Modulation of charge density waves in a twisted vortex moire superlattice

Haitao Yang; Hong-Jun Gao; Hui Chen; Hui Guo; Jiayi Huang; Jiayi Wang; Jingyi Duan; Qian Fang; Senhao Lv; Siyu Xu

arxiv: 2605.26510 · v1 · pith:FCRHYOUWnew · submitted 2026-05-26 · ❄️ cond-mat.mtrl-sci · cond-mat.other

Modulation of charge density waves in a twisted vortex moire superlattice

Qian Fang , Yanhao Shi , Jingyi Duan , Hui Guo , Yikai Chen , Senhao Lv , Jiayi Wang , Zhongyi Cao

show 6 more authors

Jiayi Huang Siyu Xu Haitao Yang Wei Jiang Hui Chen Hong-Jun Gao

This is my paper

Pith reviewed 2026-06-29 17:33 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.other

keywords charge density wavemoire superlatticevan der Waals heterostructurestrain modulationscanning tunneling microscopyproximity superconductivityVTe2NbSe2

0 comments

The pith

Local strain variation in a twisted moire superlattice reconstructs the charge density wave of monolayer VTe2 into inequivalent phases with different stabilities.

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

The paper examines a moire structure made by placing monolayer VTe2 on NbSe2 with a small twist. Scanning tunneling measurements show the usual uniform charge density wave breaks into several local versions inside one moire cell, some suppressed and others showing short-range order that lasts to room temperature. First-principles calculations link the changes to strong local strain differences created by the twist, with compression helping the order persist. The altered CDW patterns then compete with superconductivity induced by the NbSe2 layer. This demonstrates a way to adjust correlated states at the nanoscale through moire geometry.

Core claim

The intrinsic long-range CDW of monolayer VTe2 is reconstructed into inequivalent local phases with distinct stability and coherence within a single moire unit cell, including suppressed CDW order and enhanced short-range CDW correlations persisting to room temperature. First-principles calculations show that the reconstructed CDW landscape originates from strong local strain variation, where compressive strain substantially stabilizes the charge order. Furthermore, the modulated CDW states exhibit competing interplay with proximity-induced superconductivity.

What carries the argument

The twisted vortex moire superlattice between VTe2 and NbSe2, which produces continuously varying local strain that modulates the CDW.

If this is right

Compressive strain can stabilize charge order in related two-dimensional materials.
Proximity-induced superconductivity competes directly with the strain-modulated CDW states.
Nanoscale control of electronic orders is achievable by engineering local environments in moire superlattices.
The same reconstruction mechanism applies to other correlated phases in van der Waals heterostructures.

Where Pith is reading between the lines

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

Twist angle could be varied to tune the range of strain values and thereby map the full strain-CDW phase diagram.
Short-range CDW correlations that survive to room temperature might be extended by combining strain with other controls such as gating.
The competition between CDW and superconductivity could be studied in devices to test whether one order can be switched by local strain.

Load-bearing premise

The observed differences in local CDW phases and their temperature stability arise mainly from the calculated local strain variation rather than from interface hybridization, charge transfer, or other electronic effects.

What would settle it

A calculation that includes interface effects but removes strain variation and still matches the measured CDW map, or an experiment that finds no spatial correlation between local compression and CDW intensity.

read the original abstract

Twisted moire superlattices in van-der-Waals heterostructures provide a powerful platform for engineering correlated states through moire-band reconstruction. However, whether globally coherent electronic orders can be continuously manipulated at the nanoscale remains largely unexplored. Reconstructed moire structures in small-angle and near-commensurate regime feature continuously varying local environments, offering new opportunities for nanoscale manipulation of correlated phases. Here, we report the modulation of charge density wave (CDW) states in a twisted vortex moire superlattice formed between monolayer VTe2 and superconducting NbSe2. Scanning tunneling microscopy/spectroscopy reveals that the intrinsic long-range CDW of monolayer VTe2 is reconstructed into inequivalent local phases with distinct stability and coherence within a single moire unit cell, including suppressed CDW order and enhanced short-range CDW correlations persisting to room temperature. First-principles calculations show that the reconstructed CDW landscape originates from strong local strain variation, where compressive strain substantially stabilizes the charge order. Furthermore, the modulated CDW states exhibit competing interplay with proximity-induced superconductivity. Our results establish vortex moire superlattices as a versatile platform for nanoscale manipulation of correlated electronic orders in low-dimensional quantum 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.

Desk Editor's Note private letter to a colleague

The VTe2/NbSe2 vortex moire gives STM evidence for local CDW phase variation inside one cell that holds some short-range order to room temperature, but the strain-only DFT attribution needs checking against possible interface effects.

read the letter

The new piece here is the specific VTe2 on NbSe2 twisted vortex moire where STM maps show the native CDW breaking into inequivalent local phases with different coherence lengths inside a single cell, plus some short-range correlations that survive to room temperature. The competing interplay with proximity superconductivity is also noted. That combination of material and geometry looks fresh relative to earlier moire CDW work.

The experimental mapping is the stronger part. They have real-space data showing the reconstruction and temperature dependence, which gives a concrete platform claim for nanoscale CDW control.

The softer spot is the DFT side. The abstract ties the landscape to local strain variation with compressive strain stabilizing order, but it does not say whether the calculations used a full heterostructure supercell that includes NbSe2 atoms and orbital overlap. If they only strained a freestanding VTe2 monolayer, then charge transfer or hybridization at the interface remain possible contributors, exactly as the stress-test flags. Without the methods and full figures it is hard to tell how cleanly they separated those. The circularity burden is low since the STM is independent of the calculations, but the interpretation still rests on the strain model holding up.

This is for the 2D materials and moire CDW subfield. The experimental observations are solid enough to merit referee time even if the theory needs more detail on the interface modeling. I would send it to review rather than desk reject.

Referee Report

1 major / 2 minor

Summary. The paper reports STM/S observations in a twisted VTe2/NbSe2 moiré superlattice showing that the intrinsic CDW of monolayer VTe2 is reconstructed into inequivalent local phases with varying stability and coherence inside a single moiré cell, including suppressed order and enhanced short-range correlations up to room temperature. First-principles calculations are used to attribute this landscape to strong local strain variations, with compressive strain stabilizing the CDW, while also noting a competing interplay with proximity-induced superconductivity from the NbSe2 substrate. The central claim is that vortex moiré superlattices enable nanoscale manipulation of correlated orders via strain.

Significance. If the strain attribution is robust, the work establishes a concrete experimental route to continuously tune CDW order at the nanoscale through moiré-induced strain gradients in vdW heterostructures, extending beyond global band reconstruction. The observation of competing CDW-SC interplay at the local level adds to the literature on proximity effects in 2D systems. Credit is due for the direct linkage of local STM phases to strain-dependent DFT, which provides a falsifiable microscopic mechanism rather than purely phenomenological fitting.

major comments (1)

[First-principles calculations] First-principles calculations (abstract and corresponding results section): the attribution of the reconstructed CDW landscape to 'strong local strain variation' is load-bearing for the central claim, yet the abstract provides no indication that the DFT employed a full VTe2/NbSe2 heterostructure supercell. If the calculations instead model only freestanding strained VTe2 (as the skeptic note flags), then interface hybridization, charge transfer, and orbital overlap remain unexcluded, directly weakening the conclusion that compressive strain is the primary stabilizer rather than moiré-specific electronic effects.

minor comments (2)

[Abstract] Abstract and experimental sections: the description of STM/S data on local CDW phases lacks any mention of error bars, statistical sampling across multiple moiré cells, or explicit exclusion criteria for phase identification, which would improve verifiability of the inequivalent phases.
Figure captions and methods: notation for the 'twisted vortex moiré' geometry and the definition of local strain should be clarified to allow readers to reproduce the mapping from moiré geometry to strain field.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive evaluation of the work's significance and for the constructive comment on the first-principles calculations. We address the point below and will revise the manuscript accordingly to improve clarity.

read point-by-point responses

Referee: [First-principles calculations] First-principles calculations (abstract and corresponding results section): the attribution of the reconstructed CDW landscape to 'strong local strain variation' is load-bearing for the central claim, yet the abstract provides no indication that the DFT employed a full VTe2/NbSe2 heterostructure supercell. If the calculations instead model only freestanding strained VTe2 (as the skeptic note flags), then interface hybridization, charge transfer, and orbital overlap remain unexcluded, directly weakening the conclusion that compressive strain is the primary stabilizer rather than moiré-specific electronic effects.

Authors: We thank the referee for highlighting this important clarification. The DFT calculations in the manuscript were performed on freestanding monolayer VTe2 subject to uniaxial and biaxial strain (as detailed in the methods and results sections) to isolate the effect of local strain on CDW stability. A full VTe2/NbSe2 moiré supercell is computationally prohibitive given the large real-space cell size required for the observed twist angles. We argue that strain is the dominant mechanism because the calculated CDW energy gain under compressive strain quantitatively matches the spatial variation observed in STM, while the experimental CDW suppression/enhancement correlates directly with the moiré-induced strain map extracted from STM topography. Nevertheless, we acknowledge that interface hybridization and charge transfer could play a secondary role and were not explicitly modeled. We will revise the manuscript to (i) explicitly state in the abstract and main text that the calculations use freestanding strained VTe2, (ii) add a dedicated paragraph discussing the possible contributions of interface effects and why they are expected to be secondary based on the observed strain-CDW correlation, and (iii) include a note on the computational limitations. This addresses the concern without altering the central claim. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental STM/S data plus independent first-principles calculations

full rationale

The paper reports direct STM/S observations of inequivalent local CDW phases within the moire cell and attributes the landscape to local strain via separate first-principles calculations. No equations, fitted parameters, or self-citations are presented that reduce a claimed prediction to an input defined by the same data. The derivation chain remains self-contained against external benchmarks (STM topography/spectra and standard DFT strain modeling) with no load-bearing self-definition or ansatz smuggling.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that first-principles calculations accurately capture the dominant effect of local strain on CDW stability and that STM contrast directly reflects CDW order parameters without significant tip or interface artifacts.

axioms (1)

domain assumption Standard DFT exchange-correlation functionals and pseudopotentials are sufficient to model strain-CDW coupling in VTe2.
Invoked when attributing reconstructed CDW landscape to compressive strain.

pith-pipeline@v0.9.1-grok · 5785 in / 1252 out tokens · 33160 ms · 2026-06-29T17:33:04.969186+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

12 extracted references

[1]

Y.; MacDonald, A

(1) Andrei, E. Y.; MacDonald, A. H. Graphene Bilayers with a Twist. Nat. Mater. 2020, 19, 1265–1275. (2) Nuckolls, K. P.; Yazdani, A. A Microscopic Perspective on Moiré Materials. Nat. Rev. Mater. 2024, 9, 460–480. (3) Carr, S.; Fang, S.; Kaxiras, E. Electronic -Structure Methods for Twisted Moiré Layers. Nat. Rev. Mater. 2020, 5, 748–763. (4) Andrei, E. ...

2020
[2]

L.; Luo, J

(12) Cao, Y.; Fatemi, V.; Demir, A.; Fang, S.; Tomarken, S. L.; Luo, J. Y.; Sanchez -Yamagishi, J. D.; Watanabe, K.; Taniguchi, T.; Kaxiras, E.; Ashoori, R. C.; Jarillo -Herrero, P. Correlated Insulator Behaviour at Half-Filling in Magic-Angle Graphene Superlattices. Nature 2018, 556, 80–84. (13) Xu, Y.; Liu, S.; Rhodes, D. A.; Watanabe, K.; Taniguchi, T....

2018
[3]

S.; Luo, Z.; Lu, Q.; Millis, A

(21) Chen, X.; Fan, X.; Li, L.; Zhang, N.; Niu, Z.; Guo, T.; Xu, S.; Xu, H.; Wang, D.; Zhang, H.; McLeod, A. S.; Luo, Z.; Lu, Q.; Millis, A. J.; Basov, D. N.; Liu, M.; Zeng, C. Moiré Engineering of Electronic Phenomena in Correlated Oxides. Nat. Phys. 2020, 16, 631–635. (22) Anderson, E.; Fan, F. -R.; Cai, J.; Holtzmann, W.; Taniguchi, T.; Watanabe, K.; X...

2020
[4]

ACS Nano 2020, 14, 2718–

2020
[5]

Moiré Enhanced Two-Band Superconductivity in a MnTe/NbSe2 Heterojunction

(25) Nie, J.-H.; Xie, T.; Chen, G.; Zhang, W.; Fu, Y.-S. Moiré Enhanced Two-Band Superconductivity in a MnTe/NbSe2 Heterojunction. Nano Lett. 2023, 23, 8370–8377. (26) Sung, S. H.; Goh, Y. M.; Yoo, H.; Engelke, R.; Xie, H.; Zhang, K.; Li, Z.; Ye, A.; Deotare, P. B.; Tadmor, E. B.; Mannix, A. J.; Park, J.; Zhao, L.; Kim, P.; Hovden, R. Torsional Periodic L...

2023
[6]

R.; Chuang, H

(27) Rosenberger, M. R.; Chuang, H. -J.; Phillips, M.; Oleshko, V. P.; McCreary, K. M.; Sivaram, S. V.; Hellberg, C. S.; Jonker, B. T. Twist Angle -Dependent Atomic Reconstruction and Moiré Patterns in Transition Metal Dichalcogenide Heterostructures. ACS Nano 2020, 14, 4550–4558. 18 (28) Rodríguez, Á.; Varillas, J.; Haider, G.; Kalbáč, M.; Frank, O. Comp...

2020
[7]

H.; Kretinin, A.; Wilson, N

(30) Weston, A.; Zou, Y.; Enaldiev, V.; Summerfield, A.; Clark, N.; Zó lyomi, V.; Graham, A.; Yelgel, C.; Magorrian, S.; Zhou, M.; Zultak, J.; Hopkinson, D.; Barinov, A.; Bointon, T. H.; Kretinin, A.; Wilson, N. R.; Beton, P. H.; Fal’ko, V. I.; Haigh, S. J.; Go rbachev, R. Atomic Reconstruction in Twisted Bilayers of Transition Metal Dichalcogenides. Nat....

2020
[8]

Strain -Induced Moiré Polar Vortex in Twisted Paraelectric Freestanding Bilayers

(38) Zhang, Y.; Sha, H.; Wang, X.; Liang, D.; Wang, J.; Li, Q.; Yu, R.; Huang, H. Strain -Induced Moiré Polar Vortex in Twisted Paraelectric Freestanding Bilayers. npj Quantum Mater. 2025, 10,

2025
[9]

S.; Zheng, X.; Yang, T.; Yan, Z.; Han, W.; Wong, L

(39) Tsang, C. S.; Zheng, X.; Yang, T.; Yan, Z.; Han, W.; Wong, L. W.; Liu, H.; Gao, S.; Leung, K. H.; Lee, C.-S.; Lau, S. P.; Yang, M.; Zhao, J.; Ly, T. H. Polar and Quasicrystal Vortex Observed in Twisted-Bilayer Molybdenum Disulfide. Science 2024, 386, 198–205. (40) Li, S.; Wang, Z.; Han, Y.; Xu, S.; Xu, Z.; Wang, Y.; Wang, Z.; Xue, Y.; Song, A.; Watan...

2024
[10]

W.; Chacon, C.; Girard, Y.; Repain, V.; Bellec, A.; Rousset, S.; Gonzá lez, C.; Smogunov, A.; Lagoute, J.; Dappe , Y

(47) Chazarin, U.; Lezoualc’h, M.; Karn, A.; Chou, J.-P.; Pai, W. W.; Chacon, C.; Girard, Y.; Repain, V.; Bellec, A.; Rousset, S.; Gonzá lez, C.; Smogunov, A.; Lagoute, J.; Dappe , Y. J. Spatially Extended Charge Density Wave Switching by Nanoscale Local Manipulation in a VTe2 Monolayer. Nano Lett. 2024, 24, 3470–3475. (48) Zhao, W.-M.; Ding, W.; Wang, Q....

2024
[11]

MoireStudio: A Universal Twisted Electronic Structure Calculation Package

(52) Yu, J.; Liu, Y.; Liu, C.-C. MoireStudio: A Universal Twisted Electronic Structure Calculation Package. Comput. Phys. Commun. 2026, 110216. (53) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132, 15410...

2026
[12]

M.; Isayev, O

(55) Anstine, D. M.; Isayev, O. Machine Learning Interatomic Potentials and Long-Range Physics. J. Phys. Chem. A 2023, 127, 2417–2431. (56) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865–3868. (57) Blö chl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953–17979. (5...

2023

[1] [1]

Y.; MacDonald, A

(1) Andrei, E. Y.; MacDonald, A. H. Graphene Bilayers with a Twist. Nat. Mater. 2020, 19, 1265–1275. (2) Nuckolls, K. P.; Yazdani, A. A Microscopic Perspective on Moiré Materials. Nat. Rev. Mater. 2024, 9, 460–480. (3) Carr, S.; Fang, S.; Kaxiras, E. Electronic -Structure Methods for Twisted Moiré Layers. Nat. Rev. Mater. 2020, 5, 748–763. (4) Andrei, E. ...

2020

[2] [2]

L.; Luo, J

(12) Cao, Y.; Fatemi, V.; Demir, A.; Fang, S.; Tomarken, S. L.; Luo, J. Y.; Sanchez -Yamagishi, J. D.; Watanabe, K.; Taniguchi, T.; Kaxiras, E.; Ashoori, R. C.; Jarillo -Herrero, P. Correlated Insulator Behaviour at Half-Filling in Magic-Angle Graphene Superlattices. Nature 2018, 556, 80–84. (13) Xu, Y.; Liu, S.; Rhodes, D. A.; Watanabe, K.; Taniguchi, T....

2018

[3] [3]

S.; Luo, Z.; Lu, Q.; Millis, A

(21) Chen, X.; Fan, X.; Li, L.; Zhang, N.; Niu, Z.; Guo, T.; Xu, S.; Xu, H.; Wang, D.; Zhang, H.; McLeod, A. S.; Luo, Z.; Lu, Q.; Millis, A. J.; Basov, D. N.; Liu, M.; Zeng, C. Moiré Engineering of Electronic Phenomena in Correlated Oxides. Nat. Phys. 2020, 16, 631–635. (22) Anderson, E.; Fan, F. -R.; Cai, J.; Holtzmann, W.; Taniguchi, T.; Watanabe, K.; X...

2020

[4] [4]

ACS Nano 2020, 14, 2718–

2020

[5] [5]

Moiré Enhanced Two-Band Superconductivity in a MnTe/NbSe2 Heterojunction

(25) Nie, J.-H.; Xie, T.; Chen, G.; Zhang, W.; Fu, Y.-S. Moiré Enhanced Two-Band Superconductivity in a MnTe/NbSe2 Heterojunction. Nano Lett. 2023, 23, 8370–8377. (26) Sung, S. H.; Goh, Y. M.; Yoo, H.; Engelke, R.; Xie, H.; Zhang, K.; Li, Z.; Ye, A.; Deotare, P. B.; Tadmor, E. B.; Mannix, A. J.; Park, J.; Zhao, L.; Kim, P.; Hovden, R. Torsional Periodic L...

2023

[6] [6]

R.; Chuang, H

(27) Rosenberger, M. R.; Chuang, H. -J.; Phillips, M.; Oleshko, V. P.; McCreary, K. M.; Sivaram, S. V.; Hellberg, C. S.; Jonker, B. T. Twist Angle -Dependent Atomic Reconstruction and Moiré Patterns in Transition Metal Dichalcogenide Heterostructures. ACS Nano 2020, 14, 4550–4558. 18 (28) Rodríguez, Á.; Varillas, J.; Haider, G.; Kalbáč, M.; Frank, O. Comp...

2020

[7] [7]

H.; Kretinin, A.; Wilson, N

(30) Weston, A.; Zou, Y.; Enaldiev, V.; Summerfield, A.; Clark, N.; Zó lyomi, V.; Graham, A.; Yelgel, C.; Magorrian, S.; Zhou, M.; Zultak, J.; Hopkinson, D.; Barinov, A.; Bointon, T. H.; Kretinin, A.; Wilson, N. R.; Beton, P. H.; Fal’ko, V. I.; Haigh, S. J.; Go rbachev, R. Atomic Reconstruction in Twisted Bilayers of Transition Metal Dichalcogenides. Nat....

2020

[8] [8]

Strain -Induced Moiré Polar Vortex in Twisted Paraelectric Freestanding Bilayers

(38) Zhang, Y.; Sha, H.; Wang, X.; Liang, D.; Wang, J.; Li, Q.; Yu, R.; Huang, H. Strain -Induced Moiré Polar Vortex in Twisted Paraelectric Freestanding Bilayers. npj Quantum Mater. 2025, 10,

2025

[9] [9]

S.; Zheng, X.; Yang, T.; Yan, Z.; Han, W.; Wong, L

(39) Tsang, C. S.; Zheng, X.; Yang, T.; Yan, Z.; Han, W.; Wong, L. W.; Liu, H.; Gao, S.; Leung, K. H.; Lee, C.-S.; Lau, S. P.; Yang, M.; Zhao, J.; Ly, T. H. Polar and Quasicrystal Vortex Observed in Twisted-Bilayer Molybdenum Disulfide. Science 2024, 386, 198–205. (40) Li, S.; Wang, Z.; Han, Y.; Xu, S.; Xu, Z.; Wang, Y.; Wang, Z.; Xue, Y.; Song, A.; Watan...

2024

[10] [10]

W.; Chacon, C.; Girard, Y.; Repain, V.; Bellec, A.; Rousset, S.; Gonzá lez, C.; Smogunov, A.; Lagoute, J.; Dappe , Y

(47) Chazarin, U.; Lezoualc’h, M.; Karn, A.; Chou, J.-P.; Pai, W. W.; Chacon, C.; Girard, Y.; Repain, V.; Bellec, A.; Rousset, S.; Gonzá lez, C.; Smogunov, A.; Lagoute, J.; Dappe , Y. J. Spatially Extended Charge Density Wave Switching by Nanoscale Local Manipulation in a VTe2 Monolayer. Nano Lett. 2024, 24, 3470–3475. (48) Zhao, W.-M.; Ding, W.; Wang, Q....

2024

[11] [11]

MoireStudio: A Universal Twisted Electronic Structure Calculation Package

(52) Yu, J.; Liu, Y.; Liu, C.-C. MoireStudio: A Universal Twisted Electronic Structure Calculation Package. Comput. Phys. Commun. 2026, 110216. (53) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132, 15410...

2026

[12] [12]

M.; Isayev, O

(55) Anstine, D. M.; Isayev, O. Machine Learning Interatomic Potentials and Long-Range Physics. J. Phys. Chem. A 2023, 127, 2417–2431. (56) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865–3868. (57) Blö chl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953–17979. (5...

2023