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Electron Currents from Gradual Heating in Tilted Dirac Cone Materials
by Ahmadreza Moradpouri, Mahdi Torabian, Seyed Akbar Jafari
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Seyed Akbar Jafari |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202110_00027v3 (pdf) |
| Date accepted: | 2022-10-17 |
| Date submitted: | 2022-05-18 15:12 |
| Submitted by: | Jafari, Seyed Akbar |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Materials hosting tilted Dirac/Weyl fermions provide an emergent spacetime structure for the solid state physics. They admit a geometric description in terms of an effective spacetime metric. Using this metric that is rooted in the long-distance behavior of the underlying lattice, we formulate the hydrodynamic theory for tilted Dirac/Weyl materials in $2+1$ spacetime dimensions. We find that the mingling of space and time through the off-diagonal components of the metric gives rise to: (i) heat and electric currents proportional to the {\em temporal} gradient of temperature, $\partial_t T$ and (ii) a non-zero Hall-like conductance $\sigma^{ij}\propto \zeta^i\zeta^j$ where $\zeta^j$ parameterize the tilt in $j$'th space direction. The finding (i) above that can be demonstrated in the laboratory, implies that the non-trivial emergent spacetime geometry in these materials empowers them with a fascinating capability to harness naturally available sources of $\partial_t T$ of hot deserts to produce electric current. We further find a tilt-induced non-Drude contribution to conductivity which can be experimentally disentangled from the usual Drude pole.
Author comments upon resubmission
List of changes
1- We have added discussions after Eq. (54) to show that steady-state solutions are also possible. But in addition to steady- state solutions, there are also non-steady-state solutions that are of interest to us. Hopefully this will convince the referee 1 that our theory does not miss the steady-state solutions.
2- Around newly added equations (65)-(68) we have added estimates based on the measurements done on graphene samples to estimate that for tilted Dirac cone samples that are ∼ 1cm wide, currents of ∼ 4nA are attainable.
3- We have corrected typos here and there.
Published as SciPost Phys. Core 6, 010 (2023)
Reports on this Submission
Report 2 by Carlo Beenakker on 2022-8-26 (Contributed Report)
- Cite as: Carlo Beenakker, Report on arXiv:scipost_202110_00027v3, delivered 2022-08-26, doi: 10.21468/SciPost.Report.5584
Strengths
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.
Weaknesses
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.
Report
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.
Anonymous Report 1 on 2022-7-7 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202110_00027v3, delivered 2022-07-07, doi: 10.21468/SciPost.Report.5355
Report
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.
Seyed Akbar Jafari on 2022-07-13 [id 2658]
We are happy that the present referee's grading of the version 3 suggests "High" for the originality, "Good" for the clarity and significance, and suggests "Ok" for the validity of our results.
Please note that within Eqs. (54)-(58) we have found two sets of solutions: Those with zero pressure gradient and those with non-zero pressure gradient.
As for the "Hall-like" response, we have argued that since the ordinary rotations are not symmetries of the new spacetime, the symmetric part of the response can not be "rotated away".
We thank the present referee for the improvements arising from his/her insightful comments.