SciPost Submission Page
Josephson current through the SYK model
by Luca Dell'Anna
Submission summary
| Authors (as registered SciPost users): | Luca Dell'Anna |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202312_00054v2 (pdf) |
| Date submitted: | 2024-07-20 13:01 |
| Submitted by: | Dell'Anna, Luca |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We calculate the equilibrium Josephson current through a disordered interacting quantum dot described by a Sachdev-Ye-Kitaev model contacted by two BCS superconductors. We show that, at zero temperature and at the conformal limit, i.e. in the strong interacting limit, the Josephson current is suppressed by $U$, the strength of the interaction, as $\ln(U)/U$ and becomes universal, namely it gets independent on the superconducting pairing. At finite temperature $T$, instead, it depends on the ratio between the gap $\Delta$ and the temperature. A proximity effect exists but the self-energy corrections induced by the coupling with the superconducting leads seem subleading as compared to the self-energy due to the interaction for large number of particles. Finally we compare the results of the original four-fermion model with those obtained considering zero interaction, two-fermions and a generalized q-fermion model.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
hereafter I resubmit the paper to Scipost Physics.
In the last version I fixed some typos and included, at the end of page 9, the following sentence “…The same observation is valid if we want to improve the bare SYK solution including 1/N corrections. Also in that case the leading contribution to the Josephson current remains unchanged” when discussing the 1/N corrections questioned by Gnezdilov.
Actually, the derivation by Gnezdilov in his last report is in perfect agreement with my results while some 1/N corrections were already discussed in the text and Appendix.
I hope that now he will be happy with my previous reply and this addition.
About the comment of Bagrets, I should say that the request of taking the coupling matrix elements between the dot and leads as random variables was not present in his first report. Moreover, I would like to stress that the coupling proposed by Bagrets has to have vanishing mean value. If the mean value is finite his argument is no longer valid, while mine remains valid, with the inclusion of random fluctuations that, by the way, I discussed also in the paper.
Anyway studying another model implies making a totally new and different work. I can take his comment about considering a spinful SYK model as a good suggestion for further investigations. At this stage I will keep the model as it is.
My question is the following: given the model as in Eqs(1)-(4), are the calculations presented correct or not?
Since all the three Referees said that the topic presented in the paper is interesting and timely, since I replied to all the questions raised in the first round, included several additions so to double the volume of the paper following the suggestions of the Referees, and since none of the them, so far, confuted the correctness of my results, even after a long reviewing procedure, I resubmit the paper asking for further consideration.
Best regards,
Luca Dell'Anna
List of changes
At the end of page 9, I included the following sentence “…The same observation is valid if we want to improve the bare SYK solution including 1/N corrections. Also in that case the leading contribution to the Josephson current remains unchanged” .
Some typos have been fixed.