SciPost Submission Page
Correlation functions and characteristic lengthscales in flat band superconductors
by Maxime Thumin, Georges Bouzerar
This is not the latest submitted version.
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Maxime Thumin |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202409_00012v3 (pdf) |
| Date submitted: | 2024-11-22 10:30 |
| Submitted by: | Thumin, Maxime |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approaches: | Theoretical, Computational |
Abstract
The possibility of an unconventional form of high temperature superconductivity in flat band (FB) material does not cease to challenge our understanding of the physics in correlated systems. Here, we calculate the normal and anomalous Green's functions in various one and two dimensional FB systems and systematically extract the characteristic lengthscales. When the Fermi energy is located in the FB, it is found that the coherence length ($\xi$) is of the order of the lattice spacing and weakly sensitive to the strength of the electron-electron interaction. Recently, it has been argued that in FB compounds $\xi$ could be decomposed into a conventional part of BCS type ($\xi_{BCS}$) and a geometric contribution which characterises the FB eigenstates, the quantum metric ($\langle g \rangle$). However, by calculating the coherence length in two possible ways, our calculations show that $\xi \neq \sqrt{\langle g \rangle.}$ This may suggest that the link between QM and coherence length is more complex, and leaves us with the open question: what is the appropriate definition of the coherence length in flat-band systems?
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
List of changes
* Abstract has been modified and rewritten
* Table 1 has been moved, and the caption has been extended to define “tunable QM” and “uniform pairings”
* Few sentences have been modified according to referee’s 2 suggestions
* Figure 2 has been modified according to referee's 1 suggestion
* Conclusion has been modified
Current status:
Reports on this Submission
Strengths
The authors answered all questions of both referees satisfactorily and adjusted the manuscript accordingly.
Report
I can recommend publication when the minor changes requested by the second referee are fulfilled.
Requested changes
I agree with the three minor changes the second referee requested and ask the authors to adjust their manuscript accordingly.
Recommendation
Publish (meets expectations and criteria for this Journal)
Report #1 by Sebastiano Peotta (Referee 2) on 2024-11-29 (Invited Report)
- Cite as: Sebastiano Peotta, Report on arXiv:scipost_202409_00012v3, delivered 2024-11-29, doi: 10.21468/SciPost.Report.10238
Strengths
1 - This work presents interesting results regarding the coherence length in various lattices
2 - The results are both numerical and analytical
Weaknesses
1 - Despite the extensive changes, some conclusions are still questionable,
for instance the claim that the Cooper pair size is zero in the $\chi$ lattice. This is a result of the fact that only correlation functions within the same sublattice are considered when making this claim, while correlation functions $G_{\lambda \eta}(r)$ and $K_{\lambda \eta}(r)$ for $\lambda \neq \eta$ are ignored. There is no valid reason to do this and according to some definitions the Cooper size is clearly nonzero. In any case, I hope this work will stimulate further discussions on the topic and possibly some consensus regarding a general definition of the Cooper pair size can be reached.
Report
The manuscript can now be published in my opinion, provided that the minor changes listed below are taken into consideration
Requested changes
1 - In the abstract and in the main text the authors talk about Green's function. Since the time variable is absent, it is more correct to talk about generic one-particle correlation functions, or more precisely the one-body density matrix, which in the case of superconducting systems contains a normal and an anomalous part
2 - Remove spaces before the colon symbol ":" in the abstract and in the text.
3 - At the beginning of the section on the sawtooth ladder it is written "The superconductivity in the "stub lattice" has been addressed in details in Ref. [38". I think that stub lattice should be changed with" sawtooth ladder" here
Recommendation
Publish (meets expectations and criteria for this Journal)