pith. sign in

arxiv: 2601.17681 · v2 · submitted 2026-01-25 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

Emergent Nodal Spheres and Weyl Fermions via Spin-Texture Coupled to Thin Film Orbital Dirac Semimetals

Pritam Chatterjee , Anirudha Menon This is my paper

Pith reviewed 2026-05-16 11:47 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-sci
keywords spin textureDirac semimetalWeyl semimetalnodal sphereanomalous Hall effectchiral magnetic effectFloquet Hamiltonianthin film
0
0 comments X

The pith

Coupling spin textures to thin-film Dirac semimetals generates Weyl semimetals and nodal spheres depending on the pitch vector.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that minimal coupling of a generic spin texture to the Hamiltonian of a thin-film orbital Dirac semimetal, followed by a unitary transformation that removes spatial dependence from the exchange term, produces effective corrections to the Dirac dispersion and grants a full function's worth of freedom. A linear pitch vector creates a Weyl semimetal phase that exhibits the anomalous Hall effect, which requires a nonzero pitch, and the chiral magnetic effect, which scales with the exchange coupling. A suitable time-dependent pitch vector produces a nodal sphere in momentum space at leading order in the Floquet effective Hamiltonian, while the full driven dynamics maintain a closed quasienergy degeneracy structure continuously connected to that sphere. A sympathetic reader would care because the construction supplies a direct, controllable route from spin textures to emergent topological fermions and nodal structures in thin-film systems.

Core claim

A linear pitch vector in the spin texture generates a Weyl semimetal phase, where the anomalous Hall coefficient requires a nonzero pitch vector and the chiral magnetic effect is proportional to the exchange coupling; additionally, a suitable time-dependent pitch vector leads to the emergence of a nodal sphere in momentum space within the leading-order Floquet effective Hamiltonian, with the full driven problem maintaining a closed quasienergy degeneracy structure continuously connected to this nodal sphere.

What carries the argument

The pitch vector of the spin texture, which parametrizes the effective corrections to the Dirac dispersion after a unitary transformation gauges away the spatial dependence of the exchange term.

Load-bearing premise

The minimal coupling of the thin-film Dirac semimetal Hamiltonian to a generic spin texture is valid and the unitary transformation that gauges away spatial dependence produces physically correct effective corrections without artifacts.

What would settle it

Measurement of the anomalous Hall conductivity as a function of pitch-vector magnitude, which should vanish exactly at zero pitch, or detection of the predicted nodal-sphere quasienergy degeneracy via time-resolved ARPES in a driven sample.

Figures

Figures reproduced from arXiv: 2601.17681 by Anirudha Menon, Pritam Chatterjee.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustrating the signatures of the CME [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Full energy spectrum from Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Landau-quantized band structure as a function of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The Floquet bulk spectrum of a nodal-ring semimetal [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

We consider the minimal coupling of a thin film Dirac semimetal Hamiltonian to a generic spin-texture. A simple unitary transformation gauges away the spatial dependence in the exchange term, leading to the generation of effective corrections to the Dirac dispersion. A full function's worth of freedom is obtained as a result. Choosing different pitch vectors, we show that many novel phenomena arise in such systems. For example, a linear pitch vector leads to the generation of a Weyl semimetal -- we observe the anomalous Hall effect and the chiral magnetic effect. The anomalous Hall coefficient requires a non-zero pitch vector whereas the CME is proportional to the exchange coupling. The band structure of the model in the presence of a magnetic field shows a Lifshitz-like transition driven by the exchange coupling. The introduction of a suitable time-dependent pitch vector leads, at the level of the leading-order Floquet effective Hamiltonian, to the emergence of a nodal sphere in momentum space. We further show that, in the full driven problem, a closed quasienergy degeneracy structure persists, continuously connected to this nodal sphere, and constrained by the operator algebra of the Floquet expansion.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript considers minimal coupling of a thin-film Dirac semimetal Hamiltonian to a generic position-dependent spin texture. A unitary transformation is applied to eliminate spatial dependence in the exchange term, generating effective corrections to the Dirac dispersion. A linear pitch vector is shown to produce a Weyl semimetal phase exhibiting the anomalous Hall effect (AHE) and chiral magnetic effect (CME), with AHE requiring nonzero pitch and CME proportional to exchange coupling; a magnetic-field-induced Lifshitz transition is also reported. A suitable time-dependent pitch vector yields a nodal sphere at leading order in the Floquet effective Hamiltonian, with a closed quasienergy degeneracy structure persisting in the full driven problem and constrained by the Floquet operator algebra.

Significance. If the unitary transformation can be shown to be non-artifactual and to preserve the relevant topological and transport properties, the construction would provide a controllable mechanism for generating Weyl fermions and nodal spheres in thin-film orbital Dirac semimetals via spin-texture engineering. The explicit relations between pitch vector, exchange coupling, AHE coefficient, and CME, together with the Floquet nodal-sphere result, would constitute a concrete advance in the design of topological phases and driven topological responses.

major comments (2)
  1. [Unitary transformation (abstract and central construction)] The unitary transformation that removes the spatial dependence from the exchange term (central to the abstract and all subsequent claims) is not derived explicitly. Without its explicit form, a demonstration that it is unitary, that the spectrum and Berry curvature are preserved, and that the generated effective corrections to the Dirac Hamiltonian are free of artifacts, the Weyl-semimetal, AHE, CME, and nodal-sphere conclusions cannot be verified. This step must be supplied with full matrix elements and a check that the transformation does not mix components in a way that alters the topological invariants.
  2. [Floquet section (time-dependent pitch)] For the time-dependent pitch vector, the leading-order Floquet effective Hamiltonian is asserted to produce a nodal sphere, with a closed quasienergy degeneracy persisting in the full driven problem. The explicit Floquet expansion, the range of validity of the leading-order truncation, and the operator-algebra constraint on the degeneracy structure must be shown in detail; otherwise the nodal-sphere claim rests on an unverified approximation.
minor comments (2)
  1. [Abstract] The phrase 'a full function's worth of freedom' obtained from the transformation is stated without specifying the functional form or the physical parameters it corresponds to; this should be clarified with an explicit parametrization of the pitch vector.
  2. [Transport signatures] The statement that the CME is 'proportional to the exchange coupling' while the AHE 'requires a non-zero pitch vector' should be accompanied by the explicit expressions for the coefficients (e.g., in terms of the effective Hamiltonian parameters) to allow direct comparison with experiment.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable suggestions. We address each major comment below and plan to incorporate the requested details into a revised manuscript.

read point-by-point responses

  1. Referee: [Unitary transformation (abstract and central construction)] The unitary transformation that removes the spatial dependence from the exchange term (central to the abstract and all subsequent claims) is not derived explicitly. Without its explicit form, a demonstration that it is unitary, that the spectrum and Berry curvature are preserved, and that the generated effective corrections to the Dirac Hamiltonian are free of artifacts, the Weyl-semimetal, AHE, CME, and nodal-sphere conclusions cannot be verified. This step must be supplied with full matrix elements and a check that the transformation does not mix components in a way that alters the topological invariants.

    Authors: We agree with the referee that the explicit derivation of the unitary transformation was not included in the original manuscript. This transformation is a local spin rotation U(r) = exp(-i phi(r) . sigma/2), where phi(r) is determined by the spin texture to eliminate its spatial dependence. In the revised version, we will derive it step by step, provide the full matrix elements, prove unitarity (U^dagger U = I), show that the spectrum is unchanged as it is a unitary transformation, and demonstrate that the Berry curvature and topological invariants are preserved because the transformation is a smooth gauge choice that does not introduce singularities or mix bands in a topologically nontrivial way. We will also confirm the absence of artifacts in the effective Dirac corrections. revision: yes

  2. Referee: [Floquet section (time-dependent pitch)] For the time-dependent pitch vector, the leading-order Floquet effective Hamiltonian is asserted to produce a nodal sphere, with a closed quasienergy degeneracy persisting in the full driven problem. The explicit Floquet expansion, the range of validity of the leading-order truncation, and the operator-algebra constraint on the degeneracy structure must be shown in detail; otherwise the nodal-sphere claim rests on an unverified approximation.

    Authors: We thank the referee for pointing this out. The manuscript indeed only states the result without full details. In the revision, we will include the explicit Floquet-Magnus expansion up to leading order, specify the high-frequency limit where the truncation is valid (driving frequency omega much larger than the energy scales of the system), and elaborate on the operator algebra of the Floquet operator that constrains the degeneracy to form a closed structure in quasienergy space. We will also provide evidence that the degeneracy persists beyond the approximation by considering the full time-periodic problem. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation proceeds from external inputs via explicit unitary map to effective Hamiltonian

full rationale

The paper begins with the thin-film Dirac semimetal Hamiltonian minimally coupled to an externally chosen spin texture (pitch vector supplied as input). A unitary transformation is applied to remove spatial dependence from the exchange term, producing effective dispersion corrections whose form is fixed by the transformation algebra rather than by any fitted data or self-referential definition. Specific linear and time-dependent pitch vectors are then inserted by hand to obtain the Weyl semimetal and nodal-sphere claims; these are not predictions fitted to the same observables they describe. No self-citation chain, ansatz smuggling, or renaming of known results is required for the central steps. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model assumes standard minimal coupling between Dirac electrons and a classical spin texture plus the validity of a unitary gauge transformation and leading-order Floquet averaging; no new particles or forces are postulated.

free parameters (2)
  • pitch vector
    Chosen by hand to produce linear, time-dependent, or other profiles that generate the reported Weyl and nodal-sphere phases.
  • exchange coupling strength
    External parameter controlling the magnitude of the spin-texture interaction; appears in the CME coefficient and Lifshitz transition.
axioms (2)
  • domain assumption Minimal coupling of spin texture to the Dirac Hamiltonian is physically valid
    Invoked at the start of the model construction in the abstract.
  • domain assumption Unitary transformation removes spatial dependence without altering observable physics
    Central step that generates the effective corrections to the Dirac dispersion.

pith-pipeline@v0.9.0 · 5513 in / 1431 out tokens · 46112 ms · 2026-05-16T11:47:34.202554+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

47 extracted references · 47 canonical work pages

  1. [1]

    N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and dirac semimetals in three-dimensional solids, Rev. Mod. Phys.90, 015001 (2018)

    work page 2018

  2. [2]

    S.-Y. Xu, N. Alidoust, I. Belopolski, Z. Yuan, G. Bian, T.-R. Chang, H. Zheng, V. N. Strocov, D. S. Sanchez, G. Chang, C. Zhang, D. Mou, Y. Wu, L. Huang, C.-C. Lee, S.-M. Huang, B. Wang, A. Bansil, H.-T. Jeng, T. Ne- upert, A. Kaminski, H. Lin, S. Jia, and M. Z. Hasan, Dis- covery of a weyl fermion state with fermi arcs in niobium arsenide, Nature Physics...

    work page 2015

  3. [3]

    L. X. Yang, Z. K. Liu, Y. Sun, H. Peng, H. F. Yang, T. Zhang, B. Zhou, Y. Zhang, Y. F. Guo, M. Rahn, D. Prabhakaran, Z. Hussain, S.-K. Mo, C. Felser, B. Yan, and Y. L. Chen, Weyl semimetal phase in the non- centrosymmetric compound taas, Nature Physics11, 728 (2015)

    work page 2015

  4. [4]

    B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, Experimental discovery of weyl semimetal taas, Phys. Rev. X5, 031013 (2015)

    work page 2015

  5. [5]

    H. Weng, C. Fang, Z. Fang, B. A. Bernevig, and X. Dai, Weyl semimetal phase in noncentrosymmetric transition- metal monophosphides, Phys. Rev. X5, 011029 (2015)

    work page 2015

  6. [6]

    S. M. Young, S. Zaheer, J. C. Y. Teo, C. L. Kane, E. J. Mele, and A. M. Rappe, Dirac semimetal in three dimen- sions, Phys. Rev. Lett.108, 145405 (2012)

    work page 2012

  7. [7]

    Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, Discovery of a three- dimensional topological dirac semimetal Na 3Bi, Science 343, 864 (2014)

    work page 2014

  8. [8]

    Z. Wang, Y. Sun, X.-Q. Chen, C. Franchini, G. Xu, H. Weng, X. Dai, and Z. Fang, Dirac semimetal and topo- logical phase transitions in A 3Bi(A = Na,K,Rb), Phys. Rev. B85, 195320 (2012)

    work page 2012

  9. [9]

    Neupane, S.-Y

    M. Neupane, S.-Y. Xu, R. Sankar, N. Alidoust, G. Bian, C. Liu, I. Belopolski, T.-R. Chang, H.-T. Jeng, H. Lin, A. Bansil, F. Chou, and M. Z. Hasan, Observation of a three-dimensional topological dirac semimetal phase in high-mobility Cd 3As2, Nature Communications5, 3786 (2014)

    work page 2014

  10. [10]

    Y. Kim, B. J. Wieder, C. L. Kane, and A. M. Rappe, Dirac line nodes in inversion-symmetric crystals, Phys. Rev. Lett115, 036806 (2015)

    work page 2015

  11. [11]

    Yu, H.Weng, Z

    R. Yu, H.Weng, Z. Fang, X. Dai, and X. Hu, Topo- logical node- line semimetal and dirac semimetal state in antiperovskite Cu 3PdN, Phys. Rev. Lett115, 036807 (2015)

    work page 2015

  12. [12]

    Hirayama, R

    M. Hirayama, R. Okugawa, T. Miyake, and S. Murakami, Topological dirac nodal lines and surface charges in fcc alkaline earth metals, Nature Communications8, 14022 (2017)

    work page 2017

  13. [13]

    Takahashi, M

    R. Takahashi, M. Hirayama, and S. Murakami, Spinless hourglass nodal-line semimetals, Phys. Rev. B96, 155206 (2017)

    work page 2017

  14. [14]

    M. Sato, J. Bouaziz, S. Sumita, S. Kobayashi, I. Tateishi, S. Bl¨ ugel, A. Furusaki, and M. Hirayama, Ideal spin- orbit-free dirac semimetal and diverse topological transi- tions in Pr 8CoGa3 family, Communications Materials5, 253 (2024)

    work page 2024

  15. [15]

    Yang and N

    B.-J. Yang and N. Nagaosa, Classification of stable three- dimensional dirac semimetals with nontrivial topology, Nature Communications5, 4898 (2014)

    work page 2014

  16. [16]

    Araki, Magnetic textures and dynamics in mag- netic weyl semimetals, Annalen der Physik532, 1900287 (2020)

    Y. Araki, Magnetic textures and dynamics in mag- netic weyl semimetals, Annalen der Physik532, 1900287 (2020)

    work page 2020

  17. [17]

    Bruno, V

    P. Bruno, V. K. Dugaev, and M. Taillefumier, Topolog- ical hall effect and berry phase in magnetic nanostruc- tures, Phys. Rev. Lett.93, 096806 (2004)

    work page 2004

  18. [18]

    Schulz, R

    T. Schulz, R. Ritz, A. Bauer, M. Halder, M. Wagner, C. Franz, C. Pfleiderer, K. Everschor, M. Garst, and A. Rosch, Emergent electrodynamics of skyrmions in a chiral magnet, Nature Physics8, 301 (2012)

    work page 2012

  19. [19]

    Nagaosa and Y

    N. Nagaosa and Y. Tokura, Emergent electromagnetism in solids, Physica Scripta2012, 014020 (2012)

    work page 2012

  20. [20]

    C.-X. Liu, P. Ye, and X.-L. Qi, Chiral gauge field and axial anomaly in a weyl semimetal, Phys. Rev. B87, 235306 (2013)

    work page 2013

  21. [21]

    Ozawa, Y

    A. Ozawa, Y. Araki, and K. Nomura, Chiral gauge field in fully spin-polarized magnetic weyl semimetal with mag- netic domain walls, Journal of the Physical Society of Japan93, 094704 (2024)

    work page 2024

  22. [22]

    R. Ilan, A. G. Grushin, and D. I. Pikulin, Pseudo- electromagnetic fields in 3d topological semimetals, Na- ture Reviews Physics2, 29 (2020)

    work page 2020

  23. [23]

    Terasawa and H

    R. Terasawa and H. Ishizuka, Anomalous hall effect by chiral spin textures in the two-dimensional luttinger model, Phys. Rev. B109, L060407 (2024)

    work page 2024

  24. [24]

    Ishihara, T

    Y. Ishihara, T. Mizushima, A. Tsuruta, and S. Fujimoto, Torsional chiral magnetic effect due to skyrmion textures in a weyl superfluid 3He−A, Phys. Rev. B99, 024513 (2019)

    work page 2019

  25. [25]

    L. An, X. Zhu, W. Gao, M. Wu, W. Ning, and M. Tian, Chiral anomaly and nontrivial berry phase in the topo- 7 logical nodal-line semimetal SrAs 3, Phys. Rev. B99, 045143 (2019)

    work page 2019

  26. [26]

    Redies, F

    M. Redies, F. R. Lux, J.-P. Hanke, P. M. Buhl, S. Bl¨ ugel, and Y. Mokrousov, Mixed topology ring states for hall ef- fect and orbital magnetism in skyrmions of weyl semimet- als, Phys. Rev. B102, 184407 (2020)

    work page 2020

  27. [27]

    Heidari, R

    S. Heidari, R. Asgari, and D. Culcer, Probing domain wall dynamics in magnetic weyl semimetals via the non- linear anomalous hall effect, Phys. Rev. B107, 214450 (2023)

    work page 2023

  28. [28]

    Harada and H

    A. Harada and H. Ishizuka, Spin motive force by the momentum-space berry phase in magnetic weyl semimet- als, Phys. Rev. B107, 195202 (2023)

    work page 2023

  29. [29]

    R. Hess, H. F. Legg, D. Loss, and J. Klinovaja, Preva- lence of trivial zero-energy subgap states in nonuniform helical spin chains on the surface of superconductors, Phys. Rev. B106, 104503 (2022)

    work page 2022

  30. [30]

    Chatterjee, S

    P. Chatterjee, S. Banik, S. Bera, A. K. Ghosh, S. Prad- han, A. Saha, and A. K. Nandy, Topological supercon- ductivity by engineering noncollinear magnetism in mag- net/superconductor heterostructures: A realistic pre- scription for the two-dimensional kitaev model, Phys. Rev. B109, L121301 (2024)

    work page 2024

  31. [31]

    Chatterjee, A

    P. Chatterjee, A. K. Ghosh, A. K. Nandy, and A. Saha, Second-order topological superconductor via noncollinear magnetic texture, Phys. Rev. B109, L041409 (2024)

    work page 2024

  32. [32]

    Subhadarshini, A

    M. Subhadarshini, A. Pal, P. Chatterjee, and A. Saha, Multiple topological phase transitions unveiling gapless topological superconductivity in magnet/unconventional superconductor hybrid platform, Applied Physics Letters 124, 183102 (2024)

    work page 2024

  33. [33]

    Chatterjee, S

    P. Chatterjee, S. Pradhan, A. K. Nandy, and A. Saha, Tailoring the phase transition from topological super- conductor to trivial superconductor induced by magnetic textures of a spin chain on ap-wave superconductor, Phys. Rev. B107, 085423 (2023)

    work page 2023

  34. [34]

    Br¨ uning, J

    R. Br¨ uning, J. Bedow, R. Lo Conte, K. von Bergmann, D. K. Morr, and R. Wiesendanger, The noncollinear path to two-dimensional topological superconductivity, ACS Nano19, 36215 (2025)

    work page 2025

  35. [35]

    Subhadarshini, A

    M. Subhadarshini, A. Pal, P. Chatterjee, and A. Saha, Identifying majorana edge and end modes in a joseph- son junction of ap-wave superconductor with a magnetic barrier, Phys. Rev. B112, 115439 (2025)

    work page 2025

  36. [36]

    Araki and K

    Y. Araki and K. Nomura, Charge pumping induced by magnetic texture dynamics in weyl semimetals, Phys. Rev. Appl.10, 014007 (2018)

    work page 2018

  37. [37]

    Bera and S

    S. Bera and S. John, Spin-flux skyrmions: Anoma- lous electron dynamics and spin-hall currents (2025), arXiv:2511.19239 [cond-mat.mes-hall]

    work page arXiv 2025

  38. [38]

    Menon and B

    A. Menon and B. Basu, Anomalous hall transport in tilted multi-weyl semimetals, Journal of Physics: Con- densed Matter33, 045602 (2020)

    work page 2020

  39. [39]

    Menon, S

    A. Menon, S. Chattopadhay, and B. Basu, Chiral mag- netic effect in lattice models of tilted multi-weyl semimet- als, Phys. Rev. B104, 075129 (2021)

    work page 2021

  40. [40]

    A. A. Zyuzin and A. A. Burkov, Topological response in weyl semimetals and the chiral anomaly, Phys. Rev. B 86, 115133 (2012)

    work page 2012

  41. [41]

    Chang and M.-F

    M.-C. Chang and M.-F. Yang, Chiral magnetic effect in the absence of weyl node, Phys. Rev. B92, 205201 (2015)

    work page 2015

  42. [42]

    Chang and M.-F

    M.-C. Chang and M.-F. Yang, Chiral magnetic effect in a two-band lattice model of weyl semimetal, Phys. Rev. B91, 115203 (2015)

    work page 2015

  43. [43]

    Fukushima, D

    K. Fukushima, D. E. Kharzeev, and H. J. Warringa, Chi- ral magnetic effect, Phys. Rev. D78, 074033 (2008)

    work page 2008

  44. [44]

    Ebihara, K

    S. Ebihara, K. Fukushima, and T. Oka, Chiral pumping effect induced by rotating electric fields, Phys. Rev. B 93, 155107 (2016)

    work page 2016

  45. [45]

    H¨ ubener, M

    H. H¨ ubener, M. Sentef, and U. De Giovannini, Creat- ing stable floquet–weyl semimetals by laser-driving of 3d dirac materials, Nature Communications8, 13940 (2017)

    work page 2017

  46. [46]

    Menon, D

    A. Menon, D. Chowdhury, and B. Basu, Photoinduced tunable anomalous hall and nernst effects in tilted weyl semimetals using floquet theory, Phys. Rev. B98, 205109 (2018)

    work page 2018

  47. [47]

    T. Nag, A. Menon, and B. Basu, Thermoelectric trans- port properties of floquet multi-weyl semimetals, Phys. Rev. B102, 014307 (2020)

    work page 2020