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Multiple Andreev reflections in diffusive SINIS and SIFIS junctions
by Artem V. Polkin, Pavel A. Ioselevich
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Submission summary
| Authors (as registered SciPost users): | Polkin Artem · Pavel Ioselevich |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202210_00057v1 (pdf) |
| Date submitted: | 2022-10-10 14:24 |
| Submitted by: | Ioselevich, Pavel |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study Multiple Andreev Reflections in long diffusive superconductor(S)-normal metal(N)- superconductor junctions with low-transparency interfaces. Assuming strong thermal- ization in the weak link we calculate the current-voltage dependence I(V ). At interme- diate temperatures, εTh ≪ T ≪ ∆, the current is dominated by noncoherent multiple Andreev reflections and is obtained analytically. The results are generalized to a ferro- magnetic junction. We find that the exchange field produces a non-trivial splitting of the subharmonic gap structure. This effect relies on thermalization and vanishes in SFS junctions with no energy relaxation in the weak link.
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Reports on this Submission
Anonymous Report 2 on 2023-2-27 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202210_00057v1, delivered 2023-02-27, doi: 10.21468/SciPost.Report.6809
Report
This is skillful and interesting contribution to the physics of nonequilibrium effects in Josephson junctions. The authors calculate I-V characteristics in long diffusive SINIS and SIFIS junctions. Strong thermalization regime is considered which allows to treat the weak link N (or F) region as a reservoir. Important result is the prediction that a subharmonic gap
structure exhibits splitting in the presence of an exchange field, with the splitting proportional to the voltage. At the same time, no splitting takes place in the case of weak energy relaxation. The developed approach is applied to analyze the experimental data from Golikova et al., Phys. Rev. B 86, 064416 (2012), where a subgap structure on I-V characteristics was observed in a Josephson junction with ferromagnetic interlayer, and it is concluded that the present model does not describe the observed effects.
To my opinion, this work deserves publication since it provides a solution of a complex theoretical problem within well-defined approximations and it may stimulate further studies in this direction. The manuscript is clearly written. Most of relevant literature is properly cited with exception of related work PRB 68, 224513 on nonequilibrium charge transport in double-barrier SINIS Josephson junctions. I can recommend the manuscript for publication if the authors add a comment on a relation of the present study and PRB 68, 224513
Requested changes
Add a reference to PRB 68, 224513 and discuss a relation to the present study
Anonymous Report 1 on 2022-12-10 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202210_00057v1, delivered 2022-12-10, doi: 10.21468/SciPost.Report.6286
Report
The paper addresses the problem of multiple Andreev reflections in diffusive SINIS/SIFIS junctions in the limit of strong thermalization and weak SN tunneling -- which allows the authors to treat the problem perturbatively in tunneling, starting from the thermal-equilibrium state as the zeroth-order approximation.
I appreciate the good introduction, where the authors explain the background, the motivation and the principles of their approach. Also, I like the informative conclusion with an analysis of the results.
However, the main technical part was less understandable. While I didn't try to reproduce the full calculation, I would like to be able to clearly understand its main steps. And here I find the presentation in the paper somewhat confusing. Below I list some of my points of confusion that I would like to be resolved before I can recommend the paper for publication.
1. The system involves several energy scales (E_Th, Delta, T, 1/tau_in), together with the tunneling probability 1/r. I would like the authors to clearly state the region of parameters, where their model is applicable. While I understand the main assumption E_Th << T << Delta, the conditions on tau_in and r are less clearly formulated and are scattered across different sections of the paper. I would like to have them all at the same place (either in the introduction, which may somewhat break the order of the presentation, or in the conclusion).
2. In connection to the previous point, below equations (8), where the authors linearize the Usadel equations, they write that this linearization is only valid at small f, and, in the formula inside the text, they give an estimate of the corresponding small energy window around the gap edge. This looks strange: the energy window given by this estimate is very small, and it is not clear how this is compatible with the rest of the calculation (which, to my understanding, involves all the energies).
3. I find notation very complicated and confusing. For example, equations (28) in Appendix D include objects like f^R_{S,+++} -- which I could not find defined anywhere. And this is not the only example of notation not clearly defined.
4. Ideally, every notation (or at least the most important ones) should be introduced in words with some explanation of what it means: this would help the reader to understand the calculation beyond a sequence of formulas. For example, in Eq.(21) I see the function u(...) and I would appreciate to have a comment below this equation, something like " where u(...) is ... introduced in ...". I would guess it is the function u(epsilon) from Eq.(10c), but, since it was 3 pages above, it would be good to confirm to the reader that it is the right function (and, ideally, explain its meaning).
5. The notation J(2)_\Sigma is only introduced in the caption to Fig.3 (at least as I could find it), and again, without any explanation. I also find it confusing that the figure is called "second-order contributions to the current" -- so I would expect that it would show different contributions from Eq.(20). Instead, it shows the first contribution only and then the total, without any explanation of this choice of plots. I find it confusing.
6. The same about Fig.6. Its caption is even more confusing, because it refers to J(2)_\Sigma, without any description, so that the reader is supposed to find the definition in the caption to Fig.3.
7. I appreciate very much the discussion of the results in Section 5, in particular mentioning the remaining unresolved questions. One of such questions is the explanation of the "even" series of features. I find it somewhat worrying that the authors do not have a full understanding of those features even in their own results. After all, their calculation is fully perturbative and controlled, and I would suppose that in this situation the origin of all the features should be crystal clear.
Finally, a couple of cosmetic comments that the authors may want to take into account in future revisions (but they are of minor importance):
8. The scale of Fig.3 is very small, which makes it hardly readable.
9. In many sentences, I would recommend to separate the introductory phrase by a comma, for better clarity. For example, in the second paragraph of Introduction there are two such sentences: "At voltages below the superconducting gap 2*Delta, electrons that ..." and "After a number of iterations, enough energy ..." There are a few other examples scattered across the paper.
To summarize, I would like to have points 1-6 clarified (and some response from the authors regarding p.7) before I can recommend the paper for publication.