Peer review of: Electronic correlations and transport in iron at Earth’s core conditions (2020)

RR2
 REVIEWERS' COMMENTS:
Reviewer #2 (Remarks to the Author):
  I am satisfied with the authors’ response to my comments and criticisms. However, I think it would be
 helpful for some of the responses in the rebuttal to be incorporated into the main text. In particular, the
 responses to the comments regarding whether 20 % was a significant reduction in regards to core dynamics,
 and the effect of impurities. I think they would answer questions readers of the paper would be asking and it
 would not take much time to add them. That aside, I am satisfied and am happy to recommend publication
 of the manuscript.
 As far as I can tell, I think that they have provided credible responses to the comments of the other
 referees. The additional calculations on the hcp phase have helped in this respect.
 One really minor comment: in the inset of Figure 3 (left-hand panel) it appears to have ‘0,5’ on the y-axis,
 when I think it should be ‘0.5’.
 Reviewer #3 (Remarks to the Author):
 I was asked by the Editor to address the Authors' reply to my comments as well as to those raised by
 Reviewer #1.
 First, I comment on the Authors' response to my report.
 -I had suggested them to improve the readability of the text and I am satisfied by their attempt to meet
 this. Now the manuscript is written more in accordance with the style of Nature Commun papers.
 -My next comment was about the literature and I can confirm that the new version give better credit to
 previous works.
 -New calculations for the hcp phase have been made by the Authors, following my suggestion. The results
 confirm their previous intuition and make the scientific content of this manuscript more robust and
 convincing.
 -As a last comment I had asked clarifications regarding the "game" with the imaginary part of the self-
 energy. The Authors have answered in great detail and have amended also the manuscript accordingly.
 I am therefore satisfied with the response to my report and can recommend the manuscript for publication
 in Nature Commun.
 My point of view about the comments by Reviewer #1, in part already quoted by the Authors in their
 rebuttal letter, is the following:
 It is of course not possible to tell the result of a full calculation including electron-electron scattering for the
 huge cell treated in the "heroic" molecular dynamics calculation by A. Belonoshko et al. Nature Geoscience
 (2017).
 Yet, the goal of the present manuscript is not an accurate calculation of the thermal conductivity in absolute
 terms. Some of the authors of the current paper have done this without DMFT in a previous Nature paper
 lifetime, the authors want to assess whether or not this wins against thermal and electron-lattice effects. Of
 course, had they used the 4.000 atom unit cell by Belonoshko they would have taken anharmonicity effects
 much more accurately into account. However, since they find that already with a small cell (i.e. with more
 constrained ions’ motions) electron-electron interaction does not prevail, it is hard to imagine that in the
 4.000 atom unit cell the opposite can occur. The more freedom for thermal disorder present in such a big
 active. On the other hand, the electron-electron part, since at these temperature they can safely neglect
 non-local correlations generated by local interactions, will not be particularly affected by the size of the unit
 cell.
 In the resubmitted version the authors report new calculations for a cell with hcp structure and find a very
 similar behaviour as that of the bcc one. I believe that this further corroborates their approach and
 and there much larger cells have been used. Anyway, since electron-electron interaction contributes a finite
 cell will result in even more room for electron-lattice effects and I would therefore expect them to be more

 interpretation.
 Therefore, even if the points by Reviewer #1 are absolutely valid in general and well taken in absolute
 terms, I judge that within the perimeter of the conclusions that the Authors want to draw in the present
 study, the study done on the small cells is enough.