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Scattering description of Andreev molecules
by J. -D. Pillet, V. Benzoni, J. Griesmar, J. -L. Smirr, Ç. Ö. Girit
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|Authors (as registered SciPost users):||Çağlar Girit · Jean-Damien Pillet|
|Preprint Link:||https://arxiv.org/abs/2002.10952v1 (pdf)|
|Date submitted:||2020-02-26 01:00|
|Submitted by:||Girit, Çağlar|
|Submitted to:||SciPost Physics|
An Andreev molecule is a system of closely spaced superconducting weak links accommodating overlapping Andreev Bound States. Recent theoretical proposals have considered one-dimensional Andreev molecules with a single conduction channel. Here we apply the scattering formalism and extend the analysis to multiple conduction channels, a situation encountered in epitaxial superconductor/semiconductor weak links. We obtain the multi-channel bound state energy spectrum and quantify the contribution of the microscopic non-local processes leading to the formation of Andreev molecules.
Submission & Refereeing History
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- Report 2 submitted on 2020-03-20 12:05 by Dr Lefloch
- Report 1 submitted on 2020-03-10 14:13 by Anonymous
Reports on this Submission
Report 2 by Francois Lefloch on 2020-3-20 (Invited Report)
- Cite as: Francois Lefloch, Report on arXiv:2002.10952v1, delivered 2020-03-20, doi: 10.21468/SciPost.Report.1588
This paper is a multi-channel extension of a previous paper published by the same authors to theoretically described the hybridization of ABS (Andreev Bound States) in three terminal Josephson junctions. Their approach is naturally based on the scattering formalism that includes both normal scattering in the junctions and Andreev reflections mechanisms at each superconducting interface.
In the context of quantum information, new quantum circuits including hybrid systems (here with superconducting and normal materials) and various geometries are widely investigated. In that sense, the results obtained by the authors, if not being ground-breaking’s, are of real interest for the community.
The paper is very well organized. In the limit of the assumptions made by the authors (see 1rst referee’s report) , the description of the model and the underlying physics phenomenon are very well described. This article a very pedagogical and clear.
Few comments that, in my opinion, limit the overall impact of this publication.
1 - The authors present results for a fixed number of channels (N = 20). It would have been interesting to discuss the effect of the number of channels in more details. This can be of real use for practical realizations with gated semiconducting nanowires.
2 - The origin of hybridization is due to (inverse) proximity effect in the central superconductor and explains the L/xi decay dependence. This inverse proximity effect is known to be strong when the transparency at the S/N interface is good (close to 1). But at the same time, the superconducting gap is locally reduced. On the contrary, when the transparency is smaller, the superconducting gap is restored but (inverse) proximity effect is less efficient.
It is not clear to me how the quality of the S/N interface will change the results but clearly the interface transparency is a real issue in experiments.
Note that the situation here seems different than in  as transport occurs necessarily though the central 3 D superconductor.
- Cite as: Anonymous, Report on arXiv:2002.10952v1, delivered 2020-03-10, doi: 10.21468/SciPost.Report.1565
The authors consider a superconducting wire interrupted by two weak links. They study the spectrum of the central region, which they refer to as an "Andreev molecule". The manuscript builds on an earlier paper by the same group of authors (arXiv:1809.11011) in which they studied a single-mode wire, while here they consider the multi-mode case. The scattering description which they employ is routine in the field and the phenomenon of crossed Andreev reflection which is obtained is also very well studied and understood. This limits the novelty and significance of the work, but should not by itself prevent publication.
I have, however, also several concerns regarding the scientific validity, which do stand in the way of publication.
1. The central region of the superconducting wire (the "Andreev molecule") is grounded, and the authors say that this allows them to fix the superconducting phase of the central region at 0. Here they are confusing voltage bias and flux bias. "Grounding" means that the voltage is zero, it does not mean that the phase is zero. The phase difference phi_L-phi_R between the outer ends of the wire can be fixed by a flux bias, but the phase of the central region should then be determined selfconsistently, it is not fixed by the voltage ground.
2. The authors assume that the electron and hole propagate through the central region with longitudinal momentum k_e,h = k_F ± i/ξ. In a multi-mode junction the longitudinal momentum can vary between 0 and the maximal value of k_F. Setting it equal to k_F for all modes does not seem justified.
3. On page 6 the authors write "we ignore fast phase oscillations in t_S and r_S arising from the small Fermi wavelength by fixing k_F l arbitrarily and independent of l". This assumption makes no sense to me. In a phase coherent treatment these phase oscillations should play a crucial role.
4. The plots are calculated by "randomly generated symmetric unitary matrices S_L and S_R". These matrices should represent the weak link, which I presume is a tunnel junction. Since no disorder is included in the superconductor, the randomness needed for this assumption is not present and I do not understand the justification for this choice.