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arxiv: 2511.09974 · v1 · submitted 2025-11-13 · ❄️ cond-mat.other

Chiral orbital/spin textures and Edelstein effects in monolayer Janus TMDs

Pratik Sahu , Sashi Satpathy , Birabar Ranjit Kumar Nanda This is my paper

Pith reviewed 2026-05-17 22:51 UTC · model grok-4.3

classification ❄️ cond-mat.other
keywords Janus transition metal dichalcogenidesorbital Edelstein effectspin Edelstein effectchiral orbital textureinternal electric fieldspin-orbit couplingtwo-dimensional materialsspin-orbitronics
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The pith

Janus TMDs form chiral orbital textures from an internal electric field that produces larger orbital than spin Edelstein effects under in-plane fields.

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

Monolayer Janus transition metal dichalcogenides break mirror symmetry because their two chalcogen layers differ. This asymmetry sets up an internal electric field perpendicular to the plane that mixes the usual d-orbitals with out-of-plane ones at the valleys. The mixing creates a strong orbital texture, and spin-orbit coupling adds a reversal in its handedness. Applying an electric field in the plane then drives both orbital and spin Edelstein effects, yet the orbital version reaches roughly ten times the strength of the spin version.

Core claim

Due to the internal electric field normal to the plane in Janus TMDs of form MXX', the wavefunctions at valence and conduction bands, normally dominated by |x²-y²>, |xy>, and |z²> orbitals, become intermixed with |xz> and |yz> orbitals. This produces a robust orbital texture around the Γ, K, and K' valleys. Spin-orbit coupling introduces a chirality reversal to this orbital texture. An applied in-plane electric field then generates both orbital and spin Edelstein effects, with the orbital effect having one order higher magnitude.

What carries the argument

The internal electric field E_int perpendicular to the plane, induced by the differing chalcogen layers breaking mirror symmetry, which causes orbital intermixing and texture formation leading to Edelstein effects.

If this is right

  • Both orbital and spin Edelstein effects arise from an applied in-plane electric field.
  • The orbital Edelstein effect reaches magnitudes about ten times larger than the spin Edelstein effect.
  • The orbital texture around the valleys reverses chirality under spin-orbit coupling.
  • Janus TMDs become suitable platforms for spin-orbitronic devices exploiting these effects.
  • Experimental investigations of orbital and spin orbital torques in these materials are motivated.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Adjusting the choice of chalcogen atoms could tune the strength of the internal field and thus the size of the orbital response.
  • Hybrid devices stacking Janus TMDs with ferromagnets might achieve efficient magnetization switching via the dominant orbital torque.
  • Valley-specific orbital textures suggest opportunities for combining with valleytronics for selective control.
  • First-principles calculations setting the internal field to zero while preserving the lattice should eliminate the reported textures if the mechanism is correct.

Load-bearing premise

The internal electric field generated by the broken mirror symmetry is the primary driver of the orbital intermixing and Edelstein effects, while effects from lattice relaxation or substrates can be ignored.

What would settle it

If density functional theory calculations or experiments on non-Janus symmetric TMDs show comparable orbital Edelstein effects to the Janus case, or if removing the internal field in the tight-binding model eliminates the texture, the dominance of the asymmetry-induced field would be questioned.

Figures

Figures reproduced from arXiv: 2511.09974 by Birabar Ranjit Kumar Nanda, Pratik Sahu, Sashi Satpathy.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) A schematic of the Edelstien effect driven by [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Band structure of monolayer MoSSe in the pres [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Orbital texture of the MoSSe near (a) Γ, (b) K and (c) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Orbital (blue) and spin textures (red) around Γ [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 1
Figure 1. Figure 1: Fig.1. We note that except for the Nb based compounds, [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Orbital moment [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Orbital magnetic moment for all occupied bands (without SOC) around Γ point( [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. A schematic diagram showing the magnetic moments [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Orbital and spin Edelstein susceptibilities as a func [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Effect of SOC ( [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
read the original abstract

We investigate the orbital and spin Edelstein effect(OEE and SEE) in two-dimensional Janus transition metal dichalcogenides (TMDs) of the form MXX$^\prime$ $(M = Mo,\ W,\ Nb;\ X/X^\prime = S,\ Se,\ Te)$ with the aid of density functional theory calculations and tight-binding model Hamiltonian studies. The chalcogen layers $X$ and $X^\prime$, break the mirror symmetry to introduce an internal electric field $E_{int}$ normal to the plane, which is responsible for OEE and SEE. Our results show that in a non-Janus framework, the wavefunctions at the valence and conduction bands are dominated with the $|x^2-y^2>$, $|xy>$, and $|z^2>$ orbitals. Due to the $E_{int}$ of the Janus system, these orbitals are now intermixed with the $|xz>$ and $|yz>$ orbitals to produce a robust orbital texture around the valleys $\Gamma,K$ and $K^\prime$. The spin orbit coupling, in addition to the formation of a spin texture, introduces a chirality reversal to the orbital texture. An applied in plane electric field creates both OEE and SEE with the former being one order higher in magnitude. This makes the Janus materials promising for spin-orbitronics. Our work paves the way for further experimental exploration for orbital and spin orbital torque in Janus TMDs.

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

1 major / 2 minor

Summary. The manuscript investigates orbital and spin Edelstein effects (OEE and SEE) in monolayer Janus TMDs MXX' (M=Mo,W,Nb; X/X'=S,Se,Te) via DFT calculations and tight-binding models. It claims that the internal out-of-plane electric field E_int from broken mirror symmetry due to asymmetric chalcogen layers intermixes |xz> and |yz> orbitals into the d_{x^2-y^2}, d_xy, d_z^2 manifold, generating chiral orbital textures at the Γ, K, and K' valleys. Spin-orbit coupling adds spin texture and chirality reversal; an applied in-plane electric field then induces both OEE and SEE, with OEE one order of magnitude larger, positioning Janus TMDs as promising for spin-orbitronics.

Significance. If the reported orbital intermixing, texture chirality, and relative OEE/SEE magnitudes are robust, the work would be significant for identifying a mechanism to generate strong orbital responses in 2D materials via intrinsic asymmetry, with potential implications for orbital torque devices. The dual DFT-plus-TB approach is a strength for connecting microscopic orbital character to macroscopic Edelstein responses. Credit is due for exploring a broad set of MXX' compositions and highlighting the non-Janus vs. Janus contrast.

major comments (1)
  1. [Abstract and workflow description] Abstract and described workflow: the central claim that E_int from chalcogen asymmetry is the dominant driver of |xz/yz> intermixing (and thus the orbital texture yielding larger OEE) is not isolated from structural contributions. No fixed-lattice vs. fully-relaxed comparisons or orbital-projection decompositions separating electrostatic vs. bond-length/angle relaxation effects are reported, even though differing X/X' radii can induce local distortions that also mix the d-manifold. This is load-bearing for the attribution of the textures and Edelstein magnitudes to E_int.
minor comments (2)
  1. [Methods/Computational details] No numerical details are supplied on k-point sampling, plane-wave cutoff, convergence criteria, or direct comparison to experimental benchmarks for the reported Edelstein magnitudes.
  2. [Results] The abstract states OEE is 'one order higher in magnitude' than SEE; the manuscript should specify the exact ratio, the valley or k-point at which it is evaluated, and whether it holds across the studied MXX' compositions.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and valuable feedback on our manuscript investigating orbital and spin Edelstein effects in Janus TMDs. We address the major comment regarding the isolation of the internal electric field contribution from structural effects.

read point-by-point responses

  1. Referee: [Abstract and workflow description] Abstract and described workflow: the central claim that E_int from chalcogen asymmetry is the dominant driver of |xz/yz> intermixing (and thus the orbital texture yielding larger OEE) is not isolated from structural contributions. No fixed-lattice vs. fully-relaxed comparisons or orbital-projection decompositions separating electrostatic vs. bond-length/angle relaxation effects are reported, even though differing X/X' radii can induce local distortions that also mix the d-manifold. This is load-bearing for the attribution of the textures and Edelstein magnitudes to E_int.

    Authors: We agree with the referee that a clearer separation between the electrostatic effects of the internal electric field E_int and the structural distortions arising from the different chalcogen radii is necessary to strengthen our claims. Although our non-Janus versus Janus comparisons highlight the importance of the asymmetry, they do not fully disentangle these contributions. In the revised manuscript, we will include additional DFT calculations using fixed lattice constants (based on the average of the parent TMDs) to minimize relaxation effects, and perform detailed orbital projections to quantify the mixing due to E_int versus geometric changes. We will also discuss how these affect the OEE and SEE magnitudes. This revision will directly address the load-bearing aspect of our attribution. revision: yes

Circularity Check

0 steps flagged

No circularity: standard first-principles computation yields outputs rather than self-referential inputs

full rationale

The paper applies density functional theory and tight-binding models to compute orbital/spin textures and Edelstein responses directly from the electronic structure of the Janus TMDs. The internal electric field arises naturally from the asymmetric chalcogen layers in the structural model; orbital intermixing and the resulting OEE/SEE magnitudes are calculated outputs, not fitted parameters or quantities defined in terms of themselves. No load-bearing steps reduce to self-citations, ansatzes imported from prior author work, or renaming of known results. The derivation chain is self-contained against external benchmarks such as standard DFT implementations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the accuracy of standard DFT for capturing orbital mixing induced by the Janus asymmetry and on the validity of the tight-binding model for extracting textures and responses.

axioms (1)
  • domain assumption Density functional theory with standard functionals accurately captures the orbital character and internal electric field in these monolayer systems.
    Invoked implicitly when attributing orbital mixing directly to E_int from the Janus structure.

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Works this paper leans on

40 extracted references · 40 canonical work pages

  1. [1]

    From the table, we find that both the transition metal(M) and the chalcogen(X) atoms contribute to the SOC. In addition, we also notice that the p-orbitals of the chalcogens have a stronger SOC than the d-orbitals of several M atoms, which is in agreement with the pre- vious reports[34, 35] based on single atoms. III. ORBITAL AND SPIN TEXTURE In this sect...

    work page

  2. [2]

    Kontani, T

    H. Kontani, T. Tanaka, D. S. Hirashima, and K. Yamada et al., Giant Orbital Hall Effect in Transition Metals: Origin of Large Spin and Anomalous Hall Effects, Phys. Rev. Lett.102, 016601 (2009)

    work page 2009

  3. [3]

    D. Go, D. Jo, C. Kim, and H-W. Lee, Intrinsic Spin and Orbital Hall Effects from Orbital Texture, Phys. Rev. Lett.121, 086602 (2018)

    work page 2018

  4. [4]

    D. Jo, D. Go and H.-W. Lee, Gigantic intrinsic orbital Hall effects in weakly spin-orbit coupled metals, Phys. Rev. B98, 214405 (2018)

    work page 2018

  5. [5]

    Bhowal and S

    S. Bhowal and S. Satpathy, Intrinsic orbital moment and prediction of a large orbital Hall effect in two- dimensional transition metal dichalcogenides, Phys. Rev. B101, 121112(R) (2020)

    work page 2020

  6. [6]

    Bhowal and S

    S. Bhowal and S. Satpathy, Intrinsic orbital and spin Hall effects in monolayer transition metal dichalcogenides, Phys. Rev. B102, 035409 (2020)

    work page 2020

  7. [7]

    P. Sahu, S. Bhowal, and S. Satpathy, Effect of the in- version symmetry breaking on the orbital Hall effect: A model study, Phys. Rev. B103, 085113 (2021)

    work page 2021

  8. [8]

    L. M. Canonico, T. P. Cysne, T. G. Rappoport, and R. B. Muniz, Two-dimensional orbital Hall insulators, Phys. Rev. B101, 075429 (2020)

    work page 2020

  9. [9]

    L. M. Canonico, T. P. Cysne, A. Molina-Sanchez, R. B. Muniz, and T. G. Rappoport, Orbital Hall insulat- ing phase in transition metal dichalcogenide monolayers, Phys. Rev. B101, 161409(R) (2020)

    work page 2020

  10. [10]

    Go and H

    D. Go and H. W. Lee, Orbital torque: Torque genera- tion by orbital current injection, Phys. Rev. Research2, 013177 (2020)

    work page 2020

  11. [11]

    Z. C. Zheng, Q. X. Guo, D. Jo, and D. Go et al., Magne- tization switching driven by current-induced torque from weakly spin-orbit coupled Zr, Phys. Rev. Research2, 013127 (2020)

    work page 2020

  12. [12]

    D. Lee, D. Go, H-J. Park, and W. Jeong et al., Orbital torque in magnetic bilayers, Nat Comm.12, 6710 (2021)

    work page 2021

  13. [13]

    Mudgal, A

    R. Mudgal, A. Jakhar, P. Gupta, and R. S. Yadav et al., Magnetic-Proximity-Induced Efficient Charge-to- Spin Conversion in Large-Area PtSe2/Ni 80Fe20 Het- erostructures, Nano Lett. 2023,23, 24 (2023). 10

    work page 2023

  14. [14]

    Tanaka, H

    T. Tanaka, H. Kontani, M. Naito, and T. Naito, et al., Intrinsic spin Hall effect and orbital Hall effect in 4d and 5d transition metals, Phys. Rev. B77, 165117 (2008)

    work page 2008

  15. [15]

    Kontani, T

    H. Kontani, T. Tanaka, D. S. Hirashima, and K. Ya- mada et al., Giant Intrinsic Spin and Orbital Hall Ef- fects in Sr2MO4 (M = Ru, Rh, Mo), Phys. Rev. Lett. 100, 096601 (2008)

    work page 2008

  16. [16]

    P. Sahu, J. Bidika, B. Biswal, S. Satpathy, and B. R. K. Nanda, Emergence of giant orbital Hall and tunable spin Hall effects in centrosymmetric transition metal dichalco- genides, Phys. Rev. B110, 054403 (2024)

    work page 2024

  17. [17]

    Y. A. Bychkov and E. I. Rashba, Properties of a 2D Elec- tron Gas with Lifted Spectral Degeneracy, JETP Lett. 39, 78 (1984)

    work page 1984

  18. [18]

    V. M. Edelstein, Spin polarization of conduction elec- trons induced by electric current in two-dimensional asymmetric electron systems, Solid State Commun.73, 233 (1990)

    work page 1990

  19. [19]

    L. S. Levitov, Y. V. Nazarov, and G. M. `Eliashberg, Magneto-electric effects in conductors with mirror isomer symmetry, Sov. Phys. JETP61, 133 (1985)

    work page 1985

  20. [20]

    Ando , Y

    S. Ando , Y. Tanaka, M. Cuoco, and L. Chirolli et al., Spin and orbital Edelstein effect in spin-orbit coupled noncentrosymmetric superconductors, Phys. Rev. B110, 184503 (2024)

    work page 2024

  21. [21]

    S. R. Park, C. H. Kim, J. Yu, J. H. Han, and C. Kim, Orbital angular-momentum based origin of Rashba-type surface band splitting, Phys. Rev. Lett.107, 156803 (2011)

    work page 2011

  22. [22]

    D. Go, J. Hanke, Patrick M. Buhl, and F. Freimuth et al., Toward surface orbitronics: giant orbital magnetism from the orbital Rashba effect at the surface of sp metals, Sci. Rep.7, 46742 (2017)

    work page 2017

  23. [23]

    D. Go, D. Jo, T. Gao, K. Ando, Orbital Rashba effect in a surface-oxidized Cu film, Phys. Rev. B103, L121113 (2021)

    work page 2021

  24. [24]

    S. Ding, Z. Liang, D. Go, and C. Yun, Observation of the Orbital Rashba-Edelstein Magnetoresistance, Phys. Rev. Lett.128, 067201 (2022)

    work page 2022

  25. [25]

    K. V. Shanavas, and S. Satpathy, Effective tight-binding model for MX 2 under electric and magnetic fields, Phys. Rev. B91, 235145 (2015)

    work page 2015

  26. [26]

    Gautam and S

    T. Gautam and S. Satpathy, Spin and Orbital Edel- stein effect in gated monolayer transition metal dichalco- genides, arXiv:2509.25634 (2025)

    work page arXiv 2025

  27. [27]

    T. Hu, F. Jia,G. Zhao, J. Wu, A. Stroppa, and W. Ren, Intrinsic and anisotropic Rashba spin splitting in Janus transition-metal dichalcogenide monolayers, Phys. Rev. B97, 235404 (2018)

    work page 2018

  28. [28]

    Y. C. Cheng, Z. Y. Zhu, M. Tahir and U. Schwingen- schl¨ ogl, Spin-orbit–induced spin splittings in polar tran- sition metal dichalcogenide monolayers, EPL10257001 (2013)

    work page 2013

  29. [29]

    Q. Yao, J. Cai, W. Tong, and S. Gong et al., Manip- ulation of the large Rashba spin splitting in polar two- dimensional transition-metal dichalcogenides, Phys. Rev. B95, 165401 (2017)

    work page 2017

  30. [30]

    J. Chen, K. Wu, H. Ma, and W. Hu et al., Tunable Rashba spin splitting in Janus transition-metal dichalco- genide monolayers via charge doping, RSC Adv.10, 6388-6394 (2020)

    work page 2020

  31. [31]

    See supplemental material for the extra results and fig- ures

    work page

  32. [32]

    Giannozzi, S

    P. Giannozzi, S. Baroni, N. Bonini, and M. Calandra et. al., QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials, J. Phys. Condens. Matter21, 395502 (2009)

    work page 2009

  33. [33]

    Pizzi, V

    G. Pizzi, V. Vitale, R. Arita, and S. Bl¨ ugel et. al., Wan- nier90 as a community code: new features and applica- tions, J. Phys. Condens. Matter32, 165902 (2020)

    work page 2020

  34. [34]

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

    work page 1996

  35. [35]

    Jha and T

    G. Jha and T. Heine, DFTB Parameters for the Periodic Table: Part III, Spin-Orbit Coupling, Journal of Chemi- cal Theory and Computation,18,7, 4472-4481 (2022)

    work page 2022

  36. [36]

    Z. S. Popovi´ c, J. M. Kurdestany, and S. Satpathy, Elec- tronic structure and anisotropic Rashba spin-orbit cou- pling in monolayer black phosphorus, Phys. Rev. B 92, 035135 (2015)

    work page 2015

  37. [37]

    Xiao, J., Shi, and Q

    D. Xiao, J., Shi, and Q. Niu, Berry phase correction to electron density of states in solids, Phys. Rev. Lett.,95, 137204 (2005)

    work page 2005

  38. [38]

    Johansson, B

    A. Johansson, B. G¨ obel, J. Henk, M. Bibes and I. Mertig, Spin and orbital Edelstein effects in a two-dimensional electron gas: Theory and application to SrTiO 3 inter- faces, Phys. Rev. Res.3, 013275 (2021)

    work page 2021

  39. [39]

    A. Pezo, D. Garc´ ıa Ovalle, and A. Manchon, Orbital Hall effect in crystals: Interatomic versus intra-atomic contri- butions, Phys. Rev. B,106, 104414 (2022)

    work page 2022

  40. [40]

    W. Y. He, and K. T. Law, Magnetoelectric effects in gyrotropic superconductors, Phys. Rev. Res.,2, 012073(2020)

    work page 2020