Controlling I-V Hysteresis in Al/Pt Bilayer Symmetric SQUIDs at Millikelvin Temperatures

Round 1

Reviewer 1 Report

This work is interesting from the point of view of developing SQUIDs based on Josephson nanobridge junctions for applications at mK temperatures. But in the current version, the paper contains wrong interpretations and statements, as well as incorrect references. I think the paper needs major revision. Please consider the following suggestions for the revision:

1.      Replace "nano-SQUID" in the title with "microSQUID" or "miniature SQUID" because the diameter of the SQUID loop is about 2.3 µm, as shown in Fig. 1a. NanoSQUID is by definition smaller than 1 µm.

2.      Line 27: Replace "which had not been still achieved, but" in the text with "[3] and it" because the resolution and the capability were achieved there.

3.      Line 27: References 5 and 6 are not about SQUID applications.

4.      Line 29: Reference 9 is not about basic of SQUID operation.

5.      Line 71 and 72: References 43, 44, 45, 47, and 48 should be about NbN nanoSQUIDs, TiN nanoSQUIDs, and NbTiN nanoSQUIDs. Please provide the correct references.

6.      Line 81: Reference 41 in not about properties of Al/Pt bilayer. Please correct the text.

7.      Lines 100 and 101: “we achieve” is not correct because the work in reference 59 is made by other group. The resolution of 30 nphi0 is achieved not in the reference 59.

8.      Line 110: 5nm Pt film will not protect Al from oxidation: It is transparent for oxygen up to thickness of 17 nm: see https://doi.org/10.1007/BF01575085

9.      The authors interpret their experiments as Little-Parks oscillations and claim that this is usual for SQUIDs. That is a completely wrong statement: SQUIDs by definition contain Josephson junction with the phase drops on them but in the Little-Parks experiment just a superconducting cylinder without any weak links was used. At a little bit larger bias current the R(B) dependence will be sinusoidal without cusps and this cannot be explained by the J2 model.

10.  Line 124: “The Al-“ is not a sentence.

11.  Lines 168 and 169: The model of thermal hysteresis is wrong. There is no hysteresis at Ic in the reference 65: see Fig. 2 and the insert in it in the reference 65. Please read about physics of the nanobridge Josephson junctions the paper of Likharev: https://doi.org/10.1103/RevModPhys.51.101

12.  Lines 191 and 192: “250nm ....is smaller than ....55nm”. Please correct the sentence there.

13.  Line 191: This estimation is not correct: Al films are in dirty limit and have coherence length about 40 nm: see https://doi.org/10.1063/1.3443716

Author Response

This work is interesting from the point of view of developing SQUIDs based on Josephson nanobridge junctions for applications at mK temperatures. But in the current version, the paper contains wrong interpretations and statements, as well as incorrect references. I think the paper needs major revision. Please consider the following suggestions for the revision.

We warmly thank Reviewer for a careful reading and understanding of the main challenges and results of our manuscript. As Reviewer will see
we point by point considered his/her criticism and substantially modified the manuscript following his/her valuable remarks. Reviewer will find a
specific pdf file submitted along with other documents in which the changes done in the main text are highlighted.

1. Replace "nano-SQUID" in the title with "microSQUID" or "miniature SQUID" because the diameter of the SQUID loop is about 2.3 µm, as shown in Fig. 1a. NanoSQUID is by definition smaller than 1 µm.

Based on this criticism, we reorganized the text and and replaced “nanoSQUID” with “SQUID” everywhere. 

2. Line 27: Replace "which had not been still achieved, but" in the text with "[3] and it" because the resolution and the capability were achieved there.

Replaced (now it is line 25 and reference [2]).

3. Line 27: References 5 and 6 are not about SQUID applications.

We absolutely agree with the reviewer and apologize for the mistaken inclusion of some references. We have carefully double-checked the list of references and removed irrelevant ones. The number of references has decreased from 74 to 59.  These references were removed (now line 26).

4. Line 29: Reference 9 is not about basic of SQUID operation.

Done. This issue is linked to the previous one. This reference was removed (now line 25).

5. Line 71 and 72: References 43, 44, 45, 47, and 48 should be about NbN nanoSQUIDs, TiN nanoSQUIDs, and NbTiN nanoSQUIDs. Please provide the correct references.

Done! Thanks for the comment. We have added the corresponding references to the line 75.

6. Line 81: Reference 41 in not about properties of Al/Pt bilayer. Please correct the text.

Done! We slightly modified the text.

7. Lines 100 and 101: “we achieve” is not correct because the work in reference 59 is made by other group. The resolution of 30 nphi0 is achieved not in the reference 59.

Done! Replaced with “was achieved”, line 91. A reference was corrected.

8. Line 110: 5nm Pt film will not protect Al from oxidation: It is transparent for oxygen up to thickness of 17 nm: see https://doi.org/10.1007/BF01575085

We would like to thank Reviewer for pointing out on this effect. We slightly modified the text.

9. The authors interpret their experiments as Little-Parks oscillations and claim that this is usual for SQUIDs. That is a completely wrong statement: SQUIDs by definition contain Josephson junction with the phase drops on them but in the Little-Parks experiment just a superconducting cylinder without any weak links was used. At a little bit larger bias current the R(B) dependence will be sinusoidal without cusps and this cannot be explained by the J2 model.

Thanks to the criticism of Reviewer, we carried out numerous additional simulation to determine the exact model of the studied phenomena. The results of these studies are presented in the revised manuscript. We have performed a new fit based on SQUID model and it has shown an evidence of correct SQUID operation. Figure 3 was replaced with a new figure containing the fit with a correct model. Methods section was also revised and now contains a correct model of a SQUID operation. 

10. Line 124: “The Al-“ is not a sentence.

Done! This is a typo and was removed (line 114). We apologize for our carelessness.

11. Lines 168 and 169: The model of thermal hysteresis is wrong. There is no hysteresis at Ic in the reference 65: see Fig. 2 and the insert in it in the reference 65. Please read about physics of the nanobridge Josephson junctions the paper of Likharev: https://doi.org/10.1103/RevModPhys.51.101

Done. Thank you! The reference to the correct hysteresis model was added (line 138).

12. Lines 191 and 192: “250nm ....is smaller than ....55nm”. Please correct the sentence there.

Done! The sentence was corrected: “…which is greater…” (line 158).

13. Line 191: This estimation is not correct: Al films are in dirty limit and have coherence length about 40 nm: see https://doi.org/10.1063/1.3443716

Reviewer is right, estimation is not correct. The overall shape of the temperature dependence of the critical current enable distinguishing between the dirty and clean limits. A coherence length for thin Al films was recalculated using the expression from https://doi.org/10.1063/1.3443716 (lines 155-158). In this approach, it is about 70 nm, which is still greater than a junction width.

Thank you for your valuable comment.

We have completely revised the conclusions of our article.

Reviewer 2 Report

Please open the attached docx file. 

Comments for author File: Comments.pdf

Author Response

In General:
It is quite well written article demonstrating really good new results in nano-SQUIDs development. It needs just a minor polishing. 

We appreciate the comment very much. We rearranged the manuscript according to the Reviewer requirements.

Introduction:

1.Reference [1] looks too common, basically useless.

We absolutely agree with the reviewer and apologize for the mistaken inclusion of some references. We have carefully double-checked the list of references and removed irrelevant ones. The number of references has decreased from 74 to 59. 

2. The sentence lines 23 – 27 is misleading and should be rewritten. “One Bohr magneton” is not magnetic field.

Thanks for the comment. The sentence was rewritten, only a thesis about single spin-flip detection was remained (lines 24-25).

3. References [4-6] and [7-9] look not quite relevant.

Done

4. Line 54: define ρ_s and ρ_n

Done. The definition was added (line 52-53)

5. Line 81: and reduces 1/f noise.

Done.

6. Fig 1: Figure 1d shows 0.1 – 0.8 temperature range but in the text T = 0.02 – 0.8.

Thank you very much for the remark. A figure was corrected. Both devices were actually measured from the temperature of 20 mK. Also a correction was made in a figure subtext.

7. Lines 100-101: “…we achieve a resolution… [59].” Reference [59] doesn’t include authors of this article.

Thank you for your valuable comment. Corrected to “a resolution was achieved” (line 100-101)

Results and discussion:

1. Line 124: The Al- The – it is a typo.

Done. A typo was corrected, this part of other sentence was removed. 

2. Lines 131, 153 and 177: should be “Al/Pt”

“Al/Pt” is already written here, we have checked it carefully. 

3. Lines 191-192: “… 250 nm, which is smaller than a junction width of 55 nm.” – Something is wrong here with numbers.

There was a typo, it must be read as “which is greater”. It was corrected (line 191). We apologize for our carelessness.

Methods:

1. Lines 204, 205: 4.2e-8 → 4.2×10-8 and 7.8e-8 → 7.8×10-8

Done. 

Conclusion:

1. Line 228: It should be “we study the temperature dependence…”

Done. The missing word was added (now it is line 244). 

2. Lines 233-235: Recommend to rewrite this sentence.

Done.

Thank you for your valuable comment.

We have completely revised the conclusions of our article.

Reviewer 3 Report

The nano-SQUID is well-known for its single spin sensitivity. To achieve the detection of a single spin flip, an ultra-low noise readout is required as well. The thermal hysteresis has been observed in many types of nano-SQUIDs as described by the authors. It is problematic to the readout of the SQUID. The authors have proposed a new combination of the bilayer films for nano-SQUIDs. The as-fabricated nano-SQUID shows single valued current-voltage curve in a wide temperature range from 0.02 to 0.8 K which is very impressive. The manuscript is well written and qualified to be published. I only have a few minor questions about the manuscript.

1.     Line 191, there is a typo. The coherence length should be greater than the junction width.

2.     The critical current of Al/Pt device is significantly lower than Al device. Have the authors measured Al device with a similar critical current to the Al/Pt device?

3.     The authors mentioned that the Al/Pt film has less oxidation centers which is advantageous to the noise performance of the nano-SQUID. Have the authors measure the intrinsic flux noise of the device?

4.     In the fitting of figure 3, the authors have assumed that the critical current modulation is a sinusoidal. Have the authors measured flux - critical current modulation?

Author Response

The nano-SQUID is well-known for its single spin sensitivity. To achieve the detection of a single spin flip, an ultra-low noise readout is required as well. The thermal hysteresis has been observed in many types of nano-SQUIDs as described by the authors. It is problematic to the readout of the SQUID. The authors have proposed a new combination of the bilayer films for nano-SQUIDs. The as-fabricated nano-SQUID shows single valued current-voltage curve in a wide temperature range from 0.02 to 0.8 K which is very impressive. The manuscript is well written and qualified to be published. I only have a few minor questions about the manuscript.

We appreciate the comment very much. We rearranged the manuscript according to the Reviewer requirements.

1. Line 191, there is a typo. The coherence length should be greater than the junction width.

Done. The typo was corrected.

2. The critical current of Al/Pt device is significantly lower than Al device. Have the authors measured Al device with a similar critical current to the Al/Pt device?

Thank you for your valuable question. The main idea of the paper was to test the properties of Al/Pt and Al nanoDQUID with the same geometry. The fabrication of such device poses a significant challenge. To reduce a critical current of a single-layer Al device with the same geometry, it is required to reduce junction dimensions, which is actually impossible, because already now the junction width is 55 nm. The other way to reduce the critical current is to reduce Al thickness, but such thin films are being rapidly oxidated after fabrication and thus are unstable. Thank you again for your question. 

3. The authors mentioned that the Al/Pt film has less oxidation centers which is advantageous to the noise performance of the nano-SQUID. Have the authors measure the intrinsic flux noise of the device?

Thank you for your valuable question. The intrinsic flux noise observed in superconducting quantum interference devices (SQUIDs) is thought to be due to the fluctuation of electron-spin impurities. We did not take such measurements within the scope of this work. In the paper [DOI: 10.1038/ncomms5119] it was shown measurements on Nb with m Pt-capping layer superconducting microresonators over previously unattainable, very long time scales that show an increase in 1/f noise at low temperatures and low microwave power. We will take this suggestion into account in our future work. 

4. In the fitting of figure 3, the authors have assumed that the critical current modulation is a sinusoidal. Have the authors measured flux - critical current modulation?

Thank you very much for the remark. In this article we focused on the study of Little Parks oscillations.  We show the proper operation of a SQIUD and have plans to the further improvement of geometry and thicknesses of metals. The  SQUIDs with optimal parameters will be rigorously characterized by the such way. 

Thank you for your valuable comment.

We have completely revised the conclusions of our article.

Round 2

Reviewer 1 Report

This work contributes to the development of SQUIDs based on Josephson nanobridge junctions that are intended for applications at mK temperatures. The manuscript has been significantly improved and from my point of view it deserves publication in Symmetry after some minor changes. Please consider the following suggestions for the revision:

1.      As shown in Fig. 1d, the critical current of Al/Pt SQUID at 0.7 K is about 1.3 µA. This contradicts to the Fig. 2a, Fig. 2c and Fig. 3b where the “bias” or “control current” is 0.63 µA. Probably in the case of the Fig. 2a, Fig. 2c and Fig. 3b the average critical current of the 2 individual junctions in the SQUID is written.

2.      Line 103: Remove "and also serves as the protective layer (see methods for details)" because it is wrong and it is not shown in Methods.

3.      Fig. 2a and Fig.2b: Write “0.7 K” and “1.35 K” instead of “700 mk” and “1350 mk” respectively.

4.      Lines 132 and 133: Remove the sentence “In this model, ...., where φ1,2 are the phase differences across junctions.” because the equation there is wrong and there are nothing about it in the Methods section.

5.      Line 176: Please provide Ar pressure that was used for the etching.

6.      Line 186: Please explain what magnetic shield was used instead of only writing “carefully shielded from magnetic fields”.

7.      Fig. 3b, Lines 205 and 206: Please explain how you obtained the theoretical dependences of the SQUID voltage modulation on the magnetic flux shown in Fig. 3b. Numerically or do you have an analytical solution of the derived differential equations?

8.      If possible, could you estimate magnetic field resolution and spin sensitivity of the best your SQUID at the most optimal conditions? This is probably for Al/Pt SQUID at 0.7 K and about 1.3µA (or 0.63µA?) bias current.

Author Response

Please open the attached docx file. 

Author Response File: Author Response.docx