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Interplay between chiral medium and perfect electromagnetic conductor plates: repulsive vs. attractive Casimir force transitions
by Thomas Oosthuyse, David Dudal
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Authors (as registered SciPost users):  David Dudal · Thomas Oosthuyse 
Submission information  

Preprint Link:  https://arxiv.org/abs/2301.12870v3 (pdf) 
Date submitted:  20230302 13:50 
Submitted by:  Oosthuyse, Thomas 
Submitted to:  SciPost Physics 
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Academic field:  Physics 
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Approach:  Theoretical 
Abstract
We determine the Casimir energies and forces in a variety of potentially experimentally viable setups, consisting of parallel, fixed finite width slabs of Weyl semimetals (WSMs) and perfect electromagnetic conductor (PEMCs) plates, which are a generalization of perfect electric conductors (PECs) and perfect magnetic conductor (PMCs) plates. Where comparison is possible, our results agree with the Casimir forces calculated elsewhere in the literature, albeit with different methods. We find a multitude of known but also new cases where repulsive Casimir forces are in principle possible, but restricting the setup to PECs combined with the aforementioned WSM geometry, results in purely attractive Casimir forces.
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Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2023817 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2301.12870v3, delivered 20230817, doi: 10.21468/SciPost.Report.7669
Report
In this paper the authors develop a general method for computing the Casimir force between materials with varying electromagnetic properties in a parallelslab geometry. The types of materials considered include perfect electromagnetic conductors (PEMCs), of which Weyl semimetals (WSMs) are a special case. By considering pairings of different types of materials and the use of intermediate layers the authors identify several scenarios where their calculations yield a repulsive force.
The search for a repulsive Casimir effect resulting from exotic electromagnetic properties is not a new endeavor, as the authors acknowledge, but to my knowledge several of the configurations considered here are novel. I believe the work presented is a useful, if perhaps incremental, addition to this line of inquiry, though I have several comments and questions before I recommend publication.
1) The use of $\theta$ needs to be amended, as it is currently refers to two distinct quantities.
2) The authors have cited several references that examine the Casimir effect in PEMCs and Weyl semimetals, including some already identifying repulsive effects. How do the results obtained here compare to already known results when directly comparable, e.g. the case of two WSMs in vacuum considered in Ref 14 and by Rong, et al. in Chin. Phys. Lett. 38, 084501?
3) Can you comment on how realistic the parameters necessary for the repulsive regimes identified here are? Specifically, is it reasonable to suppose that PEMCs with arbitrary $\theta'$, or really with any value in the repulsive regime, can actually be realized?
4) In real systems, materials can only rarely be well approximated with idealized boundary conditions. For instance, it is not difficult to calculate corrections to the ideal Casimir effect between conducting plates due to imperfect EM reflection coefficients/finite conductivity. Can the authors comment or speculate on what effect deviations from the idealized behavior considered here might have on the repulsive effects they've identified? Could the imperfect case introduce a force component that washes out the repulsive effect?
5) It would be better to have the diagrams of the geometries being considered included in the relevant sections instead of in a separate appendix.
Report #1 by Anonymous (Referee 1) on 202379 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2301.12870v3, delivered 20230709, doi: 10.21468/SciPost.Report.7482
Report
The paper under the review studies the Casimir repulsion in systems consisting of perfect electromagnetic conducting plates and Weyl semimetal slabs. Similar problems have been addressed in many publications but for simpler geometries. The authors made several interesting predictions with regard to the amplitude, the sign, and the distance dependence of the Casimir force. Given the current interest in the Casimir repulsion and to Weyl semimetals, this is a relevant topic. However, before the manuscript can be recommended for publication the authors have to address the points listed below.
1. A few lines below Eq. (1) the authors claim that a constant part of $\theta$ is irrelevant for the equations of motion. This is not quite true. To derive equations of motion one has to integrate by parts in (1) which induces a surface ChernSimons type contribution which is proportional to the discontinuity of $\theta$. Such terms affect the propagation of electromagnetic waves through interface and thus influence the Casimir force. The authors have to explain this point.
2. The authors use the same letter $\theta$ to denote the axion field in (1) and a parameter in the boundary conditions (3). This is confusing and has to be corrected.
3. What are the realistic physical values of the parameters used in this work? My calculations done on the back of an envelope show that the product of the typical value of $\beta$ for Weyl semimetals and the typical scale of distances in Casimir experiments is about 0.01 or smaller. The values of $\beta d$ and $\beta L$ on Figures 14 are much larger. Also, usual metals are much closer to perfect electric conductors than to perfect magnetic ones corresponding to $\theta'\simeq \pm \pi/2$. Thus, perhaps naively, one can suspect that the physically relevant regions on the figures are very small (practically a point on each figure). Do the authors know any realistic material which allows access other regions of the parameters?