SciPost logo

SciPost Submission Page

Superfluid response of two-dimensional filamentary superconductors

by Giulia Venditti, Ilaria Maccari, Alexis Jouan, Gyanendra Singh, Ramesh C. Budhani, Cheryl Feuillet-Palma, Jérôme Lesueur, Nicolas Bergeal, Sergio Caprara, Marco Grilli

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Giulia Venditti
Submission information
Preprint Link: scipost_202310_00025v1  (pdf)
Date accepted: 2023-11-20
Date submitted: 2023-10-21 11:28
Submitted by: Venditti, Giulia
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Experiment
  • Condensed Matter Physics - Theory
Approaches: Theoretical, Experimental


Different classes of low-dimensional superconducting systems exhibit an inhomogeneous filamentary superconducting condensate whose macroscopic coherence still needs to be fully investigated and understood. Here we present a thorough analysis of the superfluid response of a prototypical filamentary superconductor embedded in a two-dimensional metallic matrix. By mapping the system into an exactly solvable random impedance network, we show how the dissipative (reactive) response of the system non-trivially depends on both the macroscopic and microscopic characteristics of the metallic (superconducting) fraction. We compare our calculations with resonant-microwave transport measurements performed on LaAlO$_3$/SrTiO$_3$ heterostructures over an extended range of temperatures and carrier densities finding that the filamentary character of superconductivity accounts for unusual peculiar features of the experimental data.

Author comments upon resubmission

Dear Editor,
We wish to resubmit our manuscript ``Superfluid response of two-dimensional filamentary superconductors".

We want to thank the referees for their careful reading of the manuscript and for their useful
comments and suggestions. We considered all the issues they raised and modified our manuscript
accordingly. We provided a point-by-point reply to all their questions and critical remarks.

We hope that with the revisions made, the paper can now be accepted for publication in SciPost Physics.

We thank you for your consideration and look forward to hearing from you.

Sincerely yours,
on behalf of all authors,
Dr Giulia Venditti

List of changes

- Authors affiliations updated (Giulia Venditti and Ilaria Maccari).

1. Introduction:
- We clarified how the inhomogeneous nature of the system can be quantified through ΔTc/Tc, as requested by referee #2.
- Following the suggestion of referee #2, we added more references from other groups, which studied different compounds displaying inhomogeneous features similar to those discussed in our manuscript.

3. Theoretical description: the Random Impedance Network:
- We improved the description of the RIN model, adding Appendix A.1 where the computational details can be found as well as a sketch of our network, according to comment (iii) of referee #1.
- We clarified that the resonant frequency chosen in the calculations is the experimental one, according to comment (i) of referee #1.
- We explicitly state that we study the system in its linear response regime so that we implicitly assume that the currents flowing in the bonds are always smaller than the critical ones, as pointed out by referee #2.

4. LaAlO3 /SrTiO3 interfaces:
- As pointed out by both referees, we understood that the relationship between the resonant microwave setup and our calculations was not clear. We thus clarified the relationship among the complex conductivity experimentally measured σ_1,2 and the relevant quantities we are interested in, namely the superfluid stiffness J_s and the optical conductivity σ_1. We specify that the terminology “optical” is used in analogy with the general terminology used in spectroscopic measurements.
- As pointed out by referee #2, Fig.6 (now Fig.7) was never called in the main text and we apologize for this. The referee also convinced us that it was not crystal clear that the same figure shows experimental results, not theoretical calculations. We clarified this is the revised version.
- To answer to referee #2, we better explained our position when we said that “this sample may not be representative of every LAO/STO interface”, intending that we chose that particular sample because it has enhanced features of the phenomenology we want to study, namely filamentary superconductivity. We underline that the measurements are fully reproducible within the same sample, but different samples might have different amounts of mesoscopic disorder, resulting in a phenomenology intermediate between the two presented in Figs.1c and 1d.

4.1. Resonant microwave transport experiment:
- We made clear that the sample and the setup are the same as in Ref. [G. Singh et al., Nat. Comm. 9(1), 1 (2018)] and added more experimental details, to answer the issue raised by referee #2. As we wrote to the referee, we believed that those experimental details were not necessary, since they are already explained in previous experimental papers whereas this work is devoted to the theoretical understanding of transport measurements as functions of temperature and at different gate voltages. We included more experimental details in order to make the paper more self-contained.
- To meet referee #2's comment, we explicitly added in Fig.2a the expected BCS behavior for the zero temperature superconducting gap Δ^BCS and changed the text and the caption accordingly.
- Caption of Fig.2 was modified to clarify again the experimental role of ω_0.

5. Theoretical results and their interpretation:
- We added that “Our goal is to infer and understand micro- and mesoscopic features of the electronic condensate from the macroscopic phenomenology given by transport measurements.”

- We cited 13 more papers from other groups to meet the request of referee #2.

Published as SciPost Phys. 15, 239 (2023)

Reports on this Submission

Anonymous Report 2 on 2023-11-14 (Invited Report)


The method is useful for determination of microwave response of filamentary superconductors, where other approaches are hardly available.

The calculations for specific material reliably reproduce their experimentally measured properties.


Some parts of this article have been published by the same authors in their previous papers.


In my opinion the authors revised their paper taking into account all my sugegstions. I am fully satisfied, especially by the added appendix explaing the technical details of RIN equations.

Requested changes

No need for any further modifications.

  • validity: high
  • significance: good
  • originality: good
  • clarity: good
  • formatting: good
  • grammar: excellent

Anonymous Report 1 on 2023-10-25 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202310_00025v1, delivered 2023-10-25, doi: 10.21468/SciPost.Report.7996


1. It is a contribution to important and interesting studies of properties of inhomogeneous superconductors.
2. It provides a comprehensive phenomenological model of filamentary superconductor which seems to describe well some class of quasi-two dimensional materials.
3. The manuscript is self-contained, it provides a comprehensive description, discussion and analysis both of experimental data, model assumptions, results, and physical conclusions related to studied phenomena.


Presented model calculation results are compared, and fitted to data of just one sample, LAO/STO interface reported earlier by some of the present authors. It remains to be seen if and how universal is their model.


The new version of the manuscript includes corrections, additions and changes as postulated by referees. In our opinion it meets now Journal criteria and in can be published, with small technical correction as listed below.

Requested changes

Small technical corrections/additions:

1. In the newest version, on page 20 caption to Figure 9 lost two lines at the end. The description of pictures (d), (e), and (f) is missing and it requires author's correction.
2. In reference [64] the journal title: "Physical Reviwew Letters" should be written with all word starting with capital letters as elsewhere.

  • validity: good
  • significance: good
  • originality: high
  • clarity: high
  • formatting: good
  • grammar: good

Login to report or comment