Electron Currents from Gradual Heating in Tilted Dirac Cone Materials

This is a contribution to an active topic that goes outside of the beaten path. It introduces an original point of view that may well lack rigor, but it has the merit that it can stimulate further research.

One referee remains skeptical of the claim [third paragraph of the conclusion] that the authors can get a heat current that grows linearly with time. As explained by that referee [report 3 of version 1, equations renumbered], the issue appears to essentially be that because of ζ, the pressure gradient term cannot be balanced in Eq. (34). However, most likely within the authors' current framework there would need to be some sort of momentum-relaxation type term added into Eq. (34) related to ζ. Otherwise all the linear response transport calculations are going to be ill-posed because Eq. (34) could not possibly be satisfied. Yet such divergences did not seem to show up in the discussion around Eqs (39-44), raising doubt that those calculations are correct as written.

The disagreement between authors and the critical referee could not be resolved by revisions. I still would recommend publication in SciPost Physics Core. The SciPost platform will include this discussion as part of the publication record, which will alert the reader to the scientific issue summarized above. This study needs follow-up work, and publication of the manuscript jointly with the critical discussion seems a productive way to go forward.

I appreciate the authors' efforts to address my comments, but I am just ultimately doubtful about the validity of some key results in the paper. For example in the discussion around Eq. 54, I do not believe the assumption of zero pressure is an experimentally sensible one -- it would require a finely tuned choice of temperature gradient and chemical potential gradient (within the sample).

I think I mentioned in an earlier report that other methods (whether memory matrix or kinetic theory) would be really valuable here, because I believe they would give alternative perspectives on whether the phenomena the authors are describing here are genuine or due to subtle mistakes. For example one would be able to determine whether the physics discussed around Eq. 54 is due to something pathological about boundary conditions, the analysis, or might really be physical.

I personally would strongly hesitate towards publishing this paper, both for the reason I mentioned above, but also because there were some earlier points I had made that I think the authors did not fully take seriously (e.g. "Hall-like" response) and I am concerned this demonstrates some fundamental misunderstandings about the physics which may have affected the remaining analysis. Anyway, while I doubt this paper is all correct, it still calls attention to an interesting problem. I'll let the editor make the final call, but I don't think I have much more to add or to help with.