Superfluid Properties of Superconductors with Disorder at the Nanoscale: A Random Impedance Model

Round 1

Reviewer 1 Report

All comments and suggestions for the authors are in the attached file.

Comments for author File: Comments.pdf

Author Response

We thank the referee for her/his appreciation of our work and for her/his stimulating comments and suggestions. The referee's report encouraged us to extend the reference list on the so-called quantum metal behavior, so we added Refs. [2-16] and [23] to provide a wider perspective on this and related issues. This and other changes are highlighted in red.

Coming to the specific comments:

1. The response at higher frequencies is definitely within the reach of our approach. However, this requires a proper modeling of dissipative processes within the superconducting puddles, hence a frequency dependence of the (complex) inductance. For this reason, in the present work we devoted our analysis to the simplest realization of the RIN and assumed a real and frequency independent inductance, which is apt to describe the low (i.e., sub-gap) frequency behavior. We had already commented on this in our previous version, but the referee's question convinced us that this discussion had to be made much clearer, so we extended the discussion in Sec. 3 and added a lengthier comment in Sec. 5.

2. Our work is mainly theoretical, as the available data on finite-frequency properties
of inhomogeneous superconductors are as yet rather scarce. We had the opportunity to see first-hand unpublished data (Ref. 29), but the data analysis is still in progress and we cannot say much more at the moment. Of course, gate-tunable superconductivity itself paves the way to a wealth of applications. For instance, the presence of both superconductivity and sizable spin-orbit coupling at LAO/STO interfaces opens the way to the possible occurrence of Majorana Fermions in suitably gate-tailored one-dimensional geometries of the two-dimensional electron gas. We tried to somewhat extend the perspective on future applications in Sec. 5. We also added Refs. [30-32].

As far as the color code of our curves is concerned, we agree with the referee's comment. Since a pink curve on a pink shaded area would hardly be visible, we kept the red color for the curve, but we now clearly state in the main text and in the figure caption that the red curve refers to the pink shaded area.

We hope that, with the above changes made, our manuscript is now suitable for publication.

Reviewer 2 Report

The authors study the role of inhomogeneities at the nanoscale in connection to the phenomenology of metal-superconductor transition. They use a mean-field approach to investigate the superconducting phase with a special focus on the finite frequency impedance. The main findings refer to the effects of the proximized metallic phase close to the critical temperature and the consequence on the transport properties.

The results are clearly presented and the analysis is well conducted. The impact of the work is relevant for materials like LAO/STO heterostructures.

I recommend the paper for publication in MDPI.

Author Response

We thank the referee for her/his appreciation of our work. We took the opportunity to further improve the quality of our presentation and hope that the referee will maintain her/his statement in favor of publication for our revised version.

Round 2

Reviewer 1 Report

I appreciate the response of the authors and I recommend the manuscript for publication in its present form.