by 2 π) so the ratio ω/(2 π ωp) should be an irrational number. So how does the integer number in the graph make sense? Apparently the answer to this is that the units of ωp is in Hz, please fix it.
Reply: Thank you for the mistake identification. We replaced (2 π ωp) to ω. (page 6, fig 3 b, d; line 140 – 142).
Comment: 3. Your method is based heavily on the following article and it also strengthens your claims, I recommend you to quote it:
https://doi.10.1103/PhysRevB. ("Simulation of I − V hysteresis branches in an intrinsic stack of Josephson junctions in high- T c superconductors")
Reply: We added the proposed article to our literature review. (page 2, line 56)
Comment: Beyond that, your equation 6 is an approximation of Equation 13 in this article, it is worth checking out your simulations results for the more general case rather than the approximation.
4. Page 1 - line 23: "which can play an important role in some technological applications". At the end of this sentence it is worth quoting articles about applications that can use the presented method, I recommend on the following two:
- https://doi.org/10.1080/ ("High sensitivity high Tc superconducting Josephson junction antenna for 200 GHz detection")
- https://doi.org/10.1088/0953- ("Towards large scale HTS Josephson detector arrays for THz imaging")
Good luck
Reply: We mentioned proposed applications in the introduction. (page 1, line 23 – 25).
Particularly, high sensitivity detectors for THz and hundreds of GHz electromagnetic waves imagining were designed recently.Author Response File: Author Response.pdf
Round 3
Reviewer 2 Report
I am pleased to see that the level of English has improved.
You did not consider one of the essential questions I asked you:
Beyond that, your equation 6 is an approximation of Equation 13 in this article, it is worth checking out your simulations results for the more general case rather than the approximation. (https://doi.10.1103/PhysRevB. ("Simulation of I − V hysteresis branches in an intrinsic stack of Josephson junctions in high- T c superconductors"))
Please respond to the above remark. Without careful attention to that question, the manuscript publication should be reconsidered.
