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REVIEW 3 major objections 5 minor 125 references

Quantum Transport with Spin Orbit Coupling: New Developments in TranSIESTA

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper reports the extension of the open-source DFT+NEGF transport code TranSIESTA to full spinor wave functions, enabling first-principles calculations of transport in devices with spin-orbit coupling and non-collinear magnetism.

desk verdict Solid spinor NEGF implementation with a genuinely new transmission projector; needs reproducibility and buffer-convergence checks before acceptance. read the letter →

arxiv 2501.16162 v2 pith:2KDJZ6RK submitted 2025-01-27 cond-mat.mes-hall

Nils Wittemeier , Nick Papior , Mads Brandbyge , Zeila Zanolli , Pablo Ordejón This is my paper · ORCID
classification cond-mat.mes-hall
keywords spin-orbitcouplingnon-equilibriumGreen'sfunctionDFT+NEGFTranSIESTAnon-collinearmagnetismquantumtransportspin-channelprojectedtransmissionmagnetoresistance
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The authors set out to remove a long-standing restriction of the open-source DFT+NEGF transport code TranSIESTA: it previously treated only spin-unpolarized or collinear-spin systems, where the Hamiltonian splits into independent spin blocks. Their new implementation promotes every NEGF matrix to 2x2 blocks in spin space, so the full spinor wave function is carried through the calculation. That makes it possible, for the first time in this code, to simulate non-equilibrium multi-terminal transport with spin-orbit coupling and non-collinear magnetic configurations from first principles. The authors demonstrate the capability on monatomic iron chains with domain walls, Fe/MgO/Fe tunnel junctions, a lateral MoS2/WS2 heterojunction, and carbon nanotubes functionalized with magnetic molecules. If correct, this closes the gap between open-source DFT transport codes and the spinor physics needed for topological materials and spintronics devices.

What carries the argument

The load-bearing object is the retarded Green's function in spinor form, $G_k(z)=[zS_k-H_k-\sum_e\Sigma_{e,k}(z)]^{-1}$, where $S_k$, $H_k$, and the self-energies $\Sigma_{e,k}$ are built with each orbital matrix element expanded as a $2\times2$ block in spin space; this is what couples the spin channels. The central analysis identity is the spin-channel projected transmission $T^{\sigma\vec n,\sigma'\vec m}_{e,e'}(z)=\int_{\mathrm{BZ}} dk\,\mathrm{Tr}\{\Gamma^{\sigma\vec n}_{e,k}(z)\,A^{\sigma'\vec m}_{e',k}(z)\}$, expressed through spin-selective broadening matrices $\Gamma^{\sigma\vec n}_{e,k}=\Gamma^{1/2}_{e,k}|\sigma\vec n\rangle\langle\sigma\vec n|\Gamma^{1/2}_{e,k}$ and the corresponding spectral density $A^{\sigma\vec n}_{e,k}=G_k\Gamma^{\sigma\vec n}_{e,k}G_k^\dagger$. This object lets the user resolve transmission into same-spin and spin-flip channels for arbitrary quantization axes in each electrode, which is the key new observable enabled by the implementation.

What would settle it

Compute the zero-bias transmission of the Fe/MgO/Fe junction with 5, 6, and 7 fixed iron layers between the MgO barrier and the electrode region; if the transmission changes by more than the numerical tolerance instead of converging, the bulk-electrode assumption is violated and the spinor transport results are not converged. The same screening test applied to the TMD heterojunction (40 vs 56 atoms) is the only place in the paper where this assumption is explicitly checked.

Watch

Extended reading notes

Core claim

The paper's central claim is that TranSIESTA can now perform self-consistent DFT+NEGF calculations for general spinors, not just collinear spins. In the collinear case the Hamiltonian is block diagonal in spin and the two channels can be treated independently; with spin-orbit coupling or non-collinear magnetization the off-diagonal spin blocks couple the channels, and the old code could not handle this. The implementation therefore expands each orbital matrix element $A_{ij}$ into a $2\times2$ spin block, keeps the sparse-matrix bandwidth small by interleaving spin indices, reuses the Sancho-Sancho-Rubio algorithm for surface self-energies (which is agnostic to spin indices), and supports both full and block-tridiagonal inversion of the spinor Green's function $G_k(z)=[zS_k-H_k-\sum_e\Sigma_{e,k}(z)]^{-1}$. The post-processing tool TBTrans is extended with a spin-channel projected transmission that projects the scattering matrix onto spin eigenstates along arbitrary axes, and the authors show that a cheaper alternative that projects the broadening matrix instead gives unphysical results wherever the electrode spin texture is non-collinear. Validation runs reproduce reference band structures and transmissions, and reveal SOC-induced effects such as band splitting, avoided crossings, spin-flip transmission through domain walls, a 1% ballistic anisotropic magnetoresistance in bulk iron, and diode-like IV behavior in the gated MoS2/WS2 junction.

Load-bearing premise

The method assumes the electrodes remain bulk-like and undisturbed by the device, so surface self-energies from a converged bulk DFT calculation stay valid; the paper directly verifies this screening only for the TMD heterojunction, not for the iron chains, Fe/MgO/Fe, or the carbon-nanotube systems.

Editorial extensions

If this is right

  • TranSIESTA can now model finite-bias, multi-terminal devices with spin-orbit coupling or non-collinear spins without a collinear-spin approximation, so topological-material and spintronics devices become accessible to open-source first-principles transport simulation.
  • Spin-flip transmission between electrodes with different magnetization directions can be computed and decomposed by quantization axis, making domain-wall resistance, anisotropic magnetoresistance, and tunneling magnetoresistance calculations routine.
  • The implementation inherits the block-tridiagonal inversion and parallel scaling of the current TranSIESTA, so the spinor capability is available for large systems (tested up to 816 atoms and 11088 orbitals).
  • For semiconductor heterojunctions, the TMD example shows that uniform gating can supply enough screening for the bulk-electrode assumption to hold, allowing self-consistent NEGF studies of lateral 2D junctions with strong spin-orbit coupling.
  • The open-system treatment of molecule-functionalized carbon nanotubes gives a converged magnetic moment for {Co4}-CNT where periodic supercell calculations did not converge, implying that transport geometry itself can be necessary for correct magnetic ground states in these hybrids.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The spin-channel projection machinery could be applied beyond total transmission, for example to decompose conductances into spin-valley or spin-momentum-locking contributions in topological surface states; the paper does not attempt this, but Eq. (28) already supplies the operator form.
  • The demonstrated failure of broadening-matrix projection for non-collinear electrode states is a caution for any transport code that uses such a shortcut; the scattering-matrix projection may be the needed default wherever electrode spin textures are energy-dependent.
  • A testable extension would be to compute the domain-wall spin-flip transmission as a function of domain-wall width and SOC strength; the code now permits this systematically, and the paper only reports widths of 4-6 atoms.
  • The {Co4}-CNT result suggests that for molecule-nanotube hybrids, transport simulations with semi-infinite electrodes may be needed to converge magnetic properties, not merely transport functions; this could be checked by computing the PBC magnetic moment for even larger supercells.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This paper reports an implementation of spinor (non-collinear and spin-orbit) DFT+NEGF in the open-source TranSIESTA code. The authors extend the Green's function, density matrix, self-energy, and transmission routines from independent spin channels to 2x2 spin blocks, implement spin-channel projected transmission via scattering-matrix projectors, and apply the code to monatomic Fe chains with domain walls, Fe/MgO/Fe junctions, a gated MoS2/WS2 lateral heterojunction, and carbon nanotubes with magnetic clusters. The results are compared with QuantumATK and previous DFT studies.

Significance. If the implementation is correct, it fills a genuine gap: an open-source DFT+NEGF code capable of multi-terminal finite-bias transport with full spinor wavefunctions. The formalism is standard and the manuscript contains useful methodological contributions, including the spin-projected transmission based on the scattering matrix (Eq. 28) and the demonstration that direct broadening-matrix projection (Eq. 29) fails for non-collinear electrode states. The cross-checks against QuantumATK and existing band-structure literature are a strength. However, the validation is uneven: key quantitative claims (TMR, MAE) are not backed by direct comparisons, and the screening assumption underpinning the NEGF construction is tested only in one system.

major comments (3)
  1. [Sec. VII.B.2] The abstract and Sec. VII.B state that the Fe/MgO/Fe junction is used to test whether the implementation reproduces previous predictions for tunneling magnetoresistance, but no quantitative TMR ratio is reported anywhere in the manuscript. Only the parallel-state Fermi-level transmission (T about 0.0044) and spin-channel decompositions are given; the antiparallel transmission and the TMR ratio are absent. Please provide T_AP, the TMR ratio (T_P - T_AP)/T_AP at the Fermi level (or over the bias window), and compare with Refs. [74,75] and other DFT results. Without this, the headline validation claim for magnetoresistance is unsubstantiated.
  2. [Sec. VII.A.3 and Sec. IV] The iron-chain transport calculations use a scattering region of only 4 Fe atoms between semi-infinite electrodes (Sec. VII.A.3), with no buffer-size convergence test for the electrode self-energy. In Sec. IV the method assumes that electrodes are bulk-like and that screening regions ensure transferability of the bulk self-energy (Fig. 1, Eq. 5). For a 1D metallic chain, screening is weak and the domain wall is a non-collinear perturbation extending over several atoms; the abrupt connection to the bulk electrode could affect the transmission. Please report convergence of the domain-wall transmission with the number of buffer atoms, or state this limitation explicitly with an estimate of its effect on the reported conductances.
  3. [Sec. VII.A.1] The MAE of the infinite Fe chain is reported to be a factor of 2 lower than Refs. [86,87] and is attributed to bond-length sensitivity. Since no bond-length dependence is shown, this discrepancy is not actually resolved. Please provide the MAE at the same lattice constant as the reference calculations or a plot of MAE versus bond length, so the reader can judge whether the discrepancy is a parameterization effect rather than an implementation error.
minor comments (5)
  1. [Abstract] The abstract contains a typo: "Exisiting" should be "Existing".
  2. [Sec. III] The spin-box Hermiticity condition is stated as H^{σσ'}_{ij} = (H^{σ'σ}_{ij})^*, but the orbital indices should also be exchanged: H^{σσ'}_{ij} = (H^{σ'σ}_{ji})^*. As written, the condition is only correct for i = j.
  3. [Sec. VII.C.3 and Sec. VII.B.2] There are typos in the text: "QunatumATK" should be "QuantumATK", and "previously obta,ined results" should be "previously obtained results".
  4. [Sec. VII.C.2 / Fig. 19] The 40-versus-56-atom screening test is performed on heavily hole-doped metallic monolayers; a sentence clarifying that this does not validate the undoped semiconducting case would help set expectations for the reader.
  5. [Sec. V.E] The weighting scheme in Eqs. 22-24 uses only the charge-density variance; a sentence explaining why the spin-block off-diagonal terms can be neglected in the weights (while still being included in the density matrix) would clarify the numerical rationale.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: spinor DFT+NEGF implementation is benchmarked against independent codes and prior results; self-citations are foundational, not load-bearing.

full rationale

The paper is an implementation and validation study of spinor DFT+NEGF in TranSIESTA. The central quantities (Green's function, transmission, current) are computed from the standard NEGF equations (Eqs. 5-12) with no fitted parameters later reported as predictions. Validation is anchored to independent external references: QuantumATK for TMD band structures and transmissions, and previously published DFT results for Fe chains, Fe/MgO/Fe TMR, and domain-wall resistance. The self-citations ([19], [37]) introduce the pre-existing TranSIESTA formalism and algorithms; they are foundational implementation references, not uniqueness arguments or ansatz justifications that force the reported results. The screening-region assumption (Sec. IV) is a physical/numerical assumption and is explicitly convergence-tested for the TMD junction (Fig. 19); lack of such a test for other systems is a completeness/robustness concern, not circularity. I find no step in which a 'prediction' reduces by construction to a fit or to a self-citation chain.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard DFT+NEGF machinery plus a set of hand-chosen system parameters (Hubbard U values, gate doping, strain, fixed layers, contour settings). The most fragile modeling assumption is the bulk-like electrode approximation. No new physical entities are introduced.

free parameters (6)
  • Hubbard U for Mn (Mn4 clusters) = 6 eV
    Adopted from Kampert et al. (Ref. [108]) to localize Mn 3d electrons; used in the {Mn4}-CNT spin-polarized calculations and affects the transmission near the Fermi level.
  • Hubbard U for Co (Co4 clusters) = 4 eV
    Chosen by hand for Co 3d electrons; no independent fitting is reported; used in the {Co4}-CNT calculations and affects magnetic moments and transmission.
  • Gate charge density for TMD heterojunction = 5.76e-3 e/A^2
    A uniform charge plane 30 Å below the monolayer is used to hole-dope MoS2/WS2 into a metallic state; sets the Fermi-level transport window and the IV asymmetry.
  • Lattice strain in MoS2/WS2 heterojunction = 0.4%
    Applied to match in-plane lattice constants of the two TMDs (aLat=3.165 A); affects band alignment and transmission of the junction.
  • Fixed-layer count in Fe/MgO/Fe junction = 1 fixed layer
    The authors find that relaxing all atoms between electrodes adds contact scattering and choose to keep one extra layer fixed; this hand-tuned choice changes the junction transmission.
  • Complex contour parameters for iron chain density matrix = circle from (-20+0.1i) eV, line at -10 k_B eV, 10 poles, 32 Fermi poles
    Numerical integration parameters for the NEGF density matrix; chosen to converge the SCF loop and influence the computed transmission.
assumptions (5)
  • standard math NEGF partition of the system into electrodes and scattering region with self-energies
    Section IV, Eqs. (5)-(8): the retarded Green's function is the inverse of zS-H minus the sum of electrode self-energies; this is the foundation of the transport formalism.
  • domain assumption Electrodes are bulk-like and unperturbed by the scattering region
    Section IV and Fig. 1: 'We further assume that electrode regions are bulk-like, i.e. unperturbed by the presence of the scattering region.' Surface self-energies are therefore computed once from a bulk DFT Hamiltonian.
  • domain assumption Spin-box Hermiticity holds for non-collinear spins without SOC
    Section III: H^{sigma sigma'} = (H^{sigma' sigma})^* and similarly for the density matrix; this symmetry is inherited from SIESTA and used in the spinor implementation.
  • domain assumption Sancho-Sancho-Rubio algorithm remains valid for 2x2 spin-block matrices
    Section V.C: 'the SSR algorithm ... is agnostic to the difference of spin and orbitals indices. Therefore, it can be reused completely.' This assumes the iterative decimation is stable for spinor matrices.
  • domain assumption Electrodes remain in equilibrium under applied bias
    Section IV: 'the NEGF formalism assumes that currents passing through the central region are not perturbing the electrodes which is assumed to be in equilibrium.'

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Pith. "Pith review of Quantum Transport with Spin Orbit Coupling: New Developments in TranSIESTA." pith.science (2026). https://pith.science/paper/2KDJZ6RK

@misc{pith2026250116162,
  author       = {Pith},
  title        = {Pith review of: Quantum Transport with Spin Orbit Coupling: New Developments in TranSIESTA},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2KDJZ6RK}},
  note         = {Machine review of arXiv:2501.16162}
}
read the original abstract

We present the implementation of spinor quantum transport within the non-equilibrium Green's function (NEGF) code TranSIESTA based on Density Functional Theory (DFT). First-principles methods play an essential role in molecular and material modelling, and the DFT+NEGF approach has become a widely-used tool for quantum transport simulation. Exisiting (open source) DFT-based quantum transport codes either model non-equilibrium/finite-bias cases in an approximate way or rely on the collinear spin approximation. Our new implementation closes this gap and enables the TranSIESTA code to use full spinor-wave functions. Thereby it provides a method for transport simulation of topological materials and devices based on spin-orbit coupling (SOC) or non-collinear spins. These materials hold enormous potential for the development of ultra-low energy electronics urgently needed for the design of sustainable technology. The new feature is tested for relevant systems determining magnetoresistance in iron nanostructures and transport properties of a lateral transition metal dichalcogenide heterojunction.

Figures

Figures reproduced from arXiv: 2501.16162 by the authors.

Figure 1
Figure 1. FIG. 1. Sketch of a setup for 3-electrode transport simulation. The three electrodes are depicted in three different colors (grey, [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Performance characterization of [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Schematic of five different spin alignments in monoatomic chains: (a) parallel spins perpendicular to the chain axis [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (23 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Comparison of scalar relativistic (SR) and fully relativistic (FR) spin band structure of a monatomic iron chains with [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Spin texture (a - d) and spin-channel projected transmission (e,f) of an iron chain with spin magnetic moments [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Spin texture (a) and spin-channel projected transmission (b,c) of an iron chain with spin magnetic moments parallel [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Infinite iron chain with a 6-atom wide domain wall (blue atoms) between two semi-infinite sections with opposite [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Direction and size of spin moments in a 4-atom-wide, constrained domain wall with ∆ [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Zero-bias transmission of 180 [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Band structure of bulk iron magnetized along the [001] direction. The band structure is calculated along a line parallel [PITH_FULL_IMAGE:figures/full_fig_p016_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Zero-bias transmission of bulk iron for magnetization parallel (a and c) and perpendicular (b and d) to the transport [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Ball and stick model of a Fe/MgO/Fe junction in side view (left) and a crosssection at the interface (right). At the [PITH_FULL_IMAGE:figures/full_fig_p018_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. Spectral function and zero-bias transmission of a Fe/MgO/Fe tunneling junction with 4 MgO layers. (a) Spectral [PITH_FULL_IMAGE:figures/full_fig_p018_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14. Spin channel projected zero-bias transmission of a Fe/MgO/Fe tunneling junction with 4 MgO layers. [PITH_FULL_IMAGE:figures/full_fig_p020_14.png]
Figure 15
Figure 15. Figure 15: FIG. 15. Convergence of the transmission function in a Fe/MgO/Fe junction with number of iron layers between the MgO [PITH_FULL_IMAGE:figures/full_fig_p021_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16. Band structure and zero-bias transmission function of monolayer MoS [PITH_FULL_IMAGE:figures/full_fig_p021_16.png]
Figure 17
Figure 17. Figure 17: FIG. 17. Crystal structure of a lateral MoS [PITH_FULL_IMAGE:figures/full_fig_p022_17.png]
Figure 18
Figure 18. Figure 18: FIG. 18. Zero-bias transmission of hole-doped (5 [PITH_FULL_IMAGE:figures/full_fig_p023_18.png]
Figure 19
Figure 19. Figure 19: FIG. 19. Planar- and macro averaged electrostatic potential of an MoS [PITH_FULL_IMAGE:figures/full_fig_p023_19.png]
Figure 20
Figure 20. Figure 20: FIG. 20. Local density of states averaged over the transverse directions of a lateral MoS [PITH_FULL_IMAGE:figures/full_fig_p024_20.png]
Figure 21
Figure 21. Figure 21: FIG. 21. Zero-bias transmission of hole-doped (5 [PITH_FULL_IMAGE:figures/full_fig_p025_21.png]
Figure 22
Figure 22. Figure 22: FIG. 22. Periodic boundary conditions (top left) and open system (bottom) set-up for first-principles simulations of [PITH_FULL_IMAGE:figures/full_fig_p026_22.png]
Figure 23
Figure 23. Figure 23: FIG. 23. Spin density of [PITH_FULL_IMAGE:figures/full_fig_p028_23.png]
Figure 24
Figure 24. Figure 24: FIG. 24. (Open System) Absolute value of spin density integrated over x and y (z = 0 located at the molecule) for the [PITH_FULL_IMAGE:figures/full_fig_p029_24.png]
Figure 25
Figure 25. Figure 25: FIG. 25. Transmission function of [PITH_FULL_IMAGE:figures/full_fig_p029_25.png]
Figure 26
Figure 26. Figure 26: FIG. 26. Bound density of states and spin-channel-projected transmission of [PITH_FULL_IMAGE:figures/full_fig_p030_26.png]

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Reference graph

Works this paper leans on

125 extracted references · 58 canonical work pages

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    We observe small differences in the total energy depending on the alignment of the spin moments relative to the chain axis

    Magnetic Anisotropy in the Ideal Iron Chain The ground state of an iron chain is characterized by an interatomic spacing of 2.26 ˚A and ferromagnetic alignment of spin magnetic moments with 3.35 µB per iron atom. We observe small differences in the total energy depending on the alignment of the spin moments relative to the chain axis. This MAE favors an a...

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