Synthesis of incommensurate moiré structures with short-range-ordered charge density modulation

Domain: physics
Published: 2025-12-12
Editorial outcome: major_revision

Abstract
Moiré structures have attracted great interest for tuning emergent quantum phenomena and enabling novel device functionalities. For the twisted bilayer graphene or semiconducting transition-metal dichalcogenides, studies have been focused on ordered systems, atomically and electronically. However, disordered/short-range-ordered moiré electronic structures, likewise involving emergence of novel physical properties and functional applications, remain elusive. Here, we report an incommensurate moiré structure with short-range-ordered charge density modulation state, which is formed between monolayer metallic NiTe2 and superconductor NbSe2. This state features intra-moiré-cell irregular charge orders with spontaneous on-site ordering at the moiré scale, while breaking the crystalline symmetries at the atomic scale. The short-range charge order likely originates from enhanced electron correlations driven by the cooperative effect of moiré-confined strain and localization of electron density. Furthermore, with the layers of NiTe2, we have successfully tuned the short-range state. Our findings provide a promising platform for exploring novel electronic states beyond conventional Bloch-based frameworks and potential applications in quantum devices.

Introduction
Moiré structures, formed by stacking two-dimensional (2D) van-der-Waals materials with a twist angle or lattice mismatch, have emerged as a powerful platform for engineering electronic structures and exploring novel quantum phenomena1–8. These structures introduce long-wavelength periodic potentials into otherwise uniform atomic lattices, fundamentally reshaping the low-energy electronic landscape and enabling precise control over the band topology, bandwidth, and electron correlations9,10. This leads to a plethora of correlated and topological phases, including unconventional superconductivity11, Mott insulating states12, stripe phases13,14, nematicity15, quantized anomalous Hall effect16,17, fractional Chern insulators18–20, and Wigner crystals21–23. The ability to design and manipulate these emergent states through structural engineering makes moiré systems a fertile ground for both fundamental research and potential quantum device applications.

To date, twisted bilayer graphene and semiconducting transition-metal dichalcogenides (TMDs) have been the primary focus of moiré research. In these systems, the low-energy electronic structures can be effectively described by continuum Hamiltonians that preserve translational symmetry at the moiré scale24–27, giving rise to well-defined minibands that underpin our understanding of the emergent ordered electronic states. Great efforts have thus far centered on moiré systems with long-range atomic and electronic orders. In contrast, electronic states featuring disorder or short-range order fall beyond the scope of conventional Bloch descriptions, and are of significance for achieving novel quantum phenomena and enabling potential applications in functional devices28–30. However, such moiré structures of disordered or short-range-ordered electronic states have never been reported, to the best of our knowledge.

Here, we synthesize an incommensurate moiré structure between two metallic TMDs, and observe a short-range-ordered charge density modulation state by using scanning tunneling microscopy/spectroscopy (STM/S). This state features short-range irregular charge orders inside each moiré cell with spontaneous on-site ordering across the moiré scale. The short-range charge orders exhibit a √3×√3 quasi-periodicity and reflect local symmetry breaking. The coexistence of global periodicity and intra-moiré-cell irregularity defines this distinct many-body state. Combined with density functional theory (DFT) calculations, the short-range charge order likely originates from the enhanced electron correlation driven by the cooperative effect of moiré-confined strain and localization of electron density at the ABHollow regions. Furthermore, by controlling the thickness of the NiTe2 layer, the short-range-ordered state has been effectively tuned.

Results
NiTe2 has recently been identified as a Type-II Dirac semimetal hosting Dirac fermions and topological surface states32,33. It exhibits pronounced thickness-dependent electronic tunability34 and has been theoretically predicted to exhibit superconducting instability in the single-layer limit35. Despite these intriguing properties, no charge density wave (CDW) transition has been experimentally observed in the NiTe2 system to date. We start with constructing the moiré structure by direct epitaxial growth of metallic monolayer (1L) NiTe2 film on a superconducting NbSe2 substrate (Fig. 1a), which enables the formation of a short-range-ordered charge density modulation state (Fig. 1b). Both the sharp diffraction spots of the low-energy electron diffraction (LEED) pattern (Fig. 1c) and large-scale STM image (Fig. 1d) indicate the ordered moiré superstructure of the NiTe2/NbSe2. Two sets of the LEED pattern of the NiTe2 (red circles) and NbSe2 (blue circles) reveal that monolayer NiTe2 share the same orientation with NbSe2, further indicating the formation of the moiré superstructure is due to lattice-mismatch. The measured in-plane lattice constants of monolayer NiTe2 and NbSe2 are approximately 3.69Å and 3.46Å, respectively. In the 1L-NiTe2/NbSe2 heterostructure, the moiré wavelength is measured to be about 3.78nm. Thus, the resulting moiré structure is incommensurate. Long-range-ordered charge modulation at the moiré scale is observed with high-resolution STM (Fig. 1e), which features three inequivalent local regions within a moiré unit cell, i.e., the bright (ABHollow), dark (AA), and intermediate (ABSe) regions, respectively (Supplementary Figs. S1, S2, see Methods). Remarkably, electronic structures at these three local regions exhibit strong intensity contrast, with the brightest ABHollow regions appearing as bubbles, suggesting a significant charge density modulation. The dI/dV spectra of the three regions in NiTe2 further corroborate the charge density modulation (Supplementary Fig. S3). The dI/dV maps reveal a distinct inversion of intensity contrast at +250meV and −250meV at the same spatial location (Supplementary Fig. S4), further confirming the large-periodic charge density modulation at the moiré scale36,37.

Next, we demonstrate the short-range charge orders inside each moiré unit cell. High-resolution STM images (Fig. 2a and Supplementary Fig. S5) reveal that the short-range charge orders emerge at each ABHollow regions of the moiré superstructure, with spontaneous on-site ordering across the moiré scale. The charge orders have a rough preference to localize on Te sites (Supplementary Fig. S6). In addition, the short-range charge orders are consistently observed across four NiTe2/NbSe2 samples using eight different STM tips, demonstrating their robustness and reproducibility (Supplementary Fig. S7). The variation in the number of charge orders within each ABHollow region arises from region-dependence across the sample, reflecting their intrinsic local inhomogeneity and short-range nature. The sharp spots of the fast Fourier transform (FFT) pattern (Fig. 2b) indicate the Bragg lattice of NiTe2 and the ordered superstructure of NiTe2/NbSe2. The broad spots surrounding six hexagonal wavevectors at (√3×√3)R30° positions (Q√3×√3) with respect to NiTe2 Bragg lattice suggest the formation of short-range orders at approximately √3×√3 of the NiTe2 unit cell. We further analyze the spatial ordering of the charge states across multiple monolayer NiTe2 samples. Each bright state is marked as a center, from which we measure the spatial distance to its nearest neighbors and extract the angular deviation between the C3 symmetry axes of adjacent states (inset in Fig. 2c, d). The short-range orders are irregular, varying between different ABHollow regions, as evident by the distribution statistics of rotation angle and periodicity (Fig. 2c, d). Thus, the overall charge density modulation has the character of long-range periodic modulation pinned by the moiré landscape, whereas the short-range orders within each moiré cell exhibit quasi-hexatic characteristics, with quasi-sixfold rotational symmetry and a quasi-periodicity of approximately √3 times of the NiTe2 lattice constant.

We further analyze the short-range charge order state inside the moiré unit cells. At the same spatial locations, the density of states (DOS) shows contrast inversion on opposite sides of EF (+100meV and −100meV) (Fig. 2e, f and Supplementary Figs. S8, S9), with the same short-range √3×√3 orders. The spatial distribution of the amplitude and phase of the Q√3×√3 reveal the short-range charge order within the ABHollow regions with phase variation (Fig. 2g, h). These results demonstrate the emergence of short-range √3×√3 charge orders inside the moiré unit cells, while it breaks the underlying crystalline symmetries and losses long-range phase coherence.

We next examine the possible origins of the observed short-range charge orders. Known defect configurations in NiTe2, such as Ni interstitials and chalcogen substitutions, can exhibit C3-symmetric orbital features, but they are generally random in distribution and lack layer dependence38,39, or instead form long-range periodic structural reconstructions40. In contrast, the localized states observed here are consistently confined within the ABHollow regions, forming a quasi-periodic pattern across extended areas. They are exclusive to monolayer NiTe2 and disappear in thicker layers (as discussed below), in contrast to defect-induced features that typically persist regardless of film thickness. Moreover, we keep T-rich atmosphere during the growth, and the average density of the short-range charge order remains nearly unchanged with increasing Ni:Te flux ratio during growth (Supplementary Fig. S10), further ruling out Ni interstitials at the interface40. These characteristics strongly suggest that the short-range charge modulation does not arise from atomic-scaled defects, but rather reflects an alternative, electronically driven mechanism.

We also note that NbSe2 hosts a 3×3 CDW below ~33K. Although the short-range-ordered charge modulations in NiTe2 exhibit local C3 symmetry, they are distinct from the long-range 3×3 CDW of the underlying NbSe2 substrate in terms of coherence length, orientation, and energy scale. Specifically, the NiTe2 charge order is short-range and rotated by ~30° relative to the lattice, and persists above room temperature (Supplementary Fig. S11). These differences suggest only weak or negligible coupling between the two charge modulations.

To further study the possible mechanism of the short-range charge order within ABHollow regions, we analyzed the moiré-confined strain distribution41,42, charge transfer, and electron density distribution in the 1L NiTe2 on NbSe2 with DFT calculations. Although such calculations, performed within the Bloch framework, cannot fully capture the experimentally observed electronic states with broken translational symmetry, they provide useful insight into possible mechanisms for the emergence of short-range charge order. The charge order is absent in the pristine NiTe232–34, and the phonon dispersion of monolayer NiTe2 shows no phonon softening, indicating its dynamical stability (Supplementary Fig. S12). The on-site Coulomb interactions also shows slight impact on the electronic band structure of the monolayer NiTe2 (Supplementary Fig. S13). However, in the moiré structure of NiTe2/NbSe2, the monolayer NiTe2 within ABHollow regions are predicted to experience significant compressive strain (about 3%, Fig. 3a). The strain field distribution in atomically-resolved STM image by using a computational framework of the atomic displacement analysis along both crystallographic axes (Method) estimate that about 3% compressive strains exist within ABHollow regions (Supplementary Fig. S14). In addition, the calculated charge distribution shows a strong localization of the electron density within ABHollow regions (Supplementary Fig. S15). While the calculation results based on a simplified model of a uniformly strained NiTe2 monolayer cannot fully describe the emergent electronic states associated with short-range ordering (Fig. 2a), they nevertheless provide valuable insight into the possible driving forces that enhance electronic correlations. Although the system still remains dynamically stable under 3% strain (Supplementary Fig. S16), larger compressive strain can, in principle, induce electronic instabilities in monolayer NiTe2. The band structure upon applying a 10% compressive strain (Fig. 3b) shows that the energy band around the K point anchored by the Dirac point is pulled closer to the Fermi level, leading to the formation of a small hole pocket located at K point precisely, and thereby enhancing its density of states. Moreover, the maximum electronic susceptibility is moved to K point, which indicates the nesting between K and K′ points, suggesting an enhanced electron correlation (Fig. 3c). As a result, the Fermi surface nesting vector gives rise to a √3×√3 charge order vector (Fig. 3d, e). The atomic structure model for the √3×√3 phase shows a lower symmetry (C3v) compared to the high-symmetry of the pristine phase (D3d) (Fig. 3f, g). Therefore, we speculate that the short-range charge order originates mainly from the enhanced electron correlations driven by the cooperative effect of moiré-confined strain and localization of electron density within the ABHollow regions.

Intriguingly, we show the tuning of the short-range charge orders by controlling the thickness of NiTe2 (Supplementary Fig. S17). In comparison to the 1L NiTe2, in the bilayer (2L), the moiré modulation remains while the √3×√3 short-range charge orders are suppressed (Fig. 4a). The density of states in equivalent local regions, e.g., ABHollow, exhibit evident inhomogeneity, suggesting that the electronic state still retains short-range nature. The dI/dV maps further reveal the distinct electronic states within different moiré regions and weaker charge modulation than that of the 1L NiTe2 at the moiré scale (Supplementary Fig. S18). The disappearance of the short-range charge order with increasing NiTe2 layer is further supported by DFT calculations (Supplementary Fig. S19), which reveal substantially reduced strain and electron localization within the ABHollow regions, insufficient to induce electron correlations. As the thickness further increases to trilayer, the moiré modulation are further suppressed and eventually disappeared at the four-layer NiTe2 (Fig. 4b, c). Furthermore, we construct a planar homojunction of 2L-NiTe2/NbSe2 and 1L-NiTe2/NbSe2 (Fig. 4d), with the interface defined by the sharp step edge of the top NiTe2 layer. The corresponding dI/dV maps reveal long-range charge density modulation with inlaid short-range charge orders in the 1L NiTe2 region, whereas the 2L exhibits much weaker modulation without charge orders (Fig. 4e and Supplementary Fig. S20), indicating the formation of a moiré junction with and without short-range charge order state. Notably, a pronounced charge edge state at about 45meV emerges at the interface across the 1L-2L junction (Fig. 4f), but is absent at the 2L-3L junction (Supplementary Fig. S21).

Finally, the short-range-ordered modulation state is also observed in the superconducting regime. The superconducting phase in NiTe2 is induced by proximity effect (Fig. 5a, b). The coherence peak height, peak-to-peak distance, and consequently the superconducting gap size show strong modulation across the ABHollow regions (Fig. 5c). Within these regions, the coherence peak height is enhanced, while the superconducting gap size is reduced. This spatially-modulated pair density represents a secondary phase of the charge density modulation at the moiré scale, as a result of the correlation between the short-range charge order and the proximity-induced superconductivity. The periodicity of the pair density modulation is obviously variable and the dI/dV map at the energy of coherence peak shows inhomogeneous characteristics (Fig. 5d, e), suggesting a quasi-ordered pair density modulation and reinforcing the disordered nature of the electronic state in such moiré system.

Methods
Sample preparation
NiTe2 film with various thickness were epitaxially grown on freshly-cleaved NbSe2 substrates by molecular beam epitaxy approach under ultra-high vacuum conditions (UHV, base pressure ~5×10−10mbar). High-quality NbSe2 single crystals used as substrates were fabricated by chemical vapor transport approach. The clean NbSe2 substrates were obtained by cleaving in vacuum and subsequently annealing in UHV at 600K for several hours. The NiTe2 films were grown by e-beam evaporation of Ni (99.9%, Goodfellow Cambridge Ltd.) and simultaneous deposition of atomic Te (99.99%, Sigma-Aldrich) from a Knudsen cell at a substrate temperature of 520K. During growth, the Te flux approximately an order of magnitude greater Ni flux (Te-rich conditions) is used. The layers of the epitaxial NiTe2 film can be precisely controlled by tuning the deposition time and flux, which allows the construction of well-defined planar homojunctions between regions of different NiTe2 layers on the same NbSe2 substrate (Supplementary Fig. S17).

STM/STS and LEED
STM/STS measurements were performed in an ultrahigh vacuum (1×10−10mbar) ultra-low temperature condition equipped with 11T magnetic field. The stable sample temperature can be kept at a base temperature of 0.4K and 4.2K, respectively. The electronic temperature is 620mK at a base temperature of 400mK. All the scanning parameters (setpoint voltage and current) of the STM topographic images are listed in the captions of the figures. Unless otherwise noted, the differential conductance (dI/dV) spectra were acquired by a standard lock-in amplifier at a modulation frequency of 973.1Hz. Tungsten tip was fabricated via electrochemical etching and calibrated on a clean Au(111) surface prepared by repeated cycles of sputtering with argon ions and annealing at 770K. LEED was employed with a 4-grid detector (Omicron Spectra LEED) in the UHV chamber at room temperature.

Two-dimensional lock-in technique and strain analysis
To explore the √3×√3 charge modulations, we employ a two-dimensional lock-in technique49 to determine the amplitude and phase of the modulations. For any arbitrary real space image:
A(r) = ΣQ aQ(r)e−iQ·r (1)
where aQ(r) is the complex amplitude at wavevector Q and position r. If Q is the wavevector of interest, it can be extracted from the Fourier transform A(q) by shifting it back to the center and multiplying a Gaussian window with a cut-off length σ in q-space. The approximate complex amplitude in real space AQ(r) can be obtained by inverse Fourier transform as following:
AQ(r) = F−1 [ A(q) ] = ∫ dR A(R)eiQ·R e−(r−R)2/2σ2 (2)
Thus, using this technique, the amplitude |AQ(r)| and spatial phase ΦA(r) of the modulation at Q can be written as:
|AQ(r)| = ReAQ(r)2+ImAQ(r)2 (3)
ΦA(r) = tan−1 ImAQ(r) / ReAQ(r) (4)
Since the phase calculated by the algorithm may have a 2π jump at certain pixels, it is necessary to perform unwrap function on the obtained amplitude and phase information. When we select the wave vector Q to perform 2D-lockin, the signal after low-pass filtering can be approximated as:
A(r) ≈ AQ(r)e−i(q0−Q)·r = e−iΔq·r (5)
The phase can be written as:
ΦQ(r) = Δq·r + Φlocal(r) (6)
If q0 = Q, then only the local phase information ΦQ(r) = Φlocal(r) remains. However, if q0 ≠ Q, In the phase, there will be an additional linear term Δq·r. Here, our short-range order is associated with a set of broad spots in blue circles (Fig. 2b), so the occurrence of a reference phase mismatch is reasonable. The linear background corresponds to a very strong and low-frequency phase gradient, which will not be filtered out by Gaussian filtering. Unwrapping causes the linear background to be more prominent after unwrapping. To avoid confusion, we use the least squares method to subtract these linear backgrounds, thereby making the obtained phase information more closely resemble the actual phase information in Fig. 2h. To obtain the amplitude and phase information in Fig. 2h, the selecting wavevector Q is at (√3×√3)30° position marked in Fig. 2b. The Gaussian filter order is 16 and the filter length scale is 28 pixels×28 pixels (1.9nm×1.9nm).
Based on 2D lock-in technique, the strain filed can be extracted with Lawler-Fujita algorithm50. For a hexagonal lattice NiTe2, considering the total displacement field u(r), the real space image can be written as:
A(r) = A1eiQ1·(r−u(r)) + A2eiQ2·(r−u(r)) + A3eiQ3·(r−u(r)) + c.c. (7)
where Q1 and Q2 are the reciprocal lattice basis and Q3 = Q1 + Q2. The fourth term c.c. represent possible displacement due to picometer scale piezoelectric drift and thermal drift. u(r) is defined as displacement filed. By applying local Gaussian filtering in the momentum space near the Bragg wavevector (20×20 pixels window), high-frequency oscillations can be filtered out. We can get the two displacement field components u1(r) and u2(r):
u i(r) = Qi·u(r) = −arg ai eiQi·u(r) (i=1,2) (8)
The components along the lattice u1(r) and u2(r) can be decomposed into x and y axes ux(r) and uy(r). Total strain field u(r) consists of strain field s(r) and drift field u(r). Drift field d(r) typically includes piezo drift and thermal drift, and it can generally be fitted using a 3-order polynomial. By fitting with the STM images, d(r) can be obtained, and thus the strain field can be determined as:
s(r) = u(r) − d(r) (9)
Next, as described in the article (Supplementary Fig. S14), the strain tensor can be expressed as:
sii = ∂sii / ∂i (r) (i=x,y) (10)

Definition of ABHollow, ABSe, and AA regions in the moiré structure of NiTe2/NbSe2
To determine the local atomic structure of the bright, dark, and intermediate regions within the moiré superstructure, we construct a structural model of monolayer NiTe2 on NbSe2. After structural optimization, the moiré superstructure shows three distinct local regions, denoted as ABHollow, ABSe, and AA based on different atomic alignments (Supplementary Fig. S1). In the ABHollow region, Ni atoms are aligned above Se and Nb atoms, respectively. The DFT simulated STM image based on the optimized atomic model shows excellent agreement with the experimental data (Supplementary Fig. S2). Consequently, we attribute the bright, dark, and intermediate regions within the moiré unit cells to ABHollow, AA, and ABSe regions, respectively.

DFT calculations
The DFT calculations were carried out using Vienna ab initio simulation package (VASP)51. The projected augmented wave (PAW) method52 was used to describe the core-valence interactions. The generalized gradient approximation (GGA)53 in the form of Perdew-Burke-Ernzerhof (PBE) is adopted for the exchange-correlation functional. In the calculations of free-standing NiTe2, a 15Å vacuum layer is used, and all atoms are fully relaxed until the residual forces on each atom are smaller than 0.01eV/Å. The k-points sampling is 27×27×1 with the Gamma scheme. Wavefunctions were expanded on a plane-wave basis set up to 500eV energy cutoff. The fully relaxed lattice constants of monolayer NiTe2, bilayer NiTe2 and NbSe2 are 3.715Å, 3.814Å and 3.459Å, respectively. A slab model is used for the moiré superlattice. For the monolayer NiTe2, the heterostructure is constructed using a 10×10 monolayer NiTe2 on an 11×11 monolayer NbSe2, resulting in a lattice mismatch of ~2.4%. The corresponding moiré lattice periodicity of this configuration is 3.81nm. For the bilayer case, the heterostructure is composed of a 9×9 bilayer NiTe2 on a 10×10 monolayer NbSe2, with a reduced lattice mismatch of ~0.8%. The resulting periodicity of the moiré lattice is 3.46nm. Wavefunctions were expanded on a plane-wave basis set up to 400eV energy cutoff. Van-der-Waals interactions were considered at the DFT-D3 level. The vacuum layer is 15Å. A Γ-only k-point sampling in the first Brillouin zone is used for the moiré superlattice. All atoms except the NbSe2 substrate are fully relaxed until the net force is smaller than 0.01eV/Å. The in-plane strain is introduced by changing the lattice constant of NiTe2. Moreover, PBE+U calculations were also used to study the effects of on-site Coulomb interaction on the Ni 3d-orbitals. Here, we used the method proposed by Dudarev et al. where only the effective Coulomb interaction Ueff defined by the difference between the correlation energy and the exchange energy was meaningful54. A Hubbard U correction of Ueff = 2eV and 4eV were applied to Ni 3d-orbitals. The strain is defined by ΔL/L, where L and ΔL are the lattice constant and compressed length of pristine NiTe2. The real part of susceptibility is calculated as the following formula,
χ0(q) = Σk f(ϵk+q) − f(ϵk) / ϵk − ϵk+q (11)
where the f denotes the electron’s Fermi distribution function.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this manuscript the authors report on an incommensurate heterostructure consisting of a monolayer NiTe2 placed on bulk NbSe2. This system is characterized through STM and LEED measurements and DFT calculations.\nI do not think the manuscript in its present form is suitable for publication in Nat. Commun. as I am not convinced by the main point the authors try to establish. Specifically, I do not think that compelling evidence is provided for the disordered nature of the charge density modulation.\nFigure 2a: STM measurement claimed to show “short-range charge order”. Based on the DFT results, the authors speculate that this order stems mainly from moiré-induced strain and localization of electrons in the AB_hollow regions of the structure. As such, the STM image in Fig. 2a and the DFT result on the charge distribution in Fig. S8 correspond well. Hence, with this explanation being demonstrated by the authors, I do not see why they claim in other parts of the manuscript that the moiré system is disordered. I cannot reconcile these two points of view, and therefor consider this a major flaw that jeopardizes the manuscript.\nFurthermore, claims by the authors like the following on the significance were not substantiated (line 56): “In contrast, electronic states featuring disorder or short-range order fall beyond the scope of conventional Bloch descriptions, and are of significance for achieving novel quantum phenomena and enabling potential applications in functional devices.” A similar statement is featured in the abstract.\nWhat is more, in this study I do not see any evidence of effects beyond the Bloch theorem, as the authors claim their experimental measurements are well-explained by DFT calculations that were obviously performed with application of the Bloch theorem.\nThe writing of the manuscript is regularly unclear, for instance: “The charge order is absent in the pristine NiTe2, and the phonon dispersion of monolayer NiTe2 shows no phonon softening, indicating its thermodynamic stability (Fig. S7).” This should be dynamical stability instead of thermodynamic stability. Also, the “negative frequencies” mentioned in the caption of Fig. S7 are in fact physically speaking imaginary.\nIt is also not clear how the lateral heterostructure discussed at some point was achieved experimentally and what the nature of the interface is.\nFurther computational details are also unclear, such as how the mismatch between the two materials was treated in the simulations. The authors also state that “The vacuum layer is larger than 10 Angstrom”. They should provide a more detailed value. Furthermore, in the simulation shown in Fig. 3, it is unclear how many layers of NbSe2 were included in the simulation. From the SM, it appears that this was just one. Is this sufficient to simulate a bulk substrate as present in the experiment.\nOne of the more interesting results of the manuscript is rather quickly glanced over, namely proximity-induced superconductivity in NiTe2, whose results are only presented in the SM, which is rather a waste.\nFor these reasons I cannot recommend this manuscript for publication in Nat. Commun.", "reviewer_2": "Guo et al report the synthesis of a moiré structure between NbSe2 and NiTe2 using MBE growth as opposed to the usual tear and stack process known in the 2D device community. The advantage of such synthesis is that the surfaces are clean and amenable to STM studies and local spectroscopy. They see short range charge orders on the length scale of the moiré lattice due to the collective effects of moiré induced periodic strain, electron localization and electron correlations. They also prove this by tuning the layer thickness of NiTe2. The paper is well written, the STM data is high quality, and the results are remarkably interesting, and of general interest to the material synthesis, theoretical and experimental condensed matter physics community. Therefore, I think the manuscript should be published in Nature Communications although I have a few clarifying questions that I believe would improve the analysis, quality, and readability of the paper for the general audience.\n1. In the abstract and in paragraph 3, the authors refer to the moire as “TMDs with incommensurate lattice wavevectors,”, which needs rephrasing. The TMD lattices by themselves are commensurate, but the resulting moire lattice is incommensurate. Also, please specify the moiré lattice constant in the manuscript.\n2. In paragraph 2, the authors say, “In contrast, electronic states featuring disorder or short-range order fall beyond the scope of conventional Bloch descriptions, and are of significance for achieving novel quantum phenomena and enabling potential applications in functional devices” , it would be good to have a few references here to show the novel phenomena and applications are the authors referring to.\n3. To show the existence of a phonon softening the authors use DFT simulations with a 10% strain. However, strain analysis from experimental data indicates 3% strain. Is there a phonon softening at this value of strain? The authors should include a statement on their reasoning behind choosing this value of strain for their DFT analysis.\n4. Do the authors know if the charge order has a preference to localize on the Nb/Se/Ni/Te sites? It will be good to show an overlay of the AB schematic and an atomically resolved AB site topography with the charge order.\nhollow hollow\n5. Can the authors comment on the relationship between the disordered CDW to the 3Q CDW of NbSe2? Since the disordered CDW prefers to have a C3 symmetry, it seems plausible. Are the disordered CDW and the underlying 3Q order of NbSe2 related based on symmetry and periodicity arguments?", "reviewer_3": "Guo et al. present the growth of atomically thin NiTe2 on NbSe2 and its atomic-scale characterization by STM/STS and LEED. STM/STS reveal atomic-scale localized states which appear in quasi-ordered clusters within periodic regions defined by the Moiré pattern. Further, DFT modelling demonstrates that strain of 10% can enhance the susceptibility towards a charge-ordered state; supporting the claim that the observed localized states are correlation-induced many-body states. Additionally, the states are demonstrated to disappear with additional layers of NiTe2. As understanding the role of heterostrain and Moiré-potential on the formation of electronic ordering holds high significance to the advancement of the field, this work has great potential impact.\nThe demonstrated MBE growth and the STM/STS data are of very high quality and the information within the manuscript is presented clearly. However, elements of the data analysis, interpretation, and conclusions of the work lack sufficient validity and robustness for publication in Nature Communications. It is my recommendation to consider this work after the following major revisions are made.\nBelow are detailed descriptions of flaws found in the manuscript with specific questions aimed to address them.\n1. Introduction lacks consideration of previous work. The authors do not reference any previous reports of NiTe2 MBE growth or STM characterization.\na. The authors should add appropriate references and place their work within the current state of the field. Has NiTe2 been grown on NbSe2 before? What characterization has been done on monolayer NiTe2 previously? Have there been previous investigations of correlated phases in NiTe2, experimental or theoretical? etc.\n2. The validity of statistical analysis cannot be determined. Information about the measurement and analysis statistics are lacking from the manuscript.\na. The sample statistics should be given. How many samples were measured and with how many tips?\nb. Fig 2a shows many bright spots within and around the ABHollow regions but the spectral maps 2e,f only show at most 3. What are the differences between these two samples?\nc. Figs. 2e,f show features reminiscent of inelastic tunneling through an adsorbate within the tunnelling junction. The authors should provide the corresponding topography measurement as well as point tunnelling spectra on and off the localized states in both measurements. Additionally, it would be helpful to know the spatial resolution of the dI/dV maps presented in the main text and SI.\nd. Ordering analysis is not described in the Methods section or in the main text. Authors need to describe how the charge centers are selected and how orientation and displacement correlation functions are analyzed. While Figures 2a and S5 do show that localized states and C3 symmetric orbitals are most intense in the ABHollow regions, they are also present in several regions across the Moiré landscape at a lower apparent height. Are these spots included in the reported statistics?\ne. The amplitude and phase maps (Figures 2g and 2h) both show long wavelength features and little-to-no correlation on the Moiré length scale. Authors should describe their procedure for selecting the wavevector Q as well as what length scale, σ, was chosen for the Fourier filtering procedure. Is the linear phase background indicative of linear strain or fitting error?\n3. Stronger experimental and theoretical evidence of an electronic correlation-induced many-body state needs to be provided and consideration of alternative descriptions should be given.\na. Contrast inversion is used to demonstrate that there is a localized state near the Fermi level, however, the energy of the localized state(s) is not identified in this work. This is essential to determine the correlation energy as a function of space within the Moiré potential. Also, contrast inversion is shown at several different energies in figure S6 which warrants further explanation.\nb. The relaxed DFT model expects strain variations of up to nearly 6% in this heterostructure and possible nesting conditions achievable at 10% compressive strain. These values of strain are measurable by atomically resolved STM. The authors should attempt to measure the experimental strain value as well as estimate the Moiré potential variation to more carefully to support their claim.\nc. Is the C3v symmetric model (Figure 3g) with larger unit cell unstable towards a real structural distortion? Or is this assumed? Was the on-site potential changed to induce the electron correlation? If so, what site in the lattice was chosen and what is the value of on-site potential assumed?\nd. Further, more likely explanations (i.e. growth-related atomic-scale defects) have not been sufficiently ruled out. Note that many atomic defects, including low formation energy Ni interstitials and chalcogen substitutions, also show C3 symmetric orbitals with approximately √3 a extent as shown in a previous STM measurement of NiTe2, for example (Wen-Xiao Wang et al 2023 Phys. Scr. 98 015020); which was not referenced by this work.\ne. The loss of localized states with thicker NiTe2 layers could also be consistent with interstitial defects or Te-Se substitutions at the growth interface. However, no reasoning is given for why the localized states disappear with increasing layer thickness. Is this observation consistent with the conclusion of strain-induced correlations?\nf. Finally, the 2H-NbSe2 substrate is known to undergo an ordering transition to an incommensurate charge density wave state below ~33K with a wavelength of nearly 3aNbSe2. The authors do not mention the implications of this charge modulation on the observed disordered localized charges. Is the CDW phase experimentally identified in this heterostructure? Has the CDW phase been accounted for in the DFT heterostructure model?\n4. Minor revisions\na. Gaussian formula needs revision\nb. The lattice contrast inverts between the topography measurements of 3L and 4L. Do the authors have an explanation for this contrast inversion?\nc. The title claims “incommensurate moiré structures,” however the Moiré pattern shown is commensurate with both lattices as evidenced by the LEED data.\nd. The Moiré pattern is claimed to be “consistent” with the lattice mismatch but no numbers are given. What are the experimental lattice parameters and Moiré wavelength?"}, "author_response": "Point-by-point responses to the comments from the Reviewers\nWe thank the Reviewers for their constructive criticisms, comments and valuable suggestions. As\nan overall response, we have added the discussions on the relationship between the observed short-\nrange-ordered charge density modulations and the DFT calculations. Additionally, we have also\nincorporated comprehensive analyses on the observed charge orders, such as spatial statistics,\ndefect considerations, and strain effects supported by DFT calculations. Furthermore, we clarified\nkey terminology and improved the presentation of experimental data with enhanced figures and\nupdated discussions on the relationship between moiré patterns and electronic states.\nBelow, we respond to the comments and suggestions of the Reviewers point-by-point. The\ncomments from the Reviewers are included in black italic typeface. Our responses are in regular\nblue typeface. The changes to the text in the revised manuscript are described or quoted in red. A\ndetailed list of changes is attached at the end of this document.\nResponse to the Reviewer #1\nIn this manuscript the authors report on an incommensurate heterostructure consisting of a\nmonolayer NiTe placed on bulk NbSe . This system is characterized through STM and LEED\n2 2\nmeasurements and DFT calculations.\nI do not think the manuscript in its present form is suitable for publication in Nat. Commun. as I\nam not convinced by the main point the authors try to establish. Specifically, I do not think that\ncompelling evidence is provided for the disordered nature of the charge density modulation.\nComment 1: Figure 2a: STM measurement claimed to show “short-range charge order”. Based\non the DFT results, the authors speculate that this order stems mainly from moiré-induced strain\nand localization of electrons in the AB_hollow regions of the structure. As such, the STM image in\nFig. 2a and the DFT result on the charge distribution in Fig. S8 correspond well. Hence, with this\nexplanation being demonstrated by the authors, I do not see why they claim in other parts of the\nmanuscript that the moiré system is disordered. I cannot reconcile these two points of view, and\ntherefor consider this a major flaw that jeopardizes the manuscript.\nResponse: We sincerely thank the Reviewer for the important and insightful comment. We\nrecognize that the comparison between Fig. 2a and Original Fig. S8 (now Fig. S15) could give the\nimpression of a globally “ordered state,” while in other parts of the manuscript we described the\nmoiré system as “disordered”. We understand that this inconsistency caused confusion, and we\nclarify below.\n(1) On the use of term “disordered”\nWe apologize for the confusion caused by using the term of “disordered” in describing the charge\nmodulation localized on the specific region of Moiré pattern. To clarify, the moiré structure itself\nis atomically periodic, as evidenced by both the lattice registry and the overall moiré pattern\nobserved in STM measurements. However, within this periodic moiré structure, the charge density\nmodulation exhibits local variations. Particularly, within AB regions, irregular short-range\nHollow\ncharge orders emerge, which appear as quasiperiodic or aperiodic features inside each moiré unit\ncell. It is this absence of long-range translational symmetry in the local charge distributions that we\ndenote as “disordered”.\nTo avoid this confusion, we have revised the term of “disordered” to “short-range-ordered” in the\ntitle, abstract and main text.\n(2) Comparison between STM image and DFT calculations\nThe STM image in Fig. 2a and DFT calculation in Original Figure S8 (now Fig. S15) should not\nbe considered as directly corresponding, as compared in Fig. R1.\nFig. R1. a, Schematic of the short-range charge orders inside moiré unit cells. b, Atomically-\nresolved STM image of monolayer NiTe on NbSe , showing periodic moiré structure (black\n2 2\nrhombus), atomic lattice of NiTe , and short-range quasiperiodic charge orders confined within\nHollow Hollow\nis indicated by yellow arrow. c, DFT calculated electron density distribution of the monolayer NiTe\n2\non NbSe , showing a strong electron localization but without short-range charge orders within\nHollow\nIn Fig. 2a, the STM data reveal short-range √3 × √3 like charge modulations localized within the\nAB regions (blue circles). While the underlying moiré lattice remains periodic, these\nHollow\nmodulations are not phase-coherent across different moiré cells (Fig. 2h), which is why we\ncharacterize them as “short-range ordered”.\nBy contrast, Fig. S15 from DFT calculations only shows electron localization in the AB\nHollow\nregions, but does not capture the √3 × √3 quasiperiodic modulation. This limitation arises because\nconventional DFT cannot fully account for short-range correlation effects or emergent electronic\nstates associated with disorder-like phenomena.\nTo explore the possible origin of the observed short-range charge order, we further considered\nmoiré-confined strain. Since direct DFT calculations are insufficient, we modeled a NiTe\n2\nmonolayer under uniform strain to examine its electronic structure, Fermi surface, and\nsusceptibility. This simplified model indicates that moiré-induced strain, combined with electron\nlocalization in AB regions, can enhance correlations and favor the emergence of the √3 × √3\nHollow\nshort-range charge order.\nWe have revised the manuscript to clarify this point (page 8, line 9-12), adding: “…shows a strong\nlocalization of the electron density within AB regions (Fig. S15). While the calculation results\nHollow\nbased on a simplified model of a uniformly strained NiTe monolayer cannot fully describe the\n2\nemergent electronic states associated with short-range ordering (Fig. 2a), they nevertheless provide\nvaluable insight into the possible driving forces that enhance electronic correlations.”\nComment 2: Furthermore, claims by the authors like the following on the significance were not\nsubstantiated (line 56): “In contrast, electronic states featuring disorder or short-range order fall\nbeyond the scope of conventional Bloch descriptions, and are of significance for achieving novel\nquantum phenomena and enabling potential applications in functional devices.” A similar\nstatement is featured in the abstract.\nWhat is more, in this study I do not see any evidence of effects beyond the Bloch theorem, as the\nauthors claim their experimental measurements are well-explained by DFT calculations that were\nobviously performed with application of the Bloch theorem\nResponse: We sincerely thank the Reviewer for this valuable comment. We would like to clarify\nthat the √3 × √3 short-range charge modulations observed in our STM experiments cannot be\nexplained by our DFT calculations, precisely because DFT inherently relies on the Bloch theorem\nand thus assumes perfect translational symmetry.\nIn this work, our DFT calculations were performed on a simplified, periodic model of strained\nNiTe . These calculations were not intended to reproduce the experimentally observed short-range\n2\nquasiperiodic modulations, but rather to reveal possible driving forces—such as moiré-confined\nstrain and electron localization—that may enhance electronic correlations. By construction, these\ncalculations neglect spatial inhomogeneity and short-range correlations, and therefore cannot\naccount for the symmetry-breaking features seen in STM.\nThe STM data, however, clearly reveal quasiperiodic charge modulations within AB regions\nHollow\nthat lack global phase coherence and long-range translational symmetry. It is this intrinsic short-\nrange and inhomogeneous nature of the electronic states that falls beyond the conventional Bloch\nframework. Our claim regarding “effects beyond the Bloch theorem” refers specifically to these\nexperimentally observed states, which cannot be faithfully captured by periodic DFT models.\nTo prevent misunderstanding, we have highlighted the limitation of applied DFT calculations when\nfirstly mentioning them (page 7, line 18-20). “To further study the possible mechanism of the short-\nrange charge order within AB regions, we analyzed the moiré-confined strain distribution40,41,\nHollow\ncharge transfer, and electron density distribution in the 1L NiTe on NbSe with DFT calculations.\n2 2\nAlthough such calculations, performed within the Bloch framework, cannot fully capture the\nexperimentally observed electronic states with broken translational symmetry, they provide useful\ninsight into possible mechanisms for the emergence of short-range charge order.”\nComment 3: The writing of the manuscript is regularly unclear, for instance: “The charge order\nis absent in the pristine NiTe2, and the phonon dispersion of monolayer NiTe2 shows no phonon\nsoftening, indicating its thermodynamic stability (Fig. S7).” This should be thermodynamic\nstability instead of thermodynamic stability. Also, the “negative frequencies” mentioned in the caption of\nFig. S7 are in fact physically speaking imaginary.\nResponse: We have taken the Reviewer’s suggestion and carefully revised the manuscript for\nclarity and precision. Specifically, “thermodynamic stability” has been corrected to “dynamical\nstability,” and “negative frequencies” has been revised to “imaginary frequencies” in both the main\ntext and figure caption.\nComment 4: It is also not clear how the lateral heterostructure discussed at some point was\nachieved experimentally and what the nature of the interface is.\nResponse: The NiTe layers were grown on the NbSe substrate using molecular beam epitaxy,\n2 2\nwhich allows precise control over the thickness by tuning the deposition time and flux. In this work,\nwe have precisely achieved regions of monolayer (1L), bilayer (2L), trilayer (3L), and four-layer\n(4L) NiTe on NbSe , as shown in the Fig. S17.\n2 2\nThe lateral heterostructure discussed in the manuscript arises naturally between the 1L-\nNiTe /NbSe and 2L-NiTe /NbSe regions, as shown in the schematic in Fig. R1. Specifically, the\n2 2 2 2\nfirst layer of NiTe forms a continuous film in the NbSe substrate, while the second layer grows in\n2 2\nan island-like fashion. The interface is defined by the step edge of the second-layer NiTe islands.\n2\nthe same NbSe substrate.\n2 2\nNiTe /NbSe .\n2 2\nIn the revised manuscript, we have changed the word “lateral heterostructure” to “planar\nhomojunction”, and added Fig. R2 to the revised Fig. S17c in the Supplementary Information as\nfollows.\nRevised Fig. S17. Large-scale STM images of NiTe with different layers. a, Large-scale STM\n2\nimage of a planar homojunction of 2L-NiTe /NbSe and 1L-NiTe /NbSe (V=-2 V, I=0.05 nA). b,\n2 2 2 2 s t\nLine profile along the black arrow in (a), showing the step height of 0.56 nm across the\nhomojunction. c, Schematic of the planar homojunction. d, Large-scale STM image of NiTe with\n2\nthick layers (V=-2 V, I=0.05 nA). e, Line profile along the black arrow in (d), showing a single-\ns t\nlayer NiTe thickness of 0.56 nm.\nconstruct a planar homojunction of 2L-NiTe /NbSe and 1L-NiTe /NbSe (Fig. 4d), with the\n2 2 2 2\ninterface defined by the sharp step edge of the top NiTe layer.”, and added the description in the\n2\nrevised Method Section (page 14, line 9-12), “The layers of the epitaxial NiTe film can be precisely\n2\ncontrolled by tuning the deposition time and flux, which allows the construction of well-defined\nplanar homojunctions between regions of different NiTe layers on the same NbSe substrate (Fig.\n2 2\nS17).”\nComment 5: Further computational details are also unclear, such as how the mismatch between\nthe two materials was treated in the simulations. The authors also state that “The vacuum layer\nis larger than 10 Angstrom”. They should provide a more detailed value. Furthermore, in the\nsimulation shown in Fig. 3, it is unclear how many layers of NbSe2 were included in the simulation.\nFrom the SM, it appears that this was just one. Is this sufficient to simulate a bulk substrate as\npresent in the experiment.\nResponse: We have added the relevant computational details to the revised manuscript. The fully\nrelaxed lattice constants of monolayer NiTe and NbSe are 3.715 Å and 3.459 Å, respectively,\n2 2\ncorresponding to a lattice mismatch of approximately 6.9% between the two materials in a 1 × 1\nunit cell configuration. We thus constructed a heterostructure composed of a 10 × 10 monolayer\nNiTe on an 11 × 11 monolayer NbSe , which reduces the mismatch to ~2.4%. The resulting moiré\n2 2\nlattice constant of this heterostructure is 3.81 nm, in good agreement with the experimentally\nobserved value of 3.78 nm. For the bilayer case, the fully relaxed lattice constant is 3.814 Å.\nAccordingly, we built a supercell comprising a 9 × 9 bilayer NiTe on a 10 × 10 monolayer NbSe ,\n2 2\nfurther reducing the mismatch to ~0.8%. The corresponding lattice constant of 3.46 nm also agrees\nwell with the experimental moiré periodicity of 3.51 nm.\nA slab model is used for the moiré superstructure. Regarding the vacuum spacing, we used a\nvacuum layer of 15 Å. All atoms except the NbSe substrate are fully relaxed until the net force is\n2\nsmaller than 0.01 eV/Å. As for the simulated structure shown in Fig. 3a, it is based on a supercell\nconsisting of a 10 × 10 monolayer NiTe atop an 11 × 11 monolayer NbSe , containing a total of\n2 2\n663 atoms. As correctly noted by the Reviewer, only one layer of NbSe was included. While\n2\nmultilayer substrates could in principle provide a more accurate representation of the experimental\nsystem, our benchmarking tests indicate that key surface features and electronic modulations are\nalready well captured by using a monolayer NbSe substrate. Furthermore, the simulated STM\n2\nimage from this model shows excellent agreement with the experimental result (Fig. S2),\nsupporting the validity of the approach.\nThe Method Section is revised as follows (page 17, line 11-19): “Wave functions were expanded\non a plane-wave basis set up to 500 eV energy cutoff. The fully relaxed lattice constants of\nmonolayer NiTe , bilayer NiTe and NbSe are 3.715 Å, 3.814 Å and 3.459 Å, respectively. A slab\n2 2 2\nmodel is used for the moiré superlattice. For the monolayer NiTe , the heterostructure is constructed\n2\nusing a 10 × 10 monolayer NiTe on an 11 × 11 monolayer NbSe , resulting in a lattice mismatch\n2 2\nof approximately 2.4%. The corresponding moiré lattice periodicity of this configuration is 3.81\nnm. For the bilayer case, the heterostructure is composed of a 9 × 9 bilayer NiTe on a 10 × 10\n2\nmonolayer NbSe , with a reduced lattice mismatch of approximately 0.8%. The resulting\n2\nperiodicity of the moiré lattice is 3.46 nm. Wave functions were expanded on a plane-wave basis\nset up to 400 eV energy cutoff. Van-der-Waals interactions were considered at the DFT-D3 level.\nThe vacuum layer is 15 Å. A Γ-only k-point sampling in the first Brillouin zone is used for the\nmoiré superlattice. All atoms except the NbSe substrate are fully relaxed until the net force is\n2\nsmaller than 0.01 eV/Å.”\nComment 6: One of the more interesting results of the manuscript is rather quickly glanced over,\nnamely proximity-induced superconductivity in NiTe2, whose results are only presented in the SM,\nwhich is rather a waste.\nResponse: We sincerely thank the Reviewer for highlighting this important point. The proximity-\ninduced superconductivity in NiTe shows correlation with the short-range charge order, which\n2\nindeed reveals intriguing pair density modulation features.\nTo better emphasize this result, we have moved the relevant data and discussion from the\nSupplementary Information to the main text, where it now appears as new Fig. 5 in the revised\nmanuscript.\nNew Fig. 5. Short-range modulation in the superconducting state of NiTe . a, The spatially-\n2\naveraged dI/dV spectra (V = -3 mV, I = 1 nA, V = 0.05 meV) at NbSe substrate, monolayer\ns t mod 2\n(1L), bilayer (2L), and trilayer (3L) NiTe , respectively, showing broadening two coherence peaks\n2\nand increasing in-gap conductance with the layer of NiTe . b, The SC gap size subtracted from\n2 2\nshowing a monotonic decrease with increasing layers, indicating the proximity effect. c, The\nwaterfall and intensity plot of the dI/dV linecut (V = -3 mV, I = 1 nA, V = 0.05 meV) across\ns t mod\nAB regions (dash circles) along the green arrow in the topography, showing strong modulation\nHollow\nof superconducting coherence peak and gap size, indicating a pair density modulation. d,e, STM\ntopography of the monolayer NiTe and corresponding dI/dV map at -0.56 meV (100 pixels × 100\n2\npixels), showing inhomogeneous superconductivity and the enhancement of in-gap states in\nAB regions (yellow dotted circles) (V = -2 mV, I = 1 nA, V = 0.05 meV), suggesting a\nHollow s t mod\nformation of quasi-ordered pair density modulation state.\nIn summary, we believe we have thoroughly addressed all the comments and questions raised by\nthe Reviewer by adding new data and discussions, as well as clarifying revisions, to mitigate\nhis/her concerns. Once again, we sincerely thank the Reviewer’s insightful, constructive and critical\ncomments/questions, which have helped us to further strengthen the manuscript, making it even\nmore suited for publication in Nature Communications.\nResponse to the Reviewer #2\nGuo et al report the synthesis of a moiré structure between NbSe2 and NiTe2 using MBE growth as\nopposed to the usual tear and stack process known in the 2D device community. The advantage of\nsuch synthesis is that the surfaces are clean and amenable to STM studies and local spectroscopy.\nThey see short range charge orders on the length scale of the moiré lattice due to the collective\neffects of moiré induced periodic strain, electron localization and electron correlations. They also\nprove this by tuning the layer thickness of NiTe2. The paper is well written, the STM data is high\nquality, and the results are remarkably interesting, and of general interest to the material synthesis,\ntheoretical and experimental condensed matter physics community. Therefore, I think the\nmanuscript should be published in Nature Communications although I have a few clarifying\nquestions that I believe would improve the analysis, quality, and readability of the paper for the\ngeneral audience.\nResponse: We thank the Reviewer for the positive remarks. We have carefully addressed all the\ncomments raised by the Reviewer.\nComment 1: In the abstract and in paragraph 3, the authors refer to the moire as “TMDs with\nincommensurate lattice wavevectors,”, which needs rephrasing. The TMD lattices by themselves\nare commensurate, but the resulting moire lattice is incommensurate. Also, please specify the moiré\nlattice constant in the manuscript.\nResponse: We have taken the Reviewer’s constructive suggestion and revised the wording in both\nthe abstract and paragraph 3 to clarify that the moiré lattice, rather than the individual TMD lattices,\nis incommensurate. Additionally, the measured in-plane lattice constants of monolayer NiTe and\n2 2 2\napproximately 3.78 nm.\nWe have deleted the phrase of “TMDs with incommensurate lattice wavevectors” and added\n“incommensurate moiré structure” in the abstract. We also provided the experimental lattice\nparameters in the revised manuscript (page 5, line 4-7): “The measured in-plane lattice constants\nof monolayer NiTe and NbSe are approximately 3.69 Å and 3.46 Å, respectively. In the 1L-\n2 2\nNiTe /NbSe heterostructure, the moiré wavelength is measured to be about 3.78 nm. Thus, the\n2 2\nresulting moiré structure is incommensurate.”\nComment 2: In paragraph 2, the authors say, “In contrast, electronic states featuring disorder or\nshort-range order fall beyond the scope of conventional Bloch descriptions, and are of significance\nfor achieving novel quantum phenomena and enabling potential applications in functional devices”,\nit would be good to have a few references here to show the novel phenomena and applications are\nthe authors referring to.\nResponse: We sincerely thank the Reviewer’s suggestion and have added several references to\nshow the novel phenomena of disordered charge modulations.\n“In contrast, electronic states featuring disorder or short-range order fall beyond the scope of\nconventional Bloch descriptions, and are of significance for achieving novel quantum phenomena\nand enabling potential applications in functional devices28-30.”\n28. Milinda Abeykoon, A. M. et al. Evidence for short-range-ordered charge stripes far above\nthe charge-ordering transition in La Sr NiO . Phys. Rev. Lett. 111, 096404 (2013).\n1.67 0.33 4\n29. Choi, J. et al. Universal stripe symmetry of short-range charge density waves in cuprate\nsuperconductors. Adv. Mater. 36, 2307515 (2024).\n30. Perring, T. G. et al. Antiferromagnetic short range order in a two-dimensional manganite\nexhibiting giant magnetoresistance. Phys. Rev. Lett. 78, 3197 (1997).\nComment 3: To show the existence of a phonon softening the authors use DFT simulations with a\n10% strain. However, strain analysis from experimental data indicates 3% strain. Is there a phonon\nsoftening at this value of strain? The authors should include a statement on their reasoning behind\nchoosing this value of strain for their DFT analysis.\nResponse: The in-plane strain distribution was estimated from DFT structural relaxations,\nrevealing approximately 3% compressive strain in the AB regions and 3% tensile strain in the\nHollow\nAA regions. To assess whether phonon softening occurs under such strain conditions, we calculated\nthe phonon dispersion of monolayer NiTe under ±3% strain, and added the results as new Fig. S16.\nand the absence of phonon softening at this strain level.\nThe phonon softening shown in our main DFT simulation was obtained by applying a 10%\ncompressive strain to the freestanding monolayer NiTe . This choice does not consider the substrate\n2\neffects and moiré modulations. The goal of this calculation was not to replicate the experimental\nconditions, but rather to demonstrate that strong compressive strain can, in principle, induce Fermi\nsurface nesting and associated instabilities. Therefore, the 10% strain serves as a theoretical probe\nto explore the possible mechanism, rather than a direct model of the experimental system.\nNew Fig. S16. DFT calculated phonon dispersion for the monolayer NiTe under (a) 3%\n2\ncompressive and (b) 3% tensile strain. There is no imaginary frequency in the phonon dispersion\ncurves, indicating that the monolayer NiTe is dynamically stable under 3% compressive and 3%\n2\ntensile strain.\nWe have added a new figure as Fig. S16 in the revised Supplementary Information and included\ncorresponding discussions in the revised manuscript (page 8, line 12-14): “Although the system\nstill remains dynamically stable under 3% strain (Fig. S16), larger compressive strain can, in\nprinciple, induce electronic instabilities in monolayer NiTe . The band structure upon applying a\n2\n10% compressive strain (Fig. 3b) shows that the energy band around the K point anchored by the\nDirac point is pulled closer to the Fermi level, leading to the formation of a small hole pocket\nlocated at K point precisely, and thereby enhancing its density of states.”\nComment 4: Do the authors know if the charge order has a preference to localize on the\nNb/Se/Ni/Te sites? It will be good to show an overlay of the ABhollow schematic and an atomically\nresolved ABhollow site topography with the charge order.\nResponse: Yes. we roughly know the preferential localization of charge order on the Nb/Se/Ni/Te\nsite based on the atomically resolved topographic image. We have taken the Reviewer’s suggestion\nand added an overlayer of AB schematic on atomically resolved AB site topography with\nHollow Hollow\nthe charge order, which indicates that the charge order has a rough preference to localized on the\nTe site (new Fig. S6).\nNew Fig. S6. Atomically-resolved STM image of the monolayer NiTe with the structural model\n2\nof the AB region overlaid, showing that the charge orders have a rough preference to localize\nHollow\non Te sites (black circles).\nAccording to Reviewer’s suggestion, we have added a new figure as Fig. S6 in the revised\nSupplementary Information and included corresponding description in the revised manuscript:\n“High-resolution STM images (Fig. 2a and S5) reveal that the short-range charge orders emerge at\neach AB regions of the moiré superstructure, with spontaneous on-site ordering across the\nHollow\nmoiré scale. The charge orders have a rough preference to localize on Te sites (Fig. S6).”\nComment 5: Can the authors comment on the relationship between the disordered CDW to the 3Q\nCDW of NbSe2? Since the disordered CDW prefers to have a C3 symmetry, it seems plausible. Are\nthe disordered CDW and the underlying 3Q order of NbSe2 related based on symmetry and\nperiodicity arguments?\nResponse: We thank the Reviewer for this insightful question. While the disordered CDW observed\nin NiTe exhibits certain local symmetries, we believe it is not directly related to the 3Q-CDW of\n2\nthe underlying NbSe substrate, for the following reasons:\n2\n(i) Order and coherence: The 3Q-CDW in NbSe is a long-range, globally coherent charge order,\n2\nwhereas the CDW in NiTe is short-range and quasiperiodic, appearing only locally within the\nHollow\n(ii) Orientation: The wavevector of the CDW in NiTe is rotated by approximately 30° with respect\n2\nto the NiTe lattice, while the 3Q-CDW in NbSe is aligned along its own high-symmetry directions.\n2 2\nThis angular mismatch suggests that the two CDWs are not directly coupled by symmetry.\n(iii) Energy scale: The CDW in NbSe emerges below its transition temperature of ~33 K, whereas\n2\nthe disordered CDW in NiTe persists above room temperature (new Fig. S11), further indicating\n2\nthat the two phenomena are independent.\nTherefore, while both CDWs exhibit C -like local symmetry, their distinct origin, periodicity,\n3\norientation, and energy scales suggest they are not directly related.\nNew Fig. S11. STM characterization of monolayer NiTe /NbSe at room temperature. a,\n2 2\nAtomically-resolved STM image of the monolayer NiTe , showing the short-range charge order\n2\npersist at room temperature. b, The corresponding FFT pattern, showing the peaks from Bragg\nlattice (red circles), moiré superstructure (green circles), and the short-range irregular orders (blue\ncircles).\nTo clarify this issue, we have added a new figure as Fig. S11 in the revised Supplementary\nInformation and corresponding discussions in the revised manuscript (page 6, line 26-31): “We also\nnote that NbSe hosts a 3×3 CDW below ~33 K. Although the short-range-ordered charge\n2\nmodulations in NiTe exhibit local C symmetry, they are distinct from the long-range 3×3 CDW\n2 3\nof the underlying NbSe substrate in terms of coherence length, orientation, and energy scale.\n2\npersists above room temperature (Fig. S11). These differences suggest only weak or negligible\ncoupling between the two charge modulations.”\nIn summary, we believe we have thoroughly addressed all the comments and questions raised by\nthe Reviewer by adding new data and discussions, as well as clarifying revisions, to mitigate\nhis/her concerns. Once again, we sincerely thank the Reviewer for his/her insightful, constructive\nand critical comments/questions, which have helped us to further strengthen the manuscript,\nmaking it even more suited for publication in Nature Communications.\nResponse to the Reviewer #3\nGuo et al. present the growth of atomically thin NiTe2 on NbSe2 and its atomic-scale\ncharacterization by STM/STS and LEED. STM/STS reveal atomic-scale localized states which\nappear in quasi-ordered clusters within periodic regions defined by the Moiré pattern. Further,\nDFT modelling demonstrates that strain of 10% can enhance the susceptibility towards a charge-\nordered state; supporting the claim that the observed localized states are correlation-induced\nmany-body states. Additionally, the states are demonstrated to disappear with additional layers of\nNiTe2. As understanding the role of heterostrain and Moiré-potential on the formation of electronic\nordering holds high significance to the advancement of the field, this work has great potential\nimpact.\nThe demonstrated MBE growth and the STM/STS data are of very high quality and the information\nin the manuscript is presented clearly. However, elements of the data analysis, interpretation,\nand conclusions of the work lack sufficient validity and robustness for publication in Nature\nCommunications. It is my recommendation to consider this work after the following major revisions\nare made.\nResponse: We thank the Reviewer for the positive remarks on this work. We also appreciate the\nReviewer’s suggestive comments which have significantly improve the quality of this work. We\nhave adopted the Reviewer’s constructive suggestions and provide experimental details requested\nby the Reviewer as follows.\nBelow are detailed descriptions of flaws found in the manuscript with specific questions aimed to\naddress them\nComment 1: Introduction lacks consideration of previous work. The authors do not reference any\nprevious reports of NiTe2 MBE growth or STM characterization. a. The authors should add\nappropriate references and place their work within the current state of the field. Has NiTe2 been\ngrown on NbSe2 before? What characterization has been done on monolayer NiTe2 previously?\nHave there been previous investigations of correlated phases in NiTe2, experimental or theoretical?\netc.\nResponse: We thank the Reviewer for this important suggestion. In the revised manuscript, we\nhave added relevant references to place our work within the current state of the field. For bulk\nNiTe , previous studies have reported its Dirac-type band structure and topological surface state\n2\nbased on STM and angle-resolved photoemission spectroscopy characterizations [For example:\nMukherjee, S. et al., Sci. Rep. 10, 12957 (2020); Wang, W. et al., Phys. Scr. 98, 015020 (2023);\nGhosh, B. et al., Phys. Rev. B 100, 195134 (2019); Huang, Z. et al., Nano Lett. 23, 3274 (2023)].\nFor ultrathin films, recent MBE studies have primarily focused on the evolution of band structure\nas layer numbers (1–5 layers) [Hlevyack, J. A. et al., npj 2D Mater. Appl. 5, 40 (2021)], as well as\non structural reconstructions induced by self-intercalation [For example: Ren, M. et al., Phys. Rev.\nB 108, 235408 (2023); Pan, S. et al., ACS Nano 16, 11444 (2022)]. In addition, superconductivity\nhas been theoretically predicted in monolayer NiTe using ab initio methods [Zheng, F. et al., Phys.\nin NiTe to date.\nNiTe on NbSe substrates, nor on studies of correlated electronic phases in this system. Our work\n2 2\ntherefore represents the first experimental realization and atomic-scale characterization of such a\nheterostructure, unveiling an emergent short-range charge ordering in the monolayer NiTe .\nprogresses on NiTe (page 4, line 14-18) “NiTe has recently been identified as a Type-II Dirac\n2 2\nsemimetal hosting Dirac fermions and topological surface states31,32. It exhibits pronounced\nthickness-dependent electronic tunability33 and has been theoretically predicted to exhibit\nsuperconducting instability in the single-layer limit34. Despite these intriguing properties, no charge\ndensity wave (CDW) transition has been experimentally observed in the NiTe system to date.”\n2\n31. Huang, Z. et al. Tuning multiple Landau quantization in transition-metal dichalcogenide\nwith strain. Nano Lett. 23, 3274-3281 (2023).\n32. Mukherjee, S. et al. Fermi-crossing Type-II Dirac fermions and topological surface states\nin NiTe . Sci. Rep. 10, 12957 (2020).\n2\n33. Hlevyack, J. A. et al. Dimensional crossover and band topology evolution in ultrathin\nsemimetallic NiTe films. npj 2D Mater. Appl. 5, 40 (2021).\n2\n34. Zheng, F. et al. Emergent superconductivity in two-dimensional NiTe crystals. Phys. Rev.\nComment 2: The validity of statistical analysis cannot be determined. Information about the\nmeasurement and analysis statistics are lacking from the manuscript.\na. The sample statistics should be given. How many samples were measured and with how many\ntips?\nResponse: We have measured four NiTe /NbSe samples using eight different STM tips. For each\n2 2\nsample, multiple monolayer NiTe regions were randomly probed. The short-range-ordered charge\n2\nmodulation reported is robust and reproducible across different samples and tips, demonstrating the\nreliability and statistical significance of our observations. We have now summarized the results for\nthe four different samples in the new Fig. S7.\nNew Fig. S7. STM images for four different NiTe /NbSe samples using eight different tips,\n2 2\nshowing that the short-range-ordered charge modulation is robust and reproducible across different\nsamples and STM tips. The sample #2 and sample #4 are measured at 77 K, which show thermal\ndrift in the STM image.\nTo clarify this issue, we have added a new figure as the Fig. S7 in the revised Supplementary\nInformation, and added the corresponding discussion in the revised manuscript (page 5, line 19-\n22): “In addition, the short-range charge orders are consistently observed across four NiTe /NbSe\n2 2\nsamples using eight different STM tips, demonstrating their robustness and reproducibility (Fig.\nS7).”\nb. Fig 2a shows many bright spots within and around the ABHollow regions but the spectral maps\n2e,f only show at most 3. What are the differences between these two samples?\nResponse: The differences in the number of bright spots observed in Fig. 2a compared to spectral\nmaps in Figs. 2e and 2f arise from region-dependence across the sample. The density and\ndistribution of bright spots vary between AB regions, with some areas exhibiting only a few\nHollow\nbright spots while others display many. This region-dependent variation reflects the intrinsic local\ninhomogeneity of the short-range charge order.\nTo avoid confusion, we have added the discussion on the region-dependence of bright spots (page\n5, line 22-24): “The variation in the number of charge orders within each AB region arises\nHollow\nfrom region-dependence across the sample, reflecting their intrinsic local inhomogeneity and short-\nrange nature.”\nc. Figs. 2e,f show features reminiscent of inelastic tunneling through an adsorbate within the\ntunnelling junction. The authors should provide the corresponding topography measurement\nas well as point tunnelling spectra on and off the localized states in both measurements.\nAdditionally, it would be helpful to know the spatial resolution of the dI/dV maps presented in\nthe main text and SI.\nResponse: We have shown the corresponding topography of the Figs. 2e,f and point tunneling\nspectra on and off the localized states, it excludes the step-shaped inelastic tunneling case.\nWe agree with the Review that it should be helpful to know the spatial resolution of the dI/dV map\nin the main text and SI. In previous version, the maps are automatically smoothed by the software\nby accident. In the revised, we have shown the original dI/dV maps with the exact spatial resolution\nin Fig. 2e, 2f, 4e, 4f, 5e in the main text and Fig. S4, S8, S9, S18, S20 in the SI.\nAccording to the Reviewer’s suggestion, we have added a new figure as Fig. S8 in the revised\nSupplementary Information.\nNew Fig. S8. Electronic properties of the localized states within AB regions. a, Topography\nHollow\nof monolayer NiTe showing localized states (solid circles), i.e., short-range charge orders, within\nHollow\nblue dots in (a). c,d, The dI/dV maps (I = 1.0 nA, V =5 mV) at +100 meV (c) and -100 meV (d),\nt mod\nrespectively, showing an inversion in intensity contrast. Each map consists of 50 pixels × 50 pixels.\ne, The dI/dV linecut along the arrow in (c).\nd. Ordering analysis is not described in the Methods section or in the main text. Authors need to\ndescribe how the charge centers are selected and how orientation and displacement correlation\nfunctions are analyzed. While Figures 2a and S5 do show that localized states and C3\nsymmetric orbitals are most intense in the ABHollow regions, they are also present in several\nregions across the Moiré landscape at a lower apparent height. Are these spots included in the\nreported statistics?\nResponse: The localized states are predominantly located within the AB regions, although a\nHollow\nsmall number also appear in adjacent areas with lower apparent height. All such bright local states\nhave been included in our statistical analysis. We performed statistical analyses over dozens of\nmonolayer NiTe regions to ensure the rationality. During the statistical procedures, each localized\n2\nbright state is identified as a center, from which we extract spatial information including the\ndistance to its nearest neighbors and the relative orientation between adjacent C -symmetric\n3\npatterns.\nThe ordering analysis, including criteria for selecting charge centers and procedures for measuring\norientations and periodicities, has now been described in detail in the revised main text (page 5,\nline 27-30). “We further analyze the spatial ordering of the charge states across multiple monolayer\nNiTe samples. Each bright state is marked as a center, from which we measure the spatial distance\n2\nto its nearest neighbors and extract the angular deviation between the C symmetry axes of adjacent\n3\nstates (inset in Fig. 2c,d).”\ne. The amplitude and phase maps (Figures 2g and 2h) both show long wavelength features and\nlittle-to-no correlation on the Moiré length scale. Authors should describe their procedure for\nselecting the wavevector Q as well as what length scale, σ, was chosen for the Fourier filtering\nprocedure. Is the linear phase background indicative of linear strain or fitting error?\nResponse: We have taken the Reviewer’s suggestion and described the procedure for selecting\nwavevector Q as well as what length scale was chosen for the Fourier filtering procedure. We have\nalso carefully checked our procedure and found that the linear phase background is the results of\nalgorithm, as we explained below.\nSince the phase calculated by the algorithm may have a 2π jump at certain pixels, it is necessary to\nperform unwrap function on the obtained results. Consider the modulation of the wave vector q =\n𝐴(𝐫) ∼ 𝑒−𝑖𝐪0⋅𝐫\nWhen we select the wave vector Q to perform 2D-lockin, the signal after low-pass filtering can be\napproximated as:\n𝐴(𝐫) ∼ 𝑒−𝑖(𝐪0−Q)⋅𝐫= 𝑒−𝑖𝛥𝐪⋅𝐫\nThe phase can be written as:\n𝛷 (𝑟) = 𝛥𝐪 ⋅𝐫+ 𝛷 (𝑟)\n𝑄 𝑙𝑜𝑐𝑎𝑙\nIf q = Q, then only the local phase information 𝛷 (𝑟) = 𝛷 (𝑟) remains. However, if q ≠ Q，\n0 𝑄 𝑙𝑜𝑐𝑎𝑙 0\nIn the phase, there will be an additional linear term 𝛥𝐪 ⋅𝐫. Here, our short-range order is associated\nwith a set of broad spots in blue circles (Fig. 2b), so the occurrence of a reference phase mismatch\nis reasonable. The linear background corresponds to a very strong and low-frequency phase\ngradient, which will not be eliminated by Gaussian filtering. Unwrapping restores the high-\nfrequency components that are weakened by Gaussian filtering, thus making the linear background\nmore prominent after unwrapping.\nTo avoid confusion, we use the least squares method to subtract these linear backgrounds, thereby\nmaking the obtained phase information more closely resemble the actual phase information in the\nrevised manuscript as follows.\nAccordingly, we have added the detailed procedure for selecting wavevector Q and the\ncorresponding length scale in the Method part. We have also revised the phase results by subtracting\nthe linear background and shown the details in the Method part.\nRevised Fig. 2g,h Spatial distribution of the amplitude (g) and phase (h) corresponding to the\nshort-range charge orders, showing that charge orders mainly occur within the AB regions\nHollow\n(white circles) with variation of the phases.\nRevised Method part (page 15, line 11-23; page 16, line 1-4):\n“Since the phase calculated by the algorithm may have a 2π jump at certain pixels, it is necessary\nto perform unwrap function on the obtained amplitude and phase information. Consider the\nmodulation of the wave vector q = Q√3×√3, the real space image can be written as:\n0\n𝐴(r) ∼ 𝑒−𝑖q0⋅r\nWhen we select the wave vector Q to perform 2D-lockin, the signal after low-pass filtering can be\napproximated as:\n𝐴(r) ∼ 𝑒−𝑖(q0−Q)⋅r= 𝑒−𝑖𝛥q⋅r\nThe phase can be written as:\n𝛷 (𝑟) = 𝛥q ⋅r+ 𝛷 (𝑟)\n𝑄 𝑙𝑜𝑐𝑎𝑙\nIf q = Q, then only the local phase information 𝛷 (𝑟) = 𝛷 (𝑟) remains. However, if q ≠ Q，\n0 𝑄 𝑙𝑜𝑐𝑎𝑙 0\nIn the phase, there will be an additional linear term 𝛥q ⋅r. Here, our short-range order is associated\nwith a set of broad spots in blue circles (Fig. 2b), so the occurrence of a reference phase mismatch\nis reasonable. The linear background corresponds to a very strong and low-frequency phase\ngradient, which will not be eliminated by Gaussian filtering. Unwrapping restores the high-\nfrequency components that are weakened by Gaussian filtering, thus making the linear background\nmore prominent after unwrapping. To avoid confusion, we use the least squares method to subtract\nthese linear backgrounds, thereby making the obtained phase information more closely resemble\nthe actual phase information in Fig. 2h. To obtain the amplitude and phase information in Fig. 2h,\nthe selecting wavevector Q is at (√3×√3)𝑅30° position marked in Fig. 2b. The Gaussian filter order\nis 16 and the filter length scale is 28 pixels × 28 pixels (1.9 nm × 1.9 nm).”\nComment 3: Stronger experimental and theoretical evidence of an electronic correlation-induced\nmany-body state needs to be provided and consideration of alternative descriptions should be given.\na. Contrast inversion is used to demonstrate that there is a localized state near the Fermi level,\nhowever, the energy of the localized state(s) is not identified in this work. This is essential to\ndetermine the correlation energy as a function of space within the Moiré potential. Also,\ncontrast inversion is shown at several different energies in figure S6 which warrants further\nexplanation.\nResponse: We have taken the Reviewer’s suggestion and identified the energy of localized state\nby showing a dI/dV linecut across these localized states. To clarify this issue, we add a new figure\nas Fig. S8 in the revised Supplementary Information.\nNew Fig. S8. Electronic properties of the localized states within AB regions. a, Topography\nHollow\nof monolayer NiTe showing localized states (solid circles), i.e., short-range charge orders, within\nHollow\nblue dots in (a). c,d, The dI/dV maps (I = 1.0 nA, V =5 mV) at +100 meV (c) and -100 meV (d),\nt mod\nrespectively, showing an inversion in intensity contrast. Each map consists of 50 pixels × 50 pixels.\ne, The dI/dV linecut along the arrow in (c).\nRevised main text (page 6, line 8):\n“We further analyze the short-range charge order state inside the moiré unit cells. At the same\nspatial locations, the density of states (DOS) shows contrast inversion on opposite sides of E (+100\nF\nmeV and -100 meV) (Fig. 2e,f and Fig. S8, S9),…”\nb. The relaxed DFT model expects strain variations of up to nearly 6% in this heterostructure and\npossible nesting conditions achievable at 10% compressive strain. These values of strain are\nmeasurable by atomically resolved STM. The authors should attempt to measure the\nexperimental strain value as well as estimate the Moiré potential variation to more carefully to\nsupport their claim.\nResponse: We have taken the Reviewer’s suggestion and used a computational framework for\natomic displacement analysis along both crystallographic axes to roughly quantify strain\ncharacteristics in experiments. The strain field distributions are represented by the displacement\nvector fields u (r) (Fig. S14c) and u (r) (Fig. S14d), which are derived through an optimized\nxx yy\nLawler-Fujita drift correction algorithm [Nature 466, 347 (2010)] based on the topographic image\n(Fig. S14a). The symmetric strain map S(r), as defined by S(r) = (U (r)+ U (r))/2 at the location r\nxx yy\n(Fig. S14b), show the compressive strain in the AB regions, which is comparable to the DFT\nHollow\nmodel.\nNew Fig. S14. Distribution of the strain field in the moiré pattern. a, Topographic image of\nmonolayer NiTe grown on NbSe substrate, showing moiré pattern with three regions, AB\n2 2 Hollow\nregion with short-range charge orders, AB and AA regions. b, Symmetric strain map S(r) =\nSe\n(U (r)+ U (r))/2 represents the symmetric strain at the location r. The color bar in (b) represents\nxx yy\nthe calculated value of strain. c,d, The U and U strain maps of the STM image in (a) obtained\nxx yy\nby the atomic displacement analysis.\nThe possible nesting conditions achievable at 10% compressive strain is larger than the estimated\nvalue from experiment. The phonon softening shown in our main DFT simulation was obtained by\napplying a 10% compressive strain to the freestanding monolayer NiTe . This choice does not\n2\nconsider the substrate effects and moiré modulations. The goal of this calculation was not to\nreplicate the experimental conditions, but rather to demonstrate that strong compressive strain can,\nin principle, induce Fermi surface nesting and associated instabilities. Therefore, the 10% strain\nserves as a theoretical probe to explore the possible mechanism, rather than a direct model of the\nexperimental system.\nAccordingly, we revised manuscript to discuss the estimated strains (page 8, line 5-14):\n“However, in the moiré structure of NiTe /NbSe , the monolayer NiTe within AB regions are\n2 2 2 Hollow\npredicted to experience significant compressive strain (about 3%, Fig. 3a). The strain field\ndistribution in atomically-resolved STM image by using a computational framework of the atomic\ndisplacement analysis along both crystallographic axes (Method) estimate that about 3%\ncompressive strains exist within AB regions (Fig. S14). In addition, the calculated charge\nHollow\ndistribution shows a strong localization of the electron density within AB regions (Fig. S15).\nHollow\nWhile the calculation results based on a simplified model of a uniformly strained NiTe monolayer\n2\ncannot fully describe the emergent electronic states associated with short-range ordering (Fig. 2a),\nthey nevertheless provide valuable insight into the possible driving forces that enhance electronic\ncorrelations. Although the system still remains dynamically stable under 3% strain (Fig. S16),\nlarger compressive strain can, in principle, induce electronic instabilities in monolayer NiTe .\nThe\n2\nband structure upon applying a 10% compressive strain (Fig. 3b) shows that the energy band around\nthe K point anchored by the Dirac point is pulled closer to the Fermi level, leading to the formation\nof a small hole pocket located at K point precisely, and thereby enhancing its density of states.”\nRevised Method (page 16, line 6-22):\n“Two-dimensional lock-in technique and strain analysis.\n…\nBased on 2D lock-in technique, the strain filed can be extracted with Lawler-Fujita algorithm49. For\na hexagonal lattice NiTe , considering the total displacement field 𝑢(𝐫), the real space image can\n2\nbe written as:\n𝐴(𝐫) = 𝑎 𝑒𝑖𝐐1⋅(r−𝑢(𝐫))+𝐴 𝑒𝑖𝐐2⋅(𝐫−𝑢(𝐫))+𝐴 𝑒𝑖𝐐3⋅(𝐫−𝑢(𝐫))+c. c\n1 2 3\nwhere Q and Q are the reciprocal lattice basis and Q = Q +Q . The fourth term c.c. represent\n1 2 3 1 2\npossible displacement due to picometer scale piezoelectric drift and thermal drift. 𝑢(𝐫) is defined\nas displacement filed. By applying local Gaussian filtering in the momentum space near the Bragg\nwave vector (20 × 20 pixels window), high-frequency oscillations can be filtered out. We can get\nthe two displacement field components 𝑢 (𝐫) and 𝑢 (𝐫):\n1 2\n𝑢 (𝐫) = 𝑄 ⋅𝑢(𝐫) = −arg(𝑎 𝑒𝑖𝐸𝑖⋅𝑢(𝒓)) (𝑖 = 1,2)\n𝑖 𝑖 𝑖\nThe components along the lattice 𝑢 (𝐫) and 𝑢 (𝐫) can be decomposed into x and y axes 𝑢 (𝐫)\n1 2 𝑥\nand 𝑢 (𝐫).Total strain field 𝑢(𝐫) consists of strain field 𝑠(𝐫) and drift field 𝑢(𝐫). Drift field 𝑑(𝐫)\n𝑦\ntypically includes piezo drift and thermal drift, and it can generally be fitted using a 3-order\npolynomial. By fitting with the STM images, 𝑑(𝐫) can be obtained, and thus the strain field can be\ndetermined as:\n𝑠(𝐫) = 𝑢(𝐫)−𝑑(𝐫)\nNext, as described in the article (Fig. S14), the strain tensor can be expressed as:\n𝜕𝑠 (𝑟)\n𝑖𝑖\n𝑠 ≡ (𝑖 = 𝑥,𝑦)\n𝑖𝑖 𝜕𝑖\n.”\n49. Lawler, M. J. et al. Intra-unit-cell electronic nematicity of the high-T copper-oxide\nc\npseudogap states. Nature 466, 347-351 (2010).\nc. Is the C3v symmetric model (Figure 3g) with larger unit cell unstable towards a real structural\ndistortion? Or is this assumed? Was the on-site potential changed to induce the electron\ncorrelation? If so, what site in the lattice was chosen and what is the value of on-site potential\nassumed?\nResponse: The structural model with C symmetry (Fig. 3g) indeed undergoes a real, albeit slight,\n3v\nstructural distortion after relaxation. We also calculated the phonon dispersion for such a distorted\nstructure. As shown in Fig. R3b, the phonon dispersion shows no phonon softening, indicating that\nthe distorted C symmetric monolayer NiTe is dynamically stable.\n3v 2\nFig. R3. a, Atomic structure of monolayer √3×√3 phase NiTe , showing the C symmetry. b, DFT\n2 3v\ncalculated phonon dispersion of monolayer √3×√3 phase NiTe .\napproach. Specifically, we examined the impact of varying the on-site Coulomb interaction (U =\neff\n2 and 4 eV) on the electronic band structures. As shown in the new Fig. S13, the overall band\nstructures remain largely unchanged compared to the case without U. The primary difference is a\nslight enlargement of the Fermi pockets near the K points with increasing U . From the projected\neff\ndensity of states (PDOS), we find that the electronic states near the Fermi level are primarily\nderived from the Te p orbitals and the Ni d orbitals.\nNew Fig. S13. Calculated band structures and PDOS of monolayer NiTe by using PBE+U method,\n2\nwhere (a) U = 0 eV, (b) U = 2 eV, and (c) U = 4 eV.\neff eff eff\nWe have added a new figure as Fig. S13 in the revised Supplementary Information and included\ncorresponding discussion in the revised manuscript (page 8, line 2-3): “The on-site Coulomb\ninteractions also show slight impact on the electronic band structure of the monolayer NiTe (Fig.\nThe DFT+U approach is also added in the Method section as follows (page 17, line 22-26):\n“Moreover, PBE+𝑈 calculations were also used to study the effects of on-site Coulomb interaction\non the Ni 3𝑑-orbitals. Here, we used the method proposed by Dudarev et al. where only the effective\nCoulomb interaction 𝑈 defined by the difference between the correlation energy and the exchange\neff\nenergy was meaningful53. A Hubbard U correction of 𝑈 = 2 eV and 4 eV were applied to Ni 3𝑑-\neff\norbitals.”\n53. Dudarev, S. L. et al. Electron-energy-loss spectra and the structural stability of nickel oxide:\nAn LSDA+U study. Phys. Rev. B 57,1505 (1988).\nd. Further, more likely explanations (i.e. growth-related atomic-scale defects) have not been\nsufficiently ruled out. Note that many atomic defects, including low formation energy Ni\ninterstitials and chalcogen substitutions, also show C3 symmetric orbitals with approximately\n√3 a extent as shown in a previous STM measurement of NiTe2, for example (Wen-Xiao Wang\net al 2023 Phys. Scr. 98 015020); which was not referenced by this work.\nResponse: We appreciate the Reviewer’s insightful suggestion. We have carefully considered the\npossible influence of atomic-scale defects such as Ni interstitials and chalcogen substitutions. As\nreported in previous work [Wang, W. X. et al., Phys. Scr. 98, 015020 (2023)], small number of\natomic defects typically exhibit a random spatial distribution in NiTe . In contrast, the bright states\n2\nobserved in our STM measurements are consistently localized within the AB regions,\nHollow\ndisplaying a quasiperiodic rather than random pattern. Moreover, if the Ni interstitial defect induces\nstructural reconstructions in NiTe thin films, it will exhibit long-range and perfect structural\n2\nperiodicity, such as the √3×√3 or 2×1 superstructures [Pan, S. et al., ACS Nano 16, 11444 (2022);\nRen, M. et al., Phys. Rev. B 108, 235408 (2023)], differing from the quasiperiodic modulations we\nobserve. Importantly, the observed localized states appear exclusively in monolayer NiTe and are\n2\nabsent in thicker layers. Since atomic defects generally do not exhibit layer-dependent formation,\nthis strongly argues against defects as the origin of the observed localized states.\nDuring growth, we keep Te-rich conditions, with the Te flux at least 20 times higher than that of\nNi, which can suppress self-intercalation and ensure the absence of Ni interstitials [Pan, S. et al.,\nACS Nano 16, 11444 (2022)]. We also compared the monolayer sample grown with different Ni\nfluxes, while keeping the Te flux constant. We found that the average density of short-range charge\norder remains nearly unchanged at ~0.45 nm-2 in both samples (new Fig. S10), indicating that the\nlocalized state does not originate from Ni intercalation at the interface.\nNew Fig. S10. STM images of monolayer NiTe /NbSe grown with Ni fluxes of 0.3 nA (a) and 0.9\n2 2\nnA (b), while keeping the Te flux constant. The average density of short-range charge order remains\nnearly unchanged at ~0.45 nm-2 in both samples, indicating that the charge order does not originate\nfrom Ni intercalation at the interface.\nTo clarify this issue, we have added a new figure as the Fig. S10 in the revised Supplementary\nInformation, and included a detailed discussion in the revised main text to rule out the possibility\nthat the localized states observed at the AB regions originate from atomic-scale defects (page\nHollow\n6, line 14-24). In addition, we have cited relevant references suggested by the Reviewer. “We next\nexamine the possible origins of the observed short-range charge orders. Known defect\nconfigurations in NiTe , such as Ni interstitials and chalcogen substitutions, can exhibit C -\n2 3\nsymmetric orbital features, but they are generally random in distribution and lack layer\ndependence37,38, or instead form long-range periodic structural reconstructions39. In contrast, the\nlocalized states observed here are consistently confined within the AB regions, forming a\nHollow\nquasiperiodic pattern across extended areas. They are exclusive to monolayer NiTe and disappear\n2\nin thicker layers (as discussed below), in contrast to defect-induced features that typically persist\nregardless of film thickness. Moreover, we keep Te-rich atmosphere during the growth, and the\naverage density of the short-range charge order remains nearly unchanged with increasing Ni:Te\nflux ratio (Fig. S10), further ruling out Ni interstitials at the interface39. These characteristics\nstrongly suggest that the short-range charge modulation does not arise from atomic-scale defects,\nbut rather reflects an alternative, electronically driven mechanism.”\n37. Wang, W. et al. Visualizing the atomic defects by scanning tunneling microscopy in the\ntype-II Dirac semimetal NiTe . Phys. Scr. 98, 015020 (2023).\n2\n38. Ren, M. et al. Epitaxial growth and atomic-scale study of type-II Dirac semimetal 1T-NiTe\n2\nfilm. Phys. Rev. B 108, 235408 (2023).\n39. Pan, S. et al. On-site synthesis and characterizations of atomically-thin nickel tellurides\nwith versatile stoichiometric phases through self-intercalation. ACS Nano 16, 11444 (2022).\ne. The loss of localized states with thicker NiTe2 layers could also be consistent with interstitial\ndefects or Te-Se substitutions at the growth interface. However, no reasoning is given for why\nthe localized states disappear with increasing layer thickness. Is this observation consistent\nwith the conclusion of strain-induced correlations?\nResponse: Yes, the disappearance of the localized states in thick layers is consistent with the\nconclusion of strain-induced correlations. Under our growth conditions, the NbSe substrate\n2\nremains stable, as confirmed by the well-preserved topography, superconductivity and CDW\nsignatures in the bare NbSe regions, with no evidence of Se-Te substitutions. Furthermore, if Se-\nexpected to be random rather than systematically localized at the AB regions.\nHollow\nBased on our DFT analysis, the localized states observed in monolayer NiTe likely originate from\n2\nstrain-induced electronic correlations. For the monolayer NiTe , the heterostructure is constructed\n2\nusing a 10 × 10 monolayer NiTe on an 11 × 11 monolayer NbSe , resulting in a lattice mismatch\n2 2\nof approximately 2.4%. For the bilayer case, the heterostructure is composed of a 9 × 9 bilayer\nNiTe on a 10 × 10 monolayer NbSe , with a reduced lattice mismatch of approximately 0.8%. As\n2 2\nthe NiTe layer thickness increases, the moiré-confined strain diminishes significantly. Therefore,\n2\nthe disappearance of these localized states in thicker layers is consistent with our conclusion that\nstrain-induced correlations underlie the observed short-range charge order.\nTo clarify this issue, we have revised the description in the main text (page 10, line 6-9): “The\ndisappearance of the short-range charge order with increasing NiTe layer is further supported by\nwithin the AB regions, insufficient to induce electron correlations.”\nHollow\nf. Finally, the 2H-NbSe2 substrate is known to undergo an ordering transition to an\nincommensurate charge density wave state below ~33K with a wavelength of nearly 3aNbSe2. The\nauthors do not mention the implications of this charge modulation on the observed disordered\nlocalized charges. Is the CDW phase experimentally identified in this heterostructure? Has the\nCDW phase been accounted for in the DFT heterostructure model?\nResponse: We thank the Reviewer for raising this important point. In our experiments, the pristine\n3a-CDW of NbSe is only observed on the bare substrate regions and not within the NiTe /NbSe\n2 2 2\nheterostructure areas. The disordered localized charge modulations observed in NiTe are thus\n2\nunlikely to be related to 3a-CDW of the NbSe for several reasons:\n2\n(i) The NbSe 3a-CDW exhibits a global, long-range order, whereas the NiTe charge modulations\n2 2\nare short-range, quasiperiodic, and confined to the AB regions of the moiré pattern.\nHollow\n(ii) The NiTe charge modulation wavevector is rotated by approximately 30° relative to its\n2\ncrystalline lattice, while the NbSe 3a-CDW aligns along the principal lattice directions.\n2 2\n(iii) The NbSe 3a-CDW transition temperature (~33 K) is much lower than the temperature range\n2\nat which the NiTe localized states persist above room temperature (new Fig. S11).\n2\npristine, non-CDW state in the DFT calculations.\nNew Fig. S11. STM characterization of monolayer NiTe /NbSe at room temperature. a,\n2 2\nAtomically-resolved STM image of the monolayer NiTe , showing the short-range charge order\n2\npersist at room temperature. b, The corresponding FFT pattern, showing the peaks from Bragg\nlattice (red circles), moiré superstructure (green circles), and the short-range irregular orders (blue\ncircles).\nTo clarify this issue, we have added a new figure as Fig. S11 in the revised Supplementary\nInformation and added discussions in the revised manuscript (page 6, line 26-31): “We also note\nthat NbSe hosts a 3×3 CDW below ~33 K. Although the short-range-ordered charge modulations\n2\nin NiTe exhibit local C symmetry, they are distinct from the long-range 3×3 CDW of the\n2 3\nunderlying NbSe substrate in terms of coherence length, orientation, and energy scale. Specifically,\n2\nthe NiTe charge order is short-range and rotated by ~30° relative to the lattice, and persists above\n2\nroom temperature (Fig. S11). These differences suggest only weak or negligible coupling between\nthe two charge modulations.”\nComment 4: 4. Minor revisions\na. Gaussian formula needs revision\nResponse: We apologize for the typo and have revised the Gaussian formula in the Method part as\nfollows.\n(𝑟−𝐑)2\n𝐴 (𝐫) = 𝐹−1[𝐴 (𝐪)] = ∫d𝐑𝐴(𝐑)e𝑖𝐐⋅𝐑e − 2𝜎2\n𝐐 𝐐\nb. The lattice contrast inverts between the topography measurements of 3L and 4L. Do the authors\nhave an explanation for this contrast inversion?\nResponse: The observed inversion of lattice contrast between the 3L and 4L topographies arises\nprimarily from the difference in sample bias. As shown in Fig. R4, the STM images of 3L-NiTe\n2\nwere acquired under different scanning conditions, and a clear inversion in lattice contrast is\nobserved.\nFig. R4. Atomically-resolved STM images for trilayer NiTe on NbSe under different sample bias,\n2 2\nshowing inversion of lattice contrast at different sample bias.\nWe have added the scanning condition and descriptions in the caption of Fig. 4b,c (page 11, line 3-\n6): “Atomically-resolved STM images of the trilayer (3L) (V = -10 mV, I = 5 nA) and four-layer\ns t\n(4L) NiTe (V = -300 mV, I = 1 nA), respectively, showing that the moiré potential and short-\n2 s t\nrange-ordered state are gradually suppressed with increasing layers. The lattice contrast inversion\nbetween the 3L and 4L topographies arises from the difference in sample bias.”\nc. The title claims “incommensurate moiré structures,” however the Moiré pattern shown is\ncommensurate with both lattices as evidenced by the LEED data.\nResponse: We thank the Reviewer for this valuable comment. The LEED pattern just shows that\nthe lattices of NiTe and NbSe are well aligned. It alone does not provide definitive evidence for\n2 2\ncommensurability. To determine the nature of the moiré structure, we combined high-resolution\nSTM measurements and DFT calculations. The measured in-plane lattice constants of monolayer\nNiTe and NbSe are approximately 3.69 Å and 3.46 Å, respectively. The experimentally observed\n2 2\nmoiré periodicity in the 1L NiTe /NbSe heterostructure is about 3.78 nm, which is close to 11 times\n2 2\nlattice constants of NbSe and 10 times lattice constants of NiTe , but does not match an exact\n2 2\nrational relation to either constituent lattice. This absence of a precise commensurate relation\nsupports our description of the system as an incommensurate moiré structure.\nTo clarify, we have added the lattice constants of NiTe , NbSe and moiré structure (page5, line 4-\n2 2\n7), “The measured in-plane lattice constants of monolayer NiTe and NbSe are approximately\n2 2\n3.69 Å and 3.46 Å, respectively. In the 1L-NiTe /NbSe heterostructure, the moiré wavelength is\n2 2\nmeasured to be about 3.78 nm. Thus, the resulting moiré structure is incommensurate.”\nd. The Moiré pattern is claimed to be “consistent” with the lattice mismatch but no numbers are\ngiven. What are the experimental lattice parameters and Moiré wavelength?\nResponse: We thank the Reviewer for the suggestion. The measured in-plane lattice constants of\nmonolayer NiTe and NbSe are approximately 3.69 Å and 3.46 Å, respectively. In the 1L\n2 2\nNiTe /NbSe heterostructure, the moiré wavelength is measured to be about 3.78 nm. As confirmed\n2 2\nby both LEED and STM, the NiTe lattice is aligned with that of NbSe , and the moiré\n2 2\nsuperstructure arises from the lattice mismatch between the two layers.\nTo clarify this issue, we have provided the experimental lattice parameters in the revised manuscript\n(page 5, line 4-6): “The measured in-plane lattice constants of monolayer NiTe and NbSe are\n2 2\napproximately 3.69 Å and 3.46 Å, respectively. In the 1L-NiTe /NbSe heterostructure, the moiré\n2 2\nwavelength is measured to be about 3.78 nm.”\nIn summary, we believe we have thoroughly addressed all the comments and questions raised by\nthe Reviewer by adding new data and discussions, as well as clarifying revisions, to mitigate\nhis/her concerns. Once again, we sincerely thank the Reviewer for his/her insightful, constructive\nand critical comments/questions, which have helped us to further strengthen the manuscript,\nmaking it even more suited for publication in Nature Communications.\nThe main changes to the manuscript are summarized below:\n We revised the term of “disordered” to “short-range-ordered” in the title, abstract and main\ntext.\n We added the discussions of the main previous reports of NiTe and related references.\n2\n We added the lattice constants of the NiTe and NbSe , and the moiré periodicity of the\n2 2\nsuperstructure.\n We provided Fig. S7 showing the robustness and reproducibility of the short-range charge\norders in different samples.\n We added discussions on the detailed ordering analysis of the short-range charge orders (Fig.\n2c,d).\n We added discussions on the exclusion of the defect origin of the short-range charge orders.\n We added discussions on relationship between the short-range charge orders in NiTe and 3×3\n2\n We updated the dI/dV maps in Fig. 2e and Fig. 2f with higher spatial resolution, and added Fig.\nS8 showing the dI/dV linecut across the charge orders.\n We updated the amplitude and phase analysis in Fig. 2g and Fig. 2h, and added detailed\nanalysis procedures in the Method parts.\n We added the calculated results in Fig. S13 showing the effect of on-site potential on the band\nstructures of the monolayer NiTe .\n2\n We added the calculated results in Fig. S16 showing the phonon dispersion of monolayer NiTe\n2\nunder 3% tensile and compressive strain.\n We added new Fig. 5 and corresponding descriptions discussing the results of the proximity-\nsuperconductivity in NiTe .\n2\n We added strain analysis from experimental results as Fig. S14 and the detailed analysis\nprocedures in the Method part.\n We have shown the original dI/dV maps with the exact spatial resolution in Fig. 2e, 2f, 4e, 4f,\n5e in the main text and Fig. S4, S8, S9, S18, S20 in the SI.\n We updated the DFT calculation methods.\n We added relevant references.\nPoint-by-point responses to the comments from the Reviewers\nResponse to the Reviewer #1\nThe authors have satisfactorily addressed my queries, especially on the relation between the DFT\nresults and STM measurements. Hence, I can now recommend the manuscript for publication in\nNature Communications.\nResponse: We sincerely thank the Reviewer for positive remarks and recommendation.\nResponse to the Reviewer #2\nThe authors have successfully and satisfactorily responded to all my concerns and have taken all\nmy comments into account. I believe the additional analysis and data have made the manuscript\nvery clear and scientifically rigorous. I think the results are interesting and intriguing for the\nscientific community and I recommend it for publication in Nature Communications.\nResponse: We sincerely thank the Reviewer for positive remarks and recommendation.\nResponse to the Reviewer #3\nGuo et al. present the growth of atomically thin NiTe2 on NbSe2 and its atomic-scale\ncharacterization by STM/STS and LEED. STM/STS reveal atomic-scale localized states which\nappear in quasi-ordered clusters within periodic regions defined by the Moiré pattern. Further,\nDFT modelling demonstrates that strain can enhance the susceptibility towards a charge-ordered\nstate; supporting the claim that the observed localized states are correlation-induced many-body\nstates. Additionally, the states are demonstrated to disappear with additional layers of NiTe2.\nThe demonstrated MBE growth and the STM/STS data are of very high quality and the information\nin the manuscript is presented clearly. The data analysis meets the standards of the field and\nthe interpretations are robust and support the conclusions made. Further, the data has been shown\nto be statistically significant and the methods have been given in sufficient detail for reproduction.\nAs understanding the role of heterostrain and Moiré-potential on the formation of electronic\nordering holds high significance to the advancement of the field, this work has great potential\nimpact. It is my recommendation to publish this work, as is, in Nature Communications.\nResponse: We sincerely thank the Reviewer for positive remarks and recommendation."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have satisfactorily addressed my queries, especially on the relation between the DFT results and STM measurements. Hence, I can now recommend the manuscript for publication in Nature Communications.", "reviewer_2": "The authors have successfully and satisfactorily responded to all my concerns and have taken all my comments into account. I believe the additional analysis and data have made the manuscript very clear and scientifically rigorous. I think the results are interesting and intriguing for the scientific community and I recommend it for publication in Nature Communications.", "reviewer_3": "Guo et al. present the growth of atomically thin NiTe2 on NbSe2 and its atomic-scale characterization by STM/STS and LEED. STM/STS reveal atomic-scale localized states which appear in quasi-ordered clusters within periodic regions defined by the Moiré pattern. Further, DFT modelling demonstrates that strain can enhance the susceptibility towards a charge-ordered state; supporting the claim that the observed localized states are correlation-induced many-body states. Additionally, the states are demonstrated to disappear with additional layers of NiTe2.\nThe demonstrated MBE growth and the STM/STS data are of very high quality and the information within the manuscript is presented clearly. The data analysis meets the standards of the field and the interpretations are robust and support the conclusions made. Further, the data has been shown to be statistically significant and the methods have been given in sufficient detail for reproduction.\nAs understanding the role of heterostrain and Moiré-potential on the formation of electronic ordering holds high significance to the advancement of the field, this work has great potential impact. It is my recommendation to publish this work, as is, in Nature Communications."}, "author_response": "Response: We sincerely thank the Reviewer for positive remarks and recommendation."}]

Decision letter