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No superconductivity in Pb$_9$Cu$_1$(PO$_4$)$_6$O found in orbital and spin fluctuation exchange calculations

by Niklas Witt, Liang Si, Jan M. Tomczak, Karsten Held, Tim O. Wehling

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Submission summary

Authors (as registered SciPost users): Jan Tomczak · Niklas Witt
Submission information
Preprint Link:  (pdf)
Code repository:
Data repository:
Date accepted: 2023-11-06
Date submitted: 2023-10-27 09:12
Submitted by: Witt, Niklas
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
  • Quantum Physics
Approaches: Theoretical, Computational


Finding a material that turns superconducting under ambient conditions has been the goal of over a century of research, and recently Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O aka LK-99 has been put forward as a possible contestant. In this work, we study the possibility of electronically driven superconductivity in LK-99 also allowing for electron or hole doping. We use an $\textit{ab initio}$ derived two-band model of the Cu $e_g$ orbitals for which we determine interaction values from the constrained random phase approximation (cRPA). For this two-band model we perform calculations in the fluctuation exchange (FLEX) approach to assess the strength of orbital and spin fluctuations. We scan over a broad range of parameters and enforce no magnetic or orbital symmetry breaking. Even under optimized conditions for superconductivity, spin and orbital fluctuations turn out to be too weak for superconductivity anywhere near to room-temperature. We contrast this finding to non-self-consistent RPA, where it is possible to induce spin-singlet $d$-wave superconductivity at $T_{\mathrm{c}}\geq300$ K if the system is put close enough to a magnetic instability.

Author comments upon resubmission

Dear Editor,

Thank you very much for managing the refereeing process and for pointing out the wrong formatting and missing DOIs of some references. We especially thank the referees for their careful and critical reading. We are pleased to see that both referees find our work interesting, clear and suitable for publication.

Only Referee 2 had a few remarks/questions concerning the hopping amplitude of our Wannierized model and the relation of Cu doped lead apatite to other triangular superconducting systems. We address both points in a direct Reply to Referee 2 and added corresponding parts in the revised manuscript (see beginning of sections **2 Results** (p. 3) and **3 Discussion and Conclusion** (p. 6), respectively).
In addition, we fixed the references (formatting + DOIs) and updated the preprints with their published version where applicable. Please find below a full list of changes.

On behalf of the authors,
Niklas Witt

List of changes

- Updated references: Fixed bad formatting, added missing DOIs and replaced arXiv preprints with published versions if available; Added Refs. [21,40-64].
- Added DOIs for the data repositories in **Data availability**
- p.2: Fixed bad line breaking of chemical formula Pb$\_{10-x}$Cu$\_x$(P$\_{1-y}$S$\_y$O$\_4$)$\_6$O$\_{1+z}$
- p.3: Added a note on the expected effect on external pressure on the system in section **2 Results** (first paragraph)
- p.6: Added discussion of other triangular lattices displaying superconductivity in section **3 Discussion and Conclusion**
- Fig. 3: Added "x10" to off-diagonal components of the gap in panel (f) with note in the caption (previously missing)
- Minor spelling fixes

Published as SciPost Phys. 15, 197 (2023)

Reports on this Submission

Anonymous Report 1 on 2023-10-27 (Invited Report)


The authors provide satisfactory answers to my comments, I can recommend the manuscript for publication

  • validity: -
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  • originality: -
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