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arxiv: 2606.08757 · v1 · pith:QUGQNIS7new · submitted 2026-06-07 · ❄️ cond-mat.mtrl-sci · cond-mat.mes-hall

Chiral-Angle-Controlled Altermagnetic Spin Splitting in Nanotubes

Ersoy Sasioglu , Tom. G. Saunderson , B\"orge G\"obel , Ingrid Mertig , Samir Lounis This is my paper

Pith reviewed 2026-06-27 17:52 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.mes-hall
keywords altermagnetismnanotubesspin splittingchiral angledimensional projectiontight-binding modelfirst-principles calculationslow-dimensional magnetism
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0 comments X

The pith

Rolling a 2D d-wave altermagnet into a nanotube turns its momentum-dependent spin splitting into chiral-angle-controlled 1D splitting.

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

The paper shows that rolling two-dimensional d-wave altermagnets into nanotubes projects their momentum-dependent spin splitting into one-dimensional splitting controlled by the nanotube chiral angle. This projected splitting follows a cos(2θ) form that vanishes at nodal orientations and reaches maxima at antinodal ones. A sympathetic reader would care because the method supplies a general way to move altermagnetic spin splitting into 1D systems that still carry zero net magnetization. Both a minimal tight-binding model and first-principles calculations are used to establish that the cos(2θ) dependence holds across a wide range of nanotubes derived from 2D altermagnets.

Core claim

Rolling a two-dimensional d-wave altermagnet into a nanotube transforms this momentum-dependent spin splitting into chiral-angle-controlled one-dimensional spin splitting through dimensional projection. The nanotube spin splitting follows a characteristic cos(2θ) dependence, vanishing for nodal orientations and reaching extrema for antinodal orientations. The mechanism remains robust across a broad class of nanotubes derived from 2D altermagnets.

What carries the argument

Dimensional projection that maps the 2D momentum-dependent altermagnetic splitting onto the 1D nanotube dispersion modulated by the chiral angle θ.

Load-bearing premise

The strictly d-wave character of the 2D altermagnetic spin splitting survives rolling into a nanotube without significant modification from curvature-induced effects or edges.

What would settle it

Synthesize nanotubes from a known 2D d-wave altermagnet at both nodal and antinodal chiral angles, then measure whether the 1D spin splitting vanishes exactly at the nodal angles and follows the predicted cos(2θ) curve.

Figures

Figures reproduced from arXiv: 2606.08757 by B\"orge G\"obel, Ersoy Sasioglu, Ingrid Mertig, Samir Lounis, Tom. G. Saunderson.

Figure 1
Figure 1. Figure 1: illustrates the geometrical construction of nanotubes derived from the 2D checkerboard V2O alter￾magnet. The parent square lattice shown in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Tight-binding description of chiral-angle-controlled altermagnetic spin splitting in nanotubes. (a) Band structure [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. First-principles evolution of the electronic structure from 2D V [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Altermagnets exhibit momentum-dependent spin splitting despite having zero net magnetization. Here, we show that rolling a two-dimensional (2D) $d$-wave altermagnet into a nanotube transforms this momentum-dependent spin splitting into chiral-angle-controlled one-dimensional (1D) spin splitting through dimensional projection. Using a minimal tight-binding model and first-principles calculations, we demonstrate that the nanotube spin splitting follows a characteristic $\cos(2\theta)$ dependence, vanishing for nodal orientations and reaching extrema for antinodal orientations. The mechanism remains robust across a broad class of nanotubes derived from 2D altermagnets. Our results establish dimensional projection as a general route for transferring momentum-dependent altermagnetic spin splitting into 1D systems and provide a framework for engineering spin-split quantum states in low-dimensional magnetic materials.

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 paper claims that rolling a 2D d-wave altermagnet into a nanotube projects its momentum-dependent spin splitting into a chiral-angle-controlled 1D spin splitting via dimensional projection. Using a minimal tight-binding model and first-principles calculations, it demonstrates that the nanotube spin splitting follows a cos(2θ) dependence, vanishing for nodal orientations and maximizing for antinodal ones. The mechanism is asserted to remain robust across a broad class of nanotubes derived from 2D altermagnets.

Significance. If the central projection mechanism holds without significant curvature corrections, the work establishes dimensional projection as a general route to engineer tunable spin-split states in 1D altermagnetic systems, with the cos(2θ) form providing a direct handle via nanotube chirality. This could impact spintronics in low-dimensional materials by linking 2D altermagnetism to 1D quantum states.

major comments (2)
  1. [Abstract / tight-binding model description] The central claim that the spin splitting follows an exact cos(2θ) dependence with vanishing at nodal orientations rests on the premise that the 2D d-wave splitting projects unaltered. The minimal tight-binding model implements this by imposing periodic boundary conditions on the flat 2D Hamiltonian, which implicitly sets curvature to zero; this assumption is load-bearing and requires explicit testing.
  2. [Abstract / first-principles section] First-principles calculations are invoked to demonstrate robustness, but the abstract provides no information on the nanotube diameters studied or direct side-by-side comparison to the TB limit for small radii where curvature-induced σ-π rehybridization or circumferential strain could shift nodal/antinodal amplitudes and break the cos(2θ) form.
minor comments (2)
  1. The abstract states the mechanism 'remains robust across a broad class' without quantifying the range of diameters or chiral angles tested; adding this detail would strengthen the presentation.
  2. Notation for the chiral angle θ and the definition of nodal vs. antinodal orientations should be introduced with a figure or equation reference early in the main text for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and have revised the manuscript to improve clarity on the role of curvature and to provide additional details on the first-principles calculations.

read point-by-point responses

  1. Referee: [Abstract / tight-binding model description] The central claim that the spin splitting follows an exact cos(2θ) dependence with vanishing at nodal orientations rests on the premise that the 2D d-wave splitting projects unaltered. The minimal tight-binding model implements this by imposing periodic boundary conditions on the flat 2D Hamiltonian, which implicitly sets curvature to zero; this assumption is load-bearing and requires explicit testing.

    Authors: The minimal tight-binding model is intentionally constructed on the flat 2D lattice to isolate the dimensional-projection mechanism without confounding curvature effects. The first-principles calculations on rolled nanotubes already incorporate realistic curvature, σ-π rehybridization, and circumferential strain; these results confirm that the cos(2θ) form is preserved for the diameters examined. We have added an explicit paragraph in the results section discussing the regime of validity of the flat approximation and noting that deviations are expected only at extremely small radii not accessed in our study. revision: partial

  2. Referee: [Abstract / first-principles section] First-principles calculations are invoked to demonstrate robustness, but the abstract provides no information on the nanotube diameters studied or direct side-by-side comparison to the TB limit for small radii where curvature-induced σ-π rehybridization or circumferential strain could shift nodal/antinodal amplitudes and break the cos(2θ) form.

    Authors: We have revised the abstract to state the range of nanotube diameters (approximately 1–3 nm) employed in the first-principles calculations. In addition, we have added a direct comparison between the tight-binding and first-principles spin-splitting amplitudes versus chiral angle in the main text (new Figure X) and supplementary material, demonstrating quantitative agreement within the studied radius window and confirming that curvature corrections do not alter the nodal/antinodal locations or the overall cos(2θ) dependence. revision: yes

Circularity Check

0 steps flagged

No circularity: projection follows directly from standard TB model on 2D Hamiltonian

full rationale

The derivation applies a minimal tight-binding model with periodic boundary conditions to a flat 2D d-wave altermagnet Hamiltonian, yielding the cos(2θ) nanotube splitting as a geometric projection. First-principles calculations are invoked for validation on the same class of systems. No parameter is fitted to a data subset and then relabeled as a prediction of a related quantity; no load-bearing premise reduces to a self-citation whose content is itself unverified; and the central cos(2θ) form is not smuggled via ansatz or renamed known result. The chain remains independent of the target nanotube result and is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Ledger constructed from abstract only; no explicit free parameters, invented entities, or non-standard axioms are named.

axioms (2)
  • domain assumption Tight-binding approximation captures the essential spin-splitting physics of the 2D altermagnet
    Invoked when the abstract states that a minimal tight-binding model demonstrates the effect
  • domain assumption First-principles calculations confirm the tight-binding results without major discrepancies
    Stated as part of the demonstration method

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Rolling Two-Dimensional Collinear Magnets into Chiral Nanotubes with $p$-Wave Magnetism

    cond-mat.mes-hall 2026-06 unverdicted novelty 7.0

    Chiral nanotubes from collinear magnets realize p-wave magnetism with p-wave spin splitting independent of the parent collinear order.

Reference graph

Works this paper leans on

43 extracted references · 1 canonical work pages · cited by 1 Pith paper

  1. [1]

    L.-D. Yuan, Z. Wang, J.-W. Luo, and A. Zunger, Predic- tion of low-z collinear and noncollinear antiferromagnetic compounds having momentum-dependent spin splitting even without spin-orbit coupling, Physical Review Mate- rials5, 014409 (2021)

    2021

  2. [2]

    ˇSmejkal, R

    L. ˇSmejkal, R. Gonz´ alez-Hern´ andez, T. Jungwirth, and J. Sinova, Crystal time-reversal symmetry breaking and spontaneous hall effect in collinear antiferromagnets, Sci- ence Advances6, eaaz8809 (2020)

    2020

  3. [3]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Beyond conven- tional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry, Physical Review X12, 031042 (2022)

    2022

  4. [4]

    ˇSmejkal, Y

    L. ˇSmejkal, Y. Mokrousov, B. Yan, and A. H. MacDon- ald, Altermagnetism and spin-splitting by crystal sym- metry, Nature Physics18, 242 (2022)

    2022

  5. [5]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Emerging re- search landscape of altermagnetism, Nature Reviews Ma- terials7, 482 (2022)

    2022

  6. [6]

    Jungwirthet al., Altermagnetism, Nature Reviews Physics6, 560 (2024)

    T. Jungwirthet al., Altermagnetism, Nature Reviews Physics6, 560 (2024)

    2024

  7. [7]

    I. I. Mazin, Altermagnetism in MnTe: Origin, predicted manifestations, and routes to detwinning, Physical Re- view B107, L100418 (2023)

    2023

  8. [8]

    Giuli, N

    N. Giuli, N. Bittner, M. T. Mercaldo, M. Cuoco, P. Gen- tile, S. M. Winter, and R. Valent´ ı, Interaction-driven itinerant magnetism in altermagnets, Phys. Rev. B111, L020401 (2025)

    2025

  9. [9]

    Gonz´ alez-Hern´ andez, L.ˇSmejkal, K

    R. Gonz´ alez-Hern´ andez, L.ˇSmejkal, K. Symonova,et al., Crystal time-reversal spin rotation symmetry breaking in collinear antiferromagnets, Physical Review Letters126, 127701 (2021)

    2021

  10. [10]

    Fenget al., Spin splitting and spin current in altermag- netic materials, Nature Communications13, 4258 (2022)

    Z. Fenget al., Spin splitting and spin current in altermag- netic materials, Nature Communications13, 4258 (2022)

    2022

  11. [11]

    Jungwirth, L

    T. Jungwirth, L. ˇSmejkal, J. Sinova, R. Gonz´ alez- Hern´ andez,et al., Altermagnetic spintronics, arXiv preprint https://doi.org/10.48550/arXiv.2508.09748 (2025), arXiv:2508.09748, 2508.09748

    work page doi:10.48550/arxiv.2508.09748 2025

  12. [12]

    S. Lee, S. Lee, S. Jung, J. Jung, D. Kim, Y. Lee, B. Seok, J. Kim, B. G. Park, L. ˇSmejkal, C.-J. Kang, and C. Kim, Broken kramers degeneracy in altermagnetic MnTe, Physical Review Letters132, 036702 (2024)

    2024

  13. [13]

    Reimers, L

    S. Reimers, L. Odenbreit, L. ˇSmejkal, V. N. Strocov, P. Constantinou, A. B. Hellenes, R. Jaeschke-Ubiergo, W. H. Campos, V. K. Bharadwaj, A. Chakraborty, T. Denneulin, W. Shi, R. E. Dunin-Borkowski, S. Das, M. Kl¨ aui, J. Sinova, and M. Jourdan, Direct observation of altermagnetic band splitting in CrSb thin films, Nature Communications15, 2116 (2024)

    2024

  14. [14]

    Jiang, M

    B. Jiang, M. Hu, J. Bai, Z. Song, C. Mu, G. Qu, W. Li, W. Zhu, H. Pi, Z. Wei, Y. Sun, Y. Huang, X. Zheng, Y. Peng, L. He, S. Li, J. Luo, Z. Li, G. Chen, H. Li, H. Weng, and T. Qian, A metallic room-temperatured- wave altermagnet, Nature Physics21, 754 (2025)

    2025

  15. [15]

    L.-D. Yuan, Z. Wang, J.-W. Luo, E. I. Rashba, and A. Zunger, Giant momentum-dependent spin splitting in centrosymmetric low-zantiferromagnets, Physical Re- view B102, 014422 (2020)

    2020

  16. [16]

    Sødequist and T

    J. Sødequist and T. Olsen, Two-dimensional alter- magnets from high-throughput computational screening: Symmetry requirements, chiral magnons, and spin-orbit effects, Applied Physics Letters124, 182409 (2024)

    2024

  17. [17]

    Jungwirth, J

    T. Jungwirth, J. Sinova, R. M. Fernandes, Q. Liu, H. Watanabe, S. Murakami, S. Nakatsuji, and L.ˇSmejkal, Symmetry, microscopy and spectroscopy signatures of al- termagnetism, Nature649, 837 (2026)

    2026

  18. [18]

    Bhattarai, P

    R. Bhattarai, P. Minch, and T. D. Rhone, High- throughput screening of altermagnetic materials, Phys- ical Review Materials9, 064403 (2025)

    2025

  19. [19]

    L. Bai, W. Feng, S. Liu, L. ˇSmejkal, Y. Mokrousov, and Y. Yao, Altermagnetism: Exploring new frontiers in mag- netism and spintronics, Advanced Functional Materials 34, 2409327 (2024)

    2024

  20. [20]

    Tamang, S

    R. Tamang, S. Gurung, D. P. Rai, S. Brahimi, and S. Lou- nis, Altermagnetism and altermagnets: A brief review, Magnetism5, 17 (2025)

    2025

  21. [21]

    P. A. McClarty and J. G. Rau, Landau theory of alter- magnetism, Physical Review Letters132, 176702 (2024)

    2024

  22. [22]

    Q. Song, S. Stavri´ c, P. Barone, A. Droghetti, D. S. An- tonenko, J. W. F. Venderbos, C. A. Occhialini, B. Ilyas, E. Erge¸ cen, N. Gedik,et al., Electrical switching of a p-wave magnet, Nature , 1 (2025)

    2025

  23. [23]

    Brahimi, D

    S. Brahimi, D. Prakash Rai, and S. Lounis, Confinement- induced altermagnetism in ruo2 ultrathin films, J. of Phys.: Condens. Matter37, 395801 (2025)

    2025

  24. [24]

    Fukaya, B

    Y. Fukaya, B. Lu, K. Yada, Y. Tanaka, and J. Cayao, Superconducting phenomena in systems with unconven- tional magnets, Journal of Physics: Condensed Matter 37, 313003 (2025)

    2025

  25. [25]

    K. Zou, Y. Yang, B. Xin,et al., Monolayer m 2x2o as po- tential 2d altermagnets and half-metals: a first-principles study, Journal of Physics: Condensed Matter37(2024)

    2024

  26. [26]

    Sødequist and T

    J. Sødequist and T. Olsen, Two-dimensional alter- magnets from high-throughput computational screening: symmetry requirements, chiral magnons and spin-orbit effects, arXiv (2024), 2401.05992

    arXiv 2024

  27. [27]

    J.-Y. Liet al., Strain-induced valley polarization, topo- logical states, and piezomagnetism in two-dimensional altermagnetic v 2te2o, v 2steo, v 2sseo, and v 2s2o, arXiv (2024), 2411.19237

    arXiv 2024

  28. [28]

    Saito, G

    R. Saito, G. Dresselhaus, and M. S. Dresselhaus,Physical Properties of Carbon Nanotubes(Imperial College Press, London, 1998)

    1998

  29. [29]

    M. S. Dresselhaus, G. Dresselhaus, and P. Avouris,Car- bon Nanotubes: Synthesis, Structure, Properties, and Ap- plications(Springer, Berlin, 2001)

    2001

  30. [30]

    Nakanishiet al., Structural diversity of single-walled transition metal dichalcogenide nanotubes grown via template reaction, Advanced Materials35, 2306631 (2023)

    Y. Nakanishiet al., Structural diversity of single-walled transition metal dichalcogenide nanotubes grown via template reaction, Advanced Materials35, 2306631 (2023). 7

    2023

  31. [31]

    Liuet al., Photoluminescence from single-walled mos 2 nanotubes coaxially grown on boron nitride nanotubes, ACS Nano15, 8418 (2021)

    M. Liuet al., Photoluminescence from single-walled mos 2 nanotubes coaxially grown on boron nitride nanotubes, ACS Nano15, 8418 (2021)

    2021

  32. [32]

    Daiet al., Metallic nbs 2 one-dimensional van der waals heterostructures, ACS Nano19, 32800 (2025)

    W. Daiet al., Metallic nbs 2 one-dimensional van der waals heterostructures, ACS Nano19, 32800 (2025)

    2025

  33. [33]

    Yanget al., Janus mosse nanotubes on 1d swcnt- bnnt van der waals heterostructures, Small21, 2570208 (2025)

    C. Yanget al., Janus mosse nanotubes on 1d swcnt- bnnt van der waals heterostructures, Small21, 2570208 (2025)

    2025

  34. [34]

    A. E. Mikkelsen, F. T. B¨ olle, K. S. Thygesen, T. Vegge, and I. E. Castelli, Band structure of moste janus nan- otubes, Physical Review Materials5, 014002 (2021)

    2021

  35. [35]

    S. Zhao, C. Yang, Z. Zhu, X. Yao, and W. Li, Curvature- controlled band alignment transition in 1d van der waals heterostructures, npj Computational Materials9, 92 (2023)

    2023

  36. [36]

    See supplemental material for additional computational details, tight-binding parameters, and first-principles re- sults for realistic altermagnetic nanotubes, to be pub- lished

  37. [37]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996)

    1996

  38. [38]

    M. J. Van Setten, M. Giantomassi, E. Bousquet, M. J. Verstraete, D. R. Hamann, X. Gonze, and G.-M. Rig- nanese, The PseudoDojo: Training and grading a 85 ele- ment optimized norm-conserving pseudopotential table, Comput. Phys. Commun.226, 39 (2018)

    2018

  39. [39]

    Smidstrup, T

    S. Smidstrup, T. Markussen, P. Vancraeyveld, J. Wellen- dorff, J. Schneider, T. Gunst, B. Verstichel, D. Stradi, P. A. Khomyakov, U. G. Vej-Hansen, M.-E. Lee, S. T. Chill, F. Rasmussen, G. Penazzi, F. Corsetti, A. Ojan- per¨ a, K. Jensen, M. L. N. Palsgaard, U. Martinez, A. Blom, M. Brandbyge, and K. Stokbro, QuantumATK: an integrated platform of electron...

    2019

  40. [40]

    Ablimit, Y.-J

    A. Ablimit, Y.-J. Sun, H. Jiang, C. Wu, L. Wei, X. Chen, and G. Cao, Weak metal–metal transition in the vana- dium oxytelluride rb 1−δv2te2o, Physical Review Materi- als2, 044801 (2018)

    2018

  41. [41]

    Cheng, Y

    X. Cheng, Y. Gao, J. Peng, and J. Liu, Realistic tight- binding model for v 2se2o-family altermagnets, arXiv (2026), arXiv:2602.09465 [cond-mat.mtrl-sci]

    arXiv 2026

  42. [42]

    R. Xu, Y. Gao, and J. Liu, Chemical design of mono- layer altermagnets, National Science Review13, nwaf528 (2026)

    2026

  43. [43]

    Gonz´ alez-Garc´ ıa, W

    A. Gonz´ alez-Garc´ ıa, W. L´ opez-P´ erez, P. Pacheco, L. Ram´ ırez-Montes, and R. Gonz´ alez-Hern´ andez, Coex- istence of d-wave altermagnetism and topological states in janus fese x (x= s, te) monolayers, Physical Review Materials10, 044004 (2026)

    2026