Phase Diagram of the Attractive Kane-Mele-Hubbard Model at Half Filling

Round 1

Reviewer 1 Report

The author studies the phase diagram of the attractive Kane-Mele-Hubbard model with the next-nearest-neighbor hoping at half-filling by diagonalizing the mean-field Hamiltonian and taking into account of the sublattice degree of freedom in single-particle Green's functions. The author further explores the superconducting instability. The slope of the Goldstone mode and the sound velocity along the direction toward the M point have been calculated using the T-matrix approximation and using the Bethe-Salpeter equation. This study provides a useful point of view in the study of topological phases of matter where sublattice degrees of freedom play an important role in interacting topological phases transitions.

Author Response

I would like to thank very much to the both Reviewers for the valuable comments. I accept all of them, and I have corrected the text in accordance.

Reviewer 2 Report

Report: atoms-892326

  The author reports on a numerical approach based on mean-field approximation to study two different features of the attractive KMH model at half-filling, in detail the expected phase diagram and the possibility to obtain the Cooperon condensation. This study is certainly interesting and brings a valuable contribution to the field of ultra-cold atoms in optical lattices, and more specifically to the lately thriving sub-domain concerning honeycomb lattices, the generation of gauge fields, and exotic ordering in materials.   I do have, however, several remarks (detailed below) that should be carefully addressed by the author to substantially improve the presentation of his manuscript; my overall advice to the Editor is that a revision is required now to make the manuscript suitable to Atoms, and more in general to increase its future impact.   The abstract should report in a concise way the work done and the main results obtained, without explicit bibliographic references, which make the reading not immediate.   The general research context is not introduced appropriately: recent relevant experimental (e.g. Esslinger and Hemmerich) and theoretical (Ritsch) results are not mentioned. A very rapid search gives several recent works not mentioned in the bibliography, like 10.1103/PhysRevX.3.011015,

10.1103/PhysRevB.85.115132.

  The manuscript must be proofread to remove several typos, punctuation and verb tense issues.   The figures are appropriate for their content but are very difficult to see: Fig 1 should be 3 times bigger, the font of Fig 2 too.   The incipit is very cryptic: if one does not know already the specific models is lost in the first sentence.   The more technical part describing the numerical approach is well structured; in my opinion, the author could make a double effort: further simplify the reading, by moving other complex formulas in Appendixes; try to give the physical meaning of the results (e.g., why the min value of U/t producing gaps does not change with and without NNN hopping term? how is justified the introduction of a boson field to deal with quartic terms?)   Just before the Discussion, a 4% difference is reported between the approach adopted and the T-matrix approx; 1.34 and 1.45 give rather an 8% difference.

Author Response

I would like to thank very much to the both Reviewers for the valuable comments. I accept all of them, and I have corrected the text in accordance with the comments as follows (please check the attachment).

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The author implemented all the suggested changes to his manuscript, which is now much easier to follow; the structure, the presentation as well as English are all improved.

Just a minor remark on the response letter, concerning the percentage difference between the approach adopted and the T-matrix approx: the value (of course) depends on the denominator, but it does not change so much as reported by the author. Notably, (1.45-1.34)/1.45 =7.6% and not 4%. In the manuscript, a correct 8% value is reported. I would just remove the qualitative "small" in "To explain the small difference of 8% in our numerical calculations" --> "To explain the 8% difference in our numerical calculations"