Chiral-Angle-Controlled Spin Splitting and Spin Transport in Nanotubes Rolled from d-wave Altermagnets

B\"orge G\"obel; Ersoy Sasioglu; Ingrid Mertig; Samir Lounis; Tom. G. Saunderson

REVIEW

Chiral-Angle-Controlled Spin Splitting and Spin Transport in Nanotubes Rolled from d-wave Altermagnets

Ersoy Sasioglu, Tom. G. Saunderson, Börge Göbel, Ingrid Mertig, Samir Lounis

Materials Science · Submitted 7 Jun 2026

Pith's verdict: The paper shows that rolling 2D d-wave altermagnets into nanotubes produces chiral-angle-dependent 1D spin splitting via cos(2θ), but the minimal model leaves curvature effects untested.

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arXiv ID2606.08757 (version 2)

Pith IDQUGQNIS7, Pith's permanent record of this paper and its review

CitationB\"orge G\"obel, Ersoy Sasioglu, Ingrid Mertig, Samir Lounis, Tom. G. Saunderson. "Chiral-Angle-Controlled Spin Splitting and Spin Transport in Nanotubes Rolled from d-wave Altermagnets." arXiv:2606.08757 (2026). https://pith.science/paper/QUGQNIS7

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Editor's note

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The main takeaway is that this work maps the momentum-dependent splitting of 2D d-wave altermagnets onto nanotubes, where the 1D splitting along the tube axis follows a cos(2θ) form set by the chiral angle θ. Splitting vanishes at nodal orientations and peaks at antinodal ones.

What is new is the explicit use of dimensional projection to turn the 2D altermagnetic feature into a tunable 1D one controlled by geometry. The abstract reports that both a minimal tight-binding model and first-principles calculations recover the same angular dependence, and the authors state the result holds across a range of nanotubes from different 2D parents.

The calculations themselves look standard and the claim of robustness is stated clearly. That gives the result a concrete, usable form for people thinking about 1D spin channels.

The soft spot is the curvature assumption. The tight-binding part imposes periodic boundaries on the flat 2D Hamiltonian, which removes any bending. If the first-principles checks were done only on larger-diameter tubes, they would not catch σ-π rehybridization or circumferential strain that could shift the nodal points or change the amplitude. Even modest deviations would break the exact cos(2θ) shape and the clean vanishing at nodes. The abstract asserts the mechanism survives, but without explicit small-diameter comparisons or error bars on that point, the load-bearing step remains unverified.

This is for the altermagnet and low-dimensional spintronics crowd. A reader already working on 2D altermagnets or nanotube spin filters would find a usable design rule. The paper is coherent on its own terms and the calculations are reproducible in principle, so it deserves a serious referee rather than a desk reject. The curvature question is fixable in revision if the authors supply the missing checks.

Referee report

Major objections (2)

[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.
[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.

Simulated authors' rebuttal

read the rebuttal and 2 point-by-point responses

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.

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
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

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The paper

The paper claims

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

The reading

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.

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.

Extended reading notes

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.

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.

Original abstract

Altermagnets combine compensated collinear magnetic order with momentum-dependent spin splitting in the electronic band structure. Here, we show that rolling a two-dimensional (2D) $d$-wave altermagnet into a nanotube converts this momentum dependence into chiral-angle-controlled one-dimensional (1D) spin splitting through dimensional projection. A minimal tight-binding model reveals a characteristic nodal--antinodal dependence on the chiral angle $\theta$, with the central circumferential subband exhibiting a $\cos(2\theta)$ scaling and the projected spin splitting vanishing for the nodal orientation and reversing sign between orthogonal antinodal orientations. First-principles calculations for V$_2$O and representative symmetric and Janus systems demonstrate that this nodal--antinodal selection rule persists despite curvature-induced structural asymmetry and magnetic moment imbalance. We further show that the projected electronic structure produces chiral-angle-controlled spin-polarized transport: antinodal nanotubes exhibit spin-polarized transmission, whereas the nodal nanotube remains conducting with identical spin-channel transmission. These results demonstrate how dimensional projection can translate the momentum-space spin splitting of a 2D altermagnet into geometrically controlled electronic and transport properties in nanotubes.

Figures

**Figure 1.** illustrates the geometrical construction of nanotubes derived from the 2D checkerboard V2O altermagnet. The parent square lattice shown in

**Figure 2.** FIG. 2. Tight-binding description of chiral-angle-controlled altermagnetic spin splitting in nanotubes. (a) Band structure

**Figure 3.** FIG. 3. First-principles evolution of the electronic structure from 2D V

Figures reproduced from arXiv:2606.08757 by the authors.

References

Forward citations

Cited by 3 Pith papers

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

Rolling Two-Dimensional Collinear Magnets into Chiral Nanotubes with $p$-Wave Magnetism
cond-mat.mes-hall 2026-06 unverdicted novelty 7.0 of 10

Chiral nanotubes from collinear magnets realize p-wave magnetism with p-wave spin splitting independent of the parent collinear order.
Coupled Spin-Orbital $p$-Wave Magnetism via Structural and Magnetic Chirality
cond-mat.mes-hall 2026-07 unverdicted novelty 6.5 of 10

Spin-orbit coupling couples structural and magnetic chirality to produce two symmetry-distinct p-wave phases with distinct longitudinal conductivity signatures.
Orbital Hall effect and orbital altermagnetism in even- and odd-parity-wave magnetic Lieb lattices
cond-mat.str-el 2026-09 accept novelty 6.0 of 10

Orbital Hall effect arises in d-wave altermagnets and p-wave magnets on a Lieb lattice without spin-orbit coupling, mirroring ferromagnetic transport.

How the literature uses it

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Note added— During the final stages of manuscript preparation, we were informed of recent related work [ref] , which investigates altermagnets rolled into chiral nanotubes with collinear magnetic order.

Rolling Two-Dimensional Collinear Magnets into Chiral Nanotubes with $p$-Wave Magnetism · Introduction · 0.80

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