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arxiv: 2606.19954 · v1 · pith:H5SGJDG7new · submitted 2026-06-18 · ❄️ cond-mat.mtrl-sci · cond-mat.mes-hall· physics.app-ph· quant-ph

Strain- and Electric-Field-Tunable Valley Polarization in Mo0.75V0.25Te2(Mo3VTe8) for Valleytronic Application

Md. Mostaqul Islam , Vivek Chowdhury , Md. Nure-Alam-Dipu , Ahmed Zubair This is my paper

Pith reviewed 2026-06-26 16:40 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.mes-hallphysics.app-phquant-ph
keywords valley polarizationMoTe2transition metal dichalcogenidealloy engineeringelectric field tuningstrain engineeringvalleytronicsdensity functional theory
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The pith

V alloying in MoTe2 monolayer creates spontaneous valley polarization tunable by electric field and strain up to 160 meV.

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

The paper examines a monolayer of MoTe2 with 25 percent of the molybdenum atoms replaced by vanadium. This substitution introduces magnetic exchange that, together with spin-orbit coupling, splits the energy of the two valleys at the K and K' points even without any external field. The resulting spontaneous valley polarization reaches 37.3 meV in the conduction band and 78.2 meV in the valence band. Both a transverse electric field and biaxial strain can increase the valence-band splitting further, reaching 132.8 meV and 160.8 meV respectively. The calculations also confirm that the alloyed structure remains energetically and dynamically stable.

Core claim

Substitutional alloying of MoTe2 with 25 percent V produces an energetically and dynamically stable monolayer that exhibits spontaneous valley polarization of 37.3 meV in the conduction band and 78.2 meV in the valence band due to magnetic exchange interaction combined with spin-orbit coupling; this polarization is enhanced to a maximum of 132.8 meV by a transverse electric field and to 160.8 meV by biaxial tensile strain.

What carries the argument

Magnetic exchange interaction from V substitution together with spin-orbit coupling, which together lift the valley degeneracy at the K and K' points.

If this is right

  • The alloyed monolayer is energetically and dynamically stable owing to the absence of imaginary phonon modes.
  • A transverse electric field along the c axis produces a maximum valence-band valley splitting of 132.8 meV.
  • Biaxial tensile strain increases the valence-band valley splitting to 160.8 meV.
  • The conduction-band valley splitting reaches a maximum of 54.4 meV under 2 percent biaxial compressive strain.
  • The material offers a platform for tunable valleytronic devices such as transistors and sensors.

Where Pith is reading between the lines

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

  • Similar vanadium or other magnetic-atom alloying could induce valley polarization in additional transition-metal dichalcogenides without requiring external magnetic fields.
  • Fabrication and optical or transport measurements on actual Mo0.75V0.25Te2 samples could test whether the calculated splittings appear in measurable valleytronic signals.
  • Stacking the alloy with other two-dimensional layers might introduce extra knobs for controlling the valley splitting through proximity effects.

Load-bearing premise

The density functional theory calculations correctly capture the magnetic exchange interaction and spin-orbit coupling that lift valley degeneracy, and the alloy remains stable at 25 percent vanadium substitution.

What would settle it

An experiment that finds no energy difference between the K and K' valleys or detects imaginary phonon modes in the Mo0.75V0.25Te2 monolayer would disprove the predicted spontaneous polarization and structural stability.

Figures

Figures reproduced from arXiv: 2606.19954 by Ahmed Zubair, Md. Mostaqul Islam, Md. Nure-Alam-Dipu, Vivek Chowdhury.

Figure 1
Figure 1. Figure 1: Structural details of (a) MoTe2 top view, (b) MoTe2 side view with lattice parameters, bond lengths, bond angles, (c) Mo0.75V0.25Te2 top view, (d) Mo0.75V0.25Te2 side view with lattice parameters, bond lengths, bond angles. Here, (Mo-Te)1 denotes a type-I bond between Mo and Te. Whereas (Mo-Te)2 denotes a type-II bond between Mo and Te [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Spin polarized band structure of pristine MoTe2 (a) without SOC, (b) with SOC. Red color indicates spin-up and blue color indicates spin-down band. CB means conduction band, and VB means valence band, (c) phonon band dispersion curve of Mo0.75V0.25Te2 , (d) projected band structure of Mo0.75V0.25Te2 , (e) projected density of states of Mo0.75V0.25Te2 , and (f) spin polarized band structure of Mo0.75V0.25Te… view at source ↗
Figure 3
Figure 3. Figure 3: Electric field applied along the crystal a axis on Mo0.75V0.25Te2 . The band structures with SOC for (a) 0.1 V∕Å , (b) 0.2 V∕Å , (c) 0.3 V∕Å , (d) 0.4 V∕Å , (e) 0.5 V∕Å , (f) Plot of valley splitting vs applied electric field. The top blue curve denotes the conduction band valley splitting, and the bottom red curve denotes the valence band valley splitting. Additional structural details are provided i… view at source ↗
Figure 4
Figure 4. Figure 4: Electric field applied along the crystal b axis on Mo0.75V0.25Te2 . The band structures with SOC for (a) 0.1 V∕Å , (b) 0.2 V∕Å , (c) 0.3 V∕Å , (d) 0.4 V∕Å , (e) 0.5 V∕Å , (f) Plot of valley splitting vs applied electric field. The top blue curve denotes the conduction band valley splitting, and the bottom red curve denotes the valence band valley splitting. CBM and the VBM occured at the same 𝑘-point … view at source ↗
Figure 5
Figure 5. Figure 5: Electric field applied along the crystal c axis on Mo0.75V0.25Te2 . The band structures with SOC for (a) 0.1 V∕Å , (b) 0.2 V∕Å , (c) 0.3 V∕Å , (d) 0.4 V∕Å , (e) 0.5 V∕Å , (f) Plot of valley splitting vs applied electric field. The top blue curve denotes the conduction band valley splitting, and the bottom red curve denotes the valence band valley splitting. formation energy was found to be −0.84 eV, i… view at source ↗
Figure 6
Figure 6. Figure 6: Compressive biaxial strain applied along the crystal ab plane. The band structures with SOC for (a) 1%, (b) 2%, (c) 3%, (d) 4%, (e) 5%, (f) 6% compressive strain. an out-of-plane field (𝐄𝑧 ) breaks layer-inversion symmetry in multi-layer structures to electrostatic-gatedly open a tun￾able energy gap, whereas an in-plane electric field (𝐄𝑥,𝑦) induces a transport momentum drift that, when combined with strai… view at source ↗
Figure 7
Figure 7. Figure 7: Tensile biaxial strain applied along the crystal ab plane. The band structures with SOC for (a) 1%, (b) 2%, (c) 3%, (d) 4%, (e) 5%, (f) 6% tensile strain. Mo0.75V0.25Te2 can be attributed to the combined effects of transition-metal alloying and SOC. Regarding the first mechanism, transition-metal alloying breaks time reversal symmetry, which leads to identical spin splitting at the K+ and the K– valleys. A… view at source ↗
Figure 8
Figure 8. Figure 8: Valley polarization vs applied biaxial strain for Mo0.75V0.25Te2 (a) Valley polarization in the conduction band vs applied compressive strain, (b) Valley polarization in the conduction band vs applied tensile strain, (c) Valley polarization in the valence band vs applied compressive strain, and (d) Valley polarization in the valence band vs applied tensile strain valley polarization. The conduction band al… view at source ↗
Figure 9
Figure 9. Figure 9: Schematic illustration of a strain-controlled valleytronic device based on monolayer Mo0.75V0.25Te2 . The alloyed monolayer is placed on a flexible substrate with source and drain electrodes, a back gate, and transverse Hall voltage probes. Under biaxial tensile strain, the energy separation between the K+ and K– valleys increases, resulting in enhanced valley polarization and a measurable voltage. mechani… view at source ↗
Figure 10
Figure 10. Figure 10: Two dimensional pristine MoTe2 with hexagonal symmetry. (a) Top view, (b) lateral view. Blue atoms are Mo, and yellow atoms are Te. Appendices A. Additional structural details [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Two dimensional V alloyed MoTe2 (Mo0.75V0.25Te2 ) with hexagonal symmetry. (a) Top view, (b) lateral view. Blue atoms are Mo, red atoms are V, and yellow atoms are Te [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Phonon band dispersion curve of pristine MoTe2 . B. Stability of pristine MoTe2 For the investigation of dynamic stability, we conducted the phonon band calculation of the Mo2 structure. From the phonon dispersion curve shown in [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Phonon band dispersion curve of pristine VTe2 . C. Stability of pristine VTe2 For the investigation of dynamic stability, we conducted the phonon band calculation of the VTe2 structure. From the phonon dispersion curve shown in [PITH_FULL_IMAGE:figures/full_fig_p019_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Spin polarized band structure of pristine VTe2 without SOC. Red color indicates spin-up and blue color indicates spin-down band. D. Band structure of pristine VTe2 without SOC We studied the electronic properties of the pristine VTe2 to match with previous literature. We studied the spin￾polarized band structure of pristine VTe2 shown in [PITH_FULL_IMAGE:figures/full_fig_p020_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Spin polarized band structure of pristine VTe2 with SOC. Red color indicates spin-up and blue color indicates spin-down band. E. Band structure of pristine VTe2 with SOC Then we studied the band structure of pristine VTe2 with SOC effect. When SOC was introduced, some interesting phenomena appeared. At first the band gap decreased to 0.18 eV after including SOC. Then, we saw valley splitting in both the c… view at source ↗
read the original abstract

Valley polarization in 2D TMDs is promising for low-power valleytronic and spin-valley information processing, but time-reversal symmetry in pristine nonmagnetic TMDs keeps the K+ and K- valleys degenerate, limiting device applications. In this work, we investigated the structural stability, electronic properties, and tunable valley polarization of V-alloyed MoTe2 monolayer, Mo0.75V0.25Te2, using first-principles density functional theory (DFT) calculations. Substitutional alloying of MoTe2 with V introduced magnetic exchange interaction, which, together with spin-orbit coupling (SOC), lifted the valley degeneracy at the unequal valleys. The alloyed structure was found to be energetically and dynamically stable due to the absence of imaginary phonon modes. In pristine MoTe2, SOC produced spin splittings of 34.0 meV and 218.9 meV in the conduction bands and valence bands, respectively, but no valley polarization was observed. In contrast, Mo0.75V0.25Te2 exhibited spontaneous valley polarization of 37.3 meV in the conduction band and 78.2 meV in the valence band. The valley polarization was further enhanced by external electric fields and biaxial strain. A transverse electric field along the crystal c axis produced the maximum valley splitting of 132.8 meV in the valence band, whereas biaxial tensile strain increased the valence band valley splitting up to 160.8 meV. The maximum conduction band valley splitting reached 54.4 meV under 2% biaxial compressive strain. These results demonstrated that V alloying, combined with electric-field and strain engineering, provides an effective strategy for achieving large and tunable valley polarization in MoTe2. Thus, Mo0.75V0.25Te2 can be considered a promising 2D platform for tunable valleytronic device applications, such as transistors and sensors.

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

3 major / 1 minor

Summary. The manuscript uses first-principles DFT to study the Mo0.75V0.25Te2 (Mo3VTe8) monolayer, claiming that 25% V substitution induces spontaneous valley polarization (37.3 meV conduction band, 78.2 meV valence band) via magnetic exchange plus SOC, that the structure is dynamically stable (no imaginary phonons), and that the splitting can be further tuned to 132.8 meV (E-field) or 160.8 meV (biaxial tensile strain) in the valence band.

Significance. If the numerical results are reproducible, the work would demonstrate a concrete materials-design route to spontaneous and externally tunable valley polarization in a 2D TMD, which is of interest for valleytronic devices. The manuscript does not, however, supply the computational parameters required to judge whether the reported splittings are robust.

major comments (3)
  1. [Abstract, §2] Abstract and §2 (Computational Methods): No exchange-correlation functional, k-mesh density, plane-wave cutoff, Hubbard U (if any) for V, or supercell construction details are provided. Without these parameters the central claims of 37.3 meV and 78.2 meV valley splittings cannot be reproduced or assessed for convergence or supercell-ordering artifacts.
  2. [Abstract] Abstract (phonon stability paragraph): The assertion of dynamical stability rests on “absence of imaginary phonon modes,” yet no q-mesh, supercell size for the phonon calculation, or convergence criteria are stated. This directly affects the reliability of the structural-stability prerequisite for the electronic results.
  3. [Abstract] Abstract (electric-field and strain results): The maximum valence-band splittings of 132.8 meV (E-field) and 160.8 meV (strain) are reported as quantitative outcomes, but the same missing methodological details prevent evaluation of whether these enhancements are numerically converged or sensitive to the chosen field/strain implementation.
minor comments (1)
  1. [Title, Abstract] The notation “Mo0.75V0.25Te2(Mo3VTe8)” in the title and abstract is redundant; a single consistent formula is sufficient.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful review and for highlighting the importance of methodological transparency to ensure reproducibility. We have revised the manuscript to supply all requested computational parameters.

read point-by-point responses

  1. Referee: [Abstract, §2] Abstract and §2 (Computational Methods): No exchange-correlation functional, k-mesh density, plane-wave cutoff, Hubbard U (if any) for V, or supercell construction details are provided. Without these parameters the central claims of 37.3 meV and 78.2 meV valley splittings cannot be reproduced or assessed for convergence or supercell-ordering artifacts.

    Authors: We agree that these parameters are required for reproducibility. In the revised manuscript we have expanded §2 to report the exchange-correlation functional, k-point mesh, plane-wave cutoff, any Hubbard U applied to V, and the supercell construction used for the 25 % V substitution. These additions directly address the concern and permit independent verification of the reported valley splittings. revision: yes

  2. Referee: [Abstract] Abstract (phonon stability paragraph): The assertion of dynamical stability rests on “absence of imaginary phonon modes,” yet no q-mesh, supercell size for the phonon calculation, or convergence criteria are stated. This directly affects the reliability of the structural-stability prerequisite for the electronic results.

    Authors: We accept the referee’s point. The revised manuscript now specifies the q-mesh, supercell size, and convergence criteria employed in the phonon calculations, allowing readers to evaluate the dynamical stability claim. revision: yes

  3. Referee: [Abstract] Abstract (electric-field and strain results): The maximum valence-band splittings of 132.8 meV (E-field) and 160.8 meV (strain) are reported as quantitative outcomes, but the same missing methodological details prevent evaluation of whether these enhancements are numerically converged or sensitive to the chosen field/strain implementation.

    Authors: We agree that the same methodological details are needed to assess the electric-field and strain results. The revised manuscript includes the implementation details and convergence information for both the transverse electric field and biaxial strain calculations. revision: yes

Circularity Check

0 steps flagged

No circularity: valley splittings are direct DFT outputs with no reduction to fitted inputs or self-citations

full rationale

The paper computes spontaneous valley polarization (37.3 meV CB, 78.2 meV VB) and its tuning under E-field/strain directly via first-principles DFT on the Mo3VTe8 supercell, including SOC and magnetic exchange from V substitution. These quantities are reported as numerical results of the electronic-structure calculation rather than quantities obtained by fitting parameters to the target splittings, by algebraic reduction of earlier equations in the paper, or by load-bearing self-citations. No ansatz, uniqueness theorem, or renaming of known results is invoked; the derivation chain is therefore self-contained standard DFT and receives score 0.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard DFT approximations whose accuracy for magnetic exchange and valley splittings in this alloy is not independently verified within the abstract.

axioms (1)
  • domain assumption Density functional theory with spin-orbit coupling and magnetic exchange accurately reproduces the valley splitting and structural stability of the V-alloyed monolayer.
    Invoked throughout the abstract when reporting polarization values and phonon-mode results.

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