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Theoretical investigations on Kerr and Faraday rotations in topological multiWeyl Semimetals
by Supriyo Ghosh, Ambaresh Sahoo, Snehasish Nandy
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Submission summary
Authors (as registered SciPost users):  Snehasish Nandy 
Submission information  

Preprint Link:  https://arxiv.org/abs/2209.11217v3 (pdf) 
Date submitted:  20221024 05:00 
Submitted by:  Nandy, Snehasish 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
Motivated by the recent proposal of giant Kerr rotation in WSMs, we investigate the Kerr and Faraday rotations in timereversal broken multiWeyl semimetals (mWSMs) in the absence of an external magnetic field. Using the framework of Kubo response theory, we find that both the longitudinal and transverse components of the optical conductivity in mWSMs are modified by the topological charge ($n$). Engendered by the optical Hall conductivity, we show in the thin film limit that, while the giant Kerr rotation and corresponding ellipticity are independent of $n$, the Faraday rotation and its ellipticity angle scale as $n$ and $n^2$, respectively. In contrast, the polarization rotation in semiinfinite mWSMs is dominated by the axion field showing $n$ dependence. In particular, its magnitude decreases with increasing $n$ in Faraday geometry, whereas in Voigt geometry, it depicts different $n$dependencies in different frequency regimes. The obtained results on the behavior of Kerr and Faraday rotations in mWSMs could be used in experiments as a probe to distinguish single, double, and triple WSMs, as well as discriminate the surfaces of mWSMs with and without hosting Fermi arcs.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 20221211 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2209.11217v3, delivered 20221211, doi: 10.21468/SciPost.Report.6288
Strengths
1. The paper provides a very detailed analysis of Kerr and Faraday rotation in mWSMs. It establishes a new electromagnetic response in mWSMs.
2. It is very well written and sufficient details are provided for the analysis.
Weaknesses
1. The paper doesn’t mention any possible candidate materials where this effect can be realized. Especially, the condition that there are only twonodes with crage greater than one with finite tilt makes the model very restrictive.
2. The paper doesn’t provide any analysis of energy scales. This is important because of many factors, especially the fact that continuum model is applicable only in a very tiny energy and momentum window for most Weyl semimetals. Usually, there are many electronic bands in the vicinity of Wey lnode and it’s difficult to disentangle the contributions arising from trivial bands and topological band crossings. For most materials even a twoband tightbinding model fails to capture these essential features as even the matrix elements between topological trivial bands start to contribute to conductivity. It would be helpful if authors can provide some estimate of energy and momentum cutoffs they have used in the continuum model on the basis of electronic band structure of existing topological weyl semimemetals.
Report
This paper investigates the electromagnetic response of topological multiWeyl semimetals. This paper satisfies the criteria of Scipost as this study opens up a new pathway to probe and utilize the topological features of multiWeyl semimetals using electromagnetic field. Most importantly, authors explore the dependence of Kerr and Faraday rotation on the charge of the Weyl node.
I highly recommend this paper for publication in Scipost. However, there are certain issues that should be addressed:
1. I don’t understand how can one measure Faraday rotation in semiinfinite geometry. Could authors please clarify what is meant by Faraday angle in Eq. 28. The Kerr rotation can be measured directly from the quantities evaluated in Eq. 27 but Faraday rotation also depends on the path light traverses inside the material. Here, it’s not so clear how would one measure the effect on the other end of the sample in semiinfinite geometry. Maybe, one can consider a bulk sample but given that the system here exhibit circular dichroisma dn circular birfringence so the rotation would also depend on the length of the sample. If I’m not missing something important here, this issue seems very concerning.
2. Now, even, in the thinfilm limit, the film thickness would play some role in deciding the Faraday rotation angle. The authors haved cited Ref. 51 which studies only Kerr and Faraday effect for monolayer graphene and hence the thickness of the sample doesn’t come into picture. It would be very helpful if authors can make some comments about the range of thickness and compare it to the wavelength of the light used which in turn would depend on the energy scales of the system which are not discussed here. Also, would Kerr rotation be modified in any way, if we also consider the reflection at the other end of the sample.
3.I would like to reemphasize that authors should also provide some estimate about the tilt as it decides the frequency range over which some of the quantities show a significantly important behavior.
There is a minor typo in the paragraph below Eq. 9. The frequency range for the region in which the vertical transitions are Pauli unblocked should be $omega>omega_2$.
4.It would help if authors can provide the derivation for equation 16 and 17. It’s not so clear how they divide the real part of the offdiagonal conductivity into DC and AC part. It seems that equation 16 is nonzero even in the Dc limit. Another worrisome aspect of these equations (1619) is that they diverge for zero tilt (C=0). Could authors please provide an interpretation for C=0 limit of these equations.
Overall the paper is very well written and the analysis is very informative.
Author: Snehasish Nandy on 20230212 [id 3346]
(in reply to Report 1 on 20221211)We are grateful to the Referee for his/her report, helpful comments and suggestions as well as positive assessment of our work. Please find our response to the comments from the Referee in the attached file.
Attachment:
Referee_Response.pdf