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Chiral Anomaly Trapped in Weyl Metals: Nonequilibrium Valley Polarization at Zero Magnetic Field
by Pablo M. Perez-Piskunow, Nicandro Bovenzi, Anton R. Akhmerov, Maxim Breitkreiz
This is not the current version.
|As Contributors:||Anton Akhmerov · Maxim Breitkreiz · Pablo M. Perez-Piskunow|
|Arxiv Link:||https://arxiv.org/abs/2104.10059v1 (pdf)|
|Date submitted:||2021-04-21 15:12|
|Submitted by:||Breitkreiz, Maxim|
|Submitted to:||SciPost Physics|
In Weyl semimetals the application of parallel electric and magnetic fields leads to valley polarization -- an occupation disbalance of valleys of opposite chirality -- a direct consequence of the chiral anomaly. In this work, we present numerical tools to explore such nonequilibrium effects in spatially confined three-dimensional systems with a variable disorder potential, giving exact solutions to leading order in the disorder potential and the applied electric field. Application to a Weyl-metal slab shows that valley polarization also occurs without an external magnetic field as an effect of chiral anomaly "trapping": Spatial confinement produces chiral bulk states, which enable the valley polarization in a similar way as the chiral states induced by a magnetic field. Despite its finite-size origin, the valley polarization can persist up to macroscopic length scales if the disorder potential is sufficiently long ranged, so that direct inter-valley scattering is suppressed and the relaxation then goes via the Fermi-arc surface states.
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 2 on 2021-6-28 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2104.10059v1, delivered 2021-06-28, doi: 10.21468/SciPost.Report.3133
This paper is well-written and, taking into account the comments of Referee 1, the results in the paper are scientifically sound. I have a more general question: A random disorder potential should allow for bound states of Weyl fermions the valleys of the potential. A similar situation shows up in QCD, where quarks have a small mass and are approximately chiral Weyl fermions. Due to the confining potential for quarks generated by the strong force, left-handed and hence left-moving quarks are reflected into right moving and hence right-handed once at the right potential wall, go back to the left potential wall, get reflected back and so on. The potential walls hence mix left and right handed quarks, and the reflection back and forth leads to a non vanishing chiral condensate <PsibarL PsiR>. In condensed matter terms, this is a inter-valley pairing condensate. In QCD, this condensate spontaneously breaks the chiral symmetry (axial U(1) in Weyl semimetals). This argument is due to Banks and Casher. The upshot is that the bound states in a confining potential lead to a chiral condensate and hence to spontaneous symmetry breaking. The resulting goldstone modes are the mesons of QCD, and are approximately massless (due to the small quark mass). My question now is: If we have Weyl fermions trapped in a random disorder potential, a similar inter valley pairing condensate should be formed, in particular in the limit that the authors consider (Delta k >> 1/xi). This condensate should contribute to the conductivity calculation. Is this taken into account in this work already? If this question is satisfactorily answered, I support publication in SciPost.
Report 1 by Titus Neupert on 2021-5-20 (Invited Report)
- Cite as: Titus Neupert, Report on arXiv:2104.10059v1, delivered 2021-05-20, doi: 10.21468/SciPost.Report.2942
1) clear writing and good presentation
2) methodological advancement combined with nice physics question
3) many future applications and extensions for the method are conceivable
The manuscript introduces a formalism for the numerical computation of transport properties in mesoscopic systems for weak potential scattering. This formalism is applied to thin slabs of a Weyl semimetal, demonstrating a conductivity enhancement not dissimilar to the chiral anomaly, but purely introduced by finite size quantization. The manuscript is very well written and organized. It addresses a relevant physics question while at the same time introducing novel methodology.
I have three clarification questions and a few concrete requests for changes. The questions are:
1) Is the algorithm that finds the states on the Fermi contours guaranteed to produce the correct density of states for each band, i.e., does it take into account the magnitude of the fermi velocity when producing the discretization?
2) Much of the arguments depend on the numbers N, Ns, Nb, W. For the simulations, we only learn about the W that has been used. Maybe the Ns, Nb, N (or their ratio) could also be incorporated in the figures (maybe visually) if the authors would also consider that beneficial for the reader.
3) The method as presented in Sec. IIA would also be applicable to 3D systems, upon introducing another momentum quantum number. I do not understand why, as stated in Sec. IIB, it becomes invalid for thick slabs. In this case, should there not be an 'emergent' momentum quantum number, the kz momentum, so that the approach remains valid? Asked the other way around: if one "forgets" to include a quantum number in the formulation, would the numerics not work?
4) I find it a bit unsettling that the contradiction with the literature stated at the end of Sec. VB is left unresolved.
The requests for changes are noted below.
In view of the high quality of the manuscript, I would recommend its publication, provided the questions and requested changes are thoroughly addressed.
1) I think the work would benefit from a discussion on the robustness of the observed phenomena in more generic Weyl fermiologies: What if additional pockets are present in the bulk or on the surface, what if the Fermi arcs are not so perfectly straight (like in TaAs and similar materials, see e.g., PRB 97, 085142), what if the bulk Weyl cones are strongly anisotropic (while still type I) as is often the case?
2) For a paper that is on the technical side, I find the introduction and review of previous results too succinct. A more in-depth summary of results from the literature (which may also require extending the rather short list of references) would be beneficial for the reader.
3) There is a typo in the exponent of Eq. 29: x-> z