Robust charge-density wave strengthened by electron correlations in monolayer 1T-TaSe2 and 1T-NbSe2

Combination of low-dimensionality and electron correlation is vital for exotic quantum phenomena such as the Mott-insulating phase and high-temperature superconductivity. Transition-metal dichalcogenide (TMD) 1T-TaS2 has evoked great interest owing to its unique nonmagnetic Mott-insulator nature coupled with a charge-density-wave (CDW). To functionalize such a complex phase, it is essential to enhance the CDW-Mott transition temperature TCDW-Mott, whereas this was difficult for bulk TMDs with TCDW-Mott < 200 K. Here we report a strong-coupling 2D CDW-Mott phase with a transition temperature onset of ~530 K in monolayer 1T-TaSe2. Furthermore, the electron correlation derived lower Hubbard band survives under external perturbations such as carrier doping and photoexcitation, in contrast to the bulk counterpart. The enhanced Mott-Hubbard and CDW gaps for monolayer TaSe2 compared to NbSe2, originating in the lattice distortion assisted by strengthened correlations and disappearance of interlayer hopping, suggest stabilization of a likely nonmagnetic CDW-Mott insulator phase well above the room temperature. The present result lays the foundation for realizing monolayer CDW-Mott insulator based devices operating at room temperature.

723 (2015)). This fact casts some doubts on the true ML nature of the TMD film and on the interlayer hopping argument (see my first comment about the samples). Authors should clarify this point.
line 51: "...U/W exceed the critical value". A Reference is required. lines 114-117: "Such spectral features..." The absence of Mott gap and the persistence of CDW phase was seen f.i. in Ref.[27] at room temperature. Authors should clarify. lines 125-126: "We expect…": what do authors mean by "transport gap" and "spectroscopic gap minimum Delta_Mott"? Data in Fig.2e seem to follow a BCS-like behavior, which normally is attributed to the CDW gap (in fact the model in Ref. [26] refers to CDW), but these data refer to the leading edge at Gamma that is the LHB. This is confusing. Authors should clarify. lines 129-130: "This is also true..." what is also true? the linear behavior (I guess)? or the finite value at high temperature? Sentence is misleading.   Sato et al. present a detailed experimental study on 1T-TaSe<sub>2</sub> and 1T-NbSe<sub>2</sub> being prepared as monolayers epitaxially grown on bilayer graphene. The graphene itself was prepared on SiC(0001) single crystals.
In the photoemission data the authors observe characteristic spectroscopic differences compared to respective the bulk material, in particular in the temperature dependence of the features in the valence band. The observations are thoroughly discussed in the well established picture of for the non-magnetic Mott-insulator with a particular focus on the lower Hubbard band (LHB). The characteristic temperature for 1T-TaSe<sub>2</sub> bulk crystals is below 200 K, whereas the authors observe no comparable temperature dependence for the system investigated here -at least not in the experimentally accessible temperature range. From the smooth changes observed, the authors extrapolate a characteristic temperature of ~530 K. Such monolayersystems have already been investigated, by photoemission spectroscopy and STM.
The spectral features (here particularly the LHB) reveal a surprising robustness against several external parameters, as temperature, electron doping by potassium deposition, or even photoexcitation with a 1.55 eV pump-laser. This robustness is in the focus of this work and has not been investigated in earlier works in this detail.
Although the complementary experimental approaches and their results are carefully discussed in a common physical frame, there remains the possibility that the observed robustness is the consequence of a much more trivial effect, namely a structural modification of the monolayer due to an interaction with the substrate. Such an elastic 2D lattice distortion might be fully unrelated the CDW-Mott picture being discussed here. Although alternative explanations for the origin of the gap are discussed briefly in the Supplementary Notes, I can not see how this possibility can be ruled out. As being stated, the interlayer coupling in bulk crystals is important for their physical properties, but here the coupling between graphene substrate and TaSe<sub>2</sub> has not been elucidated.
In contrast to earlier publications (by this and other groups), a novel and strong experimental feature of the present work is the investigation of the temperature dependence of the spectra. Unfortunately, the maximum temperature of the experiment is 450 K, clearly below the expected transition. However, there is a broadening of the so-called LHB which shifts its leading edge seemingly towards the Fermi level. This analysis (or interpretation) should be reconsidered after another fitting of the spectra which considers in particular thermal broadening of the line. The direct comparison with the BCS gap is actually misleading. Furthermore, I was wondering whether the Ta4f core-level spectra are showing a temperature dependence, since their splitting indicates the (temperature dependent) charge distribution within the star-of-David distortion. There might me more information in the temperature dependence which possibly supports the conclusions of this manuscript, namely that the observed robustness is an intrinsic property of the monolayer.
Reviewer #3 (Remarks to the Author): Authors studied how the CDW-Mott gap size changes when TaSe2 becomes a single layer. They presented a comprehensive ARPES study on epitaxially grown monolayer 1T-TaSe2 and 1T-NbSe2. They further showed how the ARPES data changes under heating, electron doping, and photoexcitation. The transition temperature is found ~530K, making this observation interesting.
In principle the main observation presented in the manuscript is interesting. However, there are some relevant information and discussion are missing, and it is difficult for me to make a judgement based on the current data. I would like to ask authors to present: 1. how the samples were prepared; how monolayer samples were achieved and their STM topographic image or atomically resolved HAADF-STEM image to see how clean the sample is; any surface effects.
2. Is it possible to obtain transport data and compare them with bulk samples? Is there a way to prove that it is indeed a Mott insulator without a magnetic ordering. If yes, please present them. If not, difficulties/challenges in obtaining such data and their implications (e.g., lack of proof on the absence of magnetic ordering) on the final conclusion need to be discussed.
3. The Hubbard interaction U is a local atomic interaction. It is not clear how the gap is controlled by U/W. A simple argument like the ratio U/W change is not convincing in low dimensional system. Indeed W is going to be smaller, since the interlayer hopping is blocked by making a system to be two dimensional. But how does it change a local U size? It is likely that the screening effect is important to understand the increase of U (which in turn increases gap and Tc). Authors need to give some convincing arguments (not a full theory, as it is not a theory paper) on how the interaction strength can be renormalized by the hopping processes allowed in 2D vs. 3D.

Response to the comments from Reviewers
Dear Reviewers; We greatly appreciate the thoughtful and constructive comments from all the reviewers. We are also deeply grateful to the reviewers for their recognition of the importance of our work by writing that, "The topic is of large interest to a wide scientific community and the methods are appropriate." (Reviewer #1), "the complementary experimental approaches and their results are carefully discussed" (Reviewer #2), and "the main observation presented in the manuscript is interesting" (Reviewer #3).
We have significantly revised the manuscript by fully incorporating all the suggestions from the reviewers. In particular, to strengthen our main claim, we have additionally performed temperaturedependent core-level spectroscopy and low-temperature STM experiments, and verified the crystal structure, its monolayer nature, and the CDW formation with the √13×√13 reconstruction. We have included all these results in the revised manuscript. We present our responses to the respective reviewers and elaborate on how we have revised the manuscript to resolve their concerns, as detailed in the following. The reviewers' comments are shown in bold italic.
We thank again all the reviewers for their useful and constructive comments to improve our manuscript. We believe that the manuscript has been appropriately revised and is now suitable for publication in Nature Communications.
We have added Hirofumi Oka and Tomoteru Fukumura in the author list, because they have greatly contributed to the additional STM experiments. All co-authors agree with this change.
To the comments from Reviewer #1:

Reviewer comment: The manuscript of Nakata et al. discuss the robustness of charge-densitywave/Mott phases in monolayer (ML) transition metal dichalcogenides (TMDs). The topic is of
large interest to a wide scientific community and the methods are appropriate. There are, however, several points that require additional clarifications before granting publication to Nat. Comm.
Our response: We thank Reviewer #1 for spending his/her precious time to carefully read our manuscript and giving several constructive suggestions to improve our manuscript. Following the useful suggestion, we have incorporated additional clarifications in the revised manuscript, by carrying out additional STM and core-level spectroscopy experiments to strengthen our main claim regarding the crystal structure, its monolayer nature, and the CDW formation in our 1T-TaSe2 film, as detailed below. Our point-by-point response to the reviewer's comments is as follows: collaboration with the STM group. As seen from the obtained STM image in a 100×100 nm 2 spatial region for our TaSe2 film at T = 4.8 K Fig. R1: a, STM image in a surface area of 100×100 nm 2 for monolayer 1T-TaSe2 on bilayer graphene measured at T = 4.8 K. b, Height profile along a cut crossing a step of TaSe2 island shown by red arrow in (a). c, STM image in a surface area of 8×8 nm 2 , together with the unit cells of original lattice (orange rhombus) and √13×√13R13.9º lattice (green rhombus). d, Fourier-transform image of (c). e, Typical dI/dV curve on the TaSe2 island measured at T = 4.8 K.
in Fig. R1a, a few triangular TaSe2 islands (yellow region) are recognized on top of bilayer graphene substrate (dark region). We have also confirmed from the height profile along a cut across a step of TaSe2 island in Fig. R1b (obtained along red arrow in Fig. R1a) that the step height is ~0.94 nm, which is in between monolayer (0.63 Å) and bilayer (1.26 Å) heights in bulk TaSe2 [Wilson et al., Adv. Phys., 24, 117-201 (1975)

Considering that (i) ARPES with 6.2 eV photons (Fig. 3f) does not bring substantial additional information compared to He lamp ARPES and that (ii) the time-resolved experiment is not truly necessary for the goal of this work, I suggest to remove this part and maybe address the timeresolved features in a different publication.
Our response: We understand that the reviewer's comment of " Fig. 2f-2g are not in agreement with such a statement" means that "it is unphysical to observe a finite photoelectron signal at the binding energy higher than 1 eV". As mentioned by the reviewer, we have estimated the upper limit of binding energy to be ~1 eV from the difference between the photon energy (hn = 6.2 eV) and the expected work function (5.2 eV). This suggests that one can trust the photoelectron signal up to ~1 eV from EF, but it does not necessarily mean that a photoelectron signal is not detected in the energy region higher than 1 eV. Such a spurious photoelectron signal is known to appear at very low kinetic energy, because the low kinetic energy cut-off of photoelectron signal is usually broad unless a bias voltage is applied between the sample and analyzer. Also, it is known that photoelectrons with kinetic energy typically lower than a half of pass energy of analyzer cannot be correctly measured by a standard ARPES apparatus. In the revised manuscript, we have added a few sentences to describe this point (p. 10, lines 1-7 from the bottom of Supplementary note 7).
As pointed out by the reviewer, one needs to be well aware of the pump fluence when discussing the melting of CDW-Mott phase. Considering the high pump fluence to trigger the electronic phase transition in bulk Ta-based TMDs, we tried to increase the pump fluence as much as possible, and found that 0.26 mJ/cm 2 is an upper limit of reliable measurements, above which an irreversible spectral broadening was observed due to the photo-induced damage of monolayer sample. Therefore, we carried out the tr-ARPES measurement with 0.26 mJ/cm 2 pump fluence. On the other hand, it is true that there exist some reports that bulk samples are still robust at this pump fluence because the pump fluence higher than 1 mJ/cm 2 can be applied without damaging the sample, as pointed out by the reviewer. This suggests that the monolayer sample is structurally and/or chemically more fragile against the pump laser irradiation than the bulk counterpart. This may be related to the absence of interlayer coupling in monolayer which perhaps helps strengthen the overall sample stability. Thus, direct comparison of the robustness of CDW-Mott phase against photo-excitations between monolayer and bulk under identical experimental condition would be difficult, as pointed out by the reviewer.
Nevertheless, we think that, aside from a comparison with the bulk, it would be still meaningful to comment on the experimental fact that the CDW-Mott phase could not be melted in monolayer even when we adopted the maximum pump fluence above which monolayer samples were damaged. We think that this information would be useful for readers, in particular, researchers who aim to carry out pump-probe experiments (including tr-ARPES experiments) of monolayer and ultrathin TMDs, so that we would like to keep the tr-ARPES data in the manuscript. Since we also agree with the reviewer that the tr-ARPES data cannot be used as a direct proof of robust Mott gap against photo excitation, we have toned down our discussion on this matter by moving the tr-ARPES data to Supplementary note. Also, we have explicitly stated the issue of pump fluence described above (

Reviewer comment: -Potassium doping -At line 172-173 the potassium dose is given in terms of "deposition time" which is not particularly useful (it depends on the experimental conditions) and very qualitative. The relevant information is the K coverage in ML. The authors should at least provide an estimate of the dose to allow a quantitative analysis of the electronic doping. As an example: is the K coverage (atoms/cm^2) comparable to the "Stars of David" density (roughly 7x10^13 cm^-2 in TaSe2)?
Our response: We thank the reviewer for this important suggestion. We have calibrated the deposition rate of K atoms by calculating the volume of p-band Fermi surface at the K point in bilayer graphene on SiC with keeping the same evaporation rate as that in the case of monolayer TaSe2, and it is estimated to be 1.6 × 10 13 atoms/cm 2 /min. Therefore, Td = 2 min (4 min) in Fig. 3 corresponds to the K coverage dK of 3.2 (6.4) × 10 13 atoms/cm 2 , i.e. ~50 % (~100 %) of the Star-of-David density. Thus, the amount of K dosing with respect to the Star-of-David density is sufficient to achieve a sizable electron doping into monolayer 1T-TaSe2. In the revised manuscript, we have added a few sentences to explain the calibration of deposition rate (Methods, p. 14, lines 339-345), and replaced the deposition time Td with the K coverage dK throughout the manuscript and Figures (Figs. 3b, 3c, 3e, 3f, 3g, and 3h).

Reviewer comment: -Hubbard bands -
Referring to the discussion starting at line 178 (and related Fig.3d-f

Therefore, the UHB should be well below E_F. Authors claim that the spectral weight appearing close to E_F in Fig. 3f might be the tail of the UHB (line 191). However, I strongly doubt this could be possible: the fully populated LHB is actually a half-filled band (1 electron per site). Any hopping event would lead to double occupancy (e-e at one site and h-h at a neighboring site). This excited state has a Coulomb cost (U) that ends up in populating the UHB. I cannot imagine a strongly or even fully populated UHB below E_F. Instead, electron doping (due to K deposition) would most likely turn the (half-filled) Hubbard band into a standard (fully occupied) metallic band, which is
energetically more convenient. The spectral weight at E_F could be simply due to potassium (as more reasonably stated in line 192).
Our response: We thank the reviewer for this insightful suggestion. The energy position of LHB shifts from 0.28 eV to 0.75 eV with K deposition. If the energy bands shift in a rigid-band manner, one would expect the UHB to be located well below EF in the high K coverage (dK = 6.4 × 10 13 atoms/cm 2 ) sample since the full Mott-gap is estimated to be 0.5 eV (this value is obtained from the tunneling spectrum shown in Fig. R1e temperature and a large metallic spectral weight emerges at EF, in contrast to the low temperature (70-220 K) data that displays a peak associated with the LHB. Our ARPES data for 1ML 1T-TaSe2 at room temperature and T = 450 K resembles that of bulk TaSe2 at low temperature (Fig. 2d), suggestive of the persistence of a Mott gap at T = 450 K. We have rephrased the ambiguous statements in the previous manuscript "because the spectral feature continuously evolves in the temperature range of 40-450 K" and stated more explicitly the spectral similarity between the high-temperature data in monolayer TaSe2 and the low-temperature data in bulk TaSe2 (p. 5, lines 125-131).

Reviewer comment: lines 125-126: "We expect…": what do authors mean by "transport gap" and "spectroscopic gap minimum Delta_Mott"? Data in Fig.2e seem to follow a BCS-like behavior, which normally is attributed to the CDW gap (in fact the model in Ref.[26] refers to CDW), but these data refer to the leading edge at Gamma that is the LHB. This is confusing. Authors should clarify.
Our response: There exist two types of definitions in estimating the gap size from the EDC, i.e. In the present study, they are named DMott and DLEM, respectively. We call DMott a spectroscopic gap, because 2DMott spans the energy positions at which the LHB and UHB take the highest (and thereby spectroscopically prominent) density of states (DOS). The DOS for both LHB and UHB is not so sharp and has a broad tail as seen from the ARPES data in Fig. 2d and tunneling spectrum in Fig. R1e. Since the thermal excitation starts as soon as the excitation energy exceeds the zero DOS range around EF, the transport measurement is sensitive to this tail. Since the definition of DLEM inherently includes the tail region of LHB, DLEM is regarded to be sensitive to the transport gap (i.e. an activation gap in transport measurements). We have elaborated on these points in the revised manuscript (p. 6, lines 140-141) by adding Supplementary note 5.

Reviewer comment: lines 129-130: "This is also true..." what is also true? the linear behavior (I guess)? or the finite value at high temperature? Sentence is misleading.
Our response: We apologize to the reviewer for this misleading sentence. We intended to mean that the nearly linear behavior as a function of T is also seen in bulk 1T-TaS2 near TCDW-Mott, as pointed out by the reviewer. We have revised this misleading sentence in the revised manuscript (p. 6, lines 143-145).

Reviewer comment: line 132: authors should report the equations.
Our    Fig. 3h with Fig. R2.

Reviewer comment: line 219: "... possible ferromagnetism was not successful". Authors should specify what kind of attempt they made.
Our response: Since the detection of ferromagnetism by macroscopic magnetization measurements like SQUID measurement is difficult in 1ML sample, we have carried out a very primitive experiment to detect possible ferromagnetism, i.e. just putting a strong Nd magnet (magnetic field ~ 500 mT) on top of a thin film to detect possible attractive force. But such an attempt has not been successful. We have described this point in the revised manuscript (p. 9, lines 225-228).  Fig.  3g and Fig. 2d. The values for bulk TaS2 measured at T = 30 and 300 K are also plotted.

Reviewer comment: line 273: "... a smaller interlayer hopping...". This is not clear: authors are arguing on the Mott and CDW gaps of the ML systems and infer about the magnitude of the interlayer hopping (which in a ML cannot exist!)
Our response: "Interlayer hopping" is a mistype of "intralayer hopping". We have corrected it (p. 12, line 295).

y-axis should report numbers (even if a.u. are used).
Our response: Following the reviewer's suggestion, we have added numbers in the y-axis in Figs. 1f ( Fig. 1d in the previous manuscript), 2d, 3g, and 4c, and Fig. S6d (Fig. 2i in the previous manuscript).

g: all experimental dots should have corresponding error bars.
Our response: We have included error bars in Figs. 2e, 3h, and 4f, and 4g.
To the comments from Reviewer #2:

Although the complementary experimental approaches and their results are carefully discussed in a common physical frame, there remains the possibility that the observed robustness is the consequence of a much more trivial effect, namely a structural modification of the monolayer due to an interaction with the substrate. Such an elastic 2D lattice distortion might be fully unrelated the CDW-Mott picture being discussed here. Although alternative explanations for the origin of the gap are discussed briefly in the Supplementary Notes, I can not see how this possibility can be ruled out. As being stated, the interlayer coupling in bulk crystals is important for their physical properties, but here the coupling between graphene substrate and TaSe2 has not been elucidated.
Our response: We thank Reviewer #2 for spending his/her precious time to carefully read our manuscript and giving us many insightful suggestions to improve our manuscript. We are very thankful to hear that the reviewer recognizes the importance of our work by writing "complementary experimental approaches and their results are carefully discussed". We also agree with the reviewer that trivial effects such as the interaction with the substrate must be excluded to account for the robust gap in monolayer 1T-TaSe2 and NbSe2. We think that the substrate effect is unlikely to be responsible for the robust gap because of the following reasons. If the robust gap opens due to the interaction with the substrate, one may expect that the LHB of TaSe2/NbSe2 is hybridized with the graphene bands through a direct band overlap. However, this band hybridization would not occur around the G point where the LHB exists, because the graphene band is located 4 eV away from EF around the G point.
Another possible explanation for the robust gap is the lattice strain by the graphene substrate and resultant change in the band structure. But this is also unlikely because the lattice strain is expected to be weak due to the existence of van der Waals gap between TaSe2/NbSe2 and graphene, as suggested by the experimental fact that the in-plane lattice constant estimated from the RHEED pattern in One may think that the gap opening is due to the moiré potential associated with the lattice mismatch between TaSe2/NbSe2 and graphene. But this is also ruled out because the folded subband associated with the moiré potential is not observed. From these arguments, we think that the substrate effect can be safely ruled out from the origin of robust gap. We have elaborated on these points in the revised manuscript (p. 4, lines 89-90; p. 2, lines 2-13 from the bottom of Supplementary note 2). Regarding the Ta 4f core-level spectra, we have performed additional temperature-dependent photoemission experiments with synchrotron radiation, and the result is shown in Fig. R4. One can see that the use of synchrotron light (hn = 260 eV) greatly reduces the spectral background seen in the He II data in previous Fig. 1d, and now the main peaks are much better visualized even without background subtraction. At T = 40 K, one can clearly see that the Ta 4f5/2 and 4f7/2 peaks split into two sub-peaks due to the formation of star-of-David clusters. On elevating temperature, the lower-binding- Fig. R3: EDC at the G point at T = 450 K (red curve) for 1ML 1T-TaSe2 and simulated EDCs (blue curves) that were generated by broadening the experimental EDC at T = 40 K with a gaussian exp(-E 2 /2s 2 ) assuming s = 0.11 eV (top) and 0.18 eV (bottom).

Reviewer comment: In contrast to earlier publications (by this and other groups), a novel and strong experimental feature of the present work is the investigation of the temperature dependence of the spectra. Unfortunately, the maximum temperature of the experiment is 450 K, clearly below the expected transition. However, there is a broadening of the so-called LHB which shifts its leading edge seemingly towards the Fermi level. This analysis (or interpretation) should be reconsidered
energy sub-peak of both Ta4f5/2 and 4f7/2 components is gradually weakened, but the shoulder feature still remains even at T = 400 K (note that this is the highest temperature we could reach with the ARPES apparatus in synchrotron).
This core-level data is consistent with our conclusion that the Mott phase survives up to T = 530 K. We have elaborated on these points (p. 5, lines 111-120) by replacing Fig. 1d (new Fig. 1f) with Fig. R4.
To the comments from Reviewer #3:

TaSe2 and 1T-NbSe2. They further showed how the ARPES data changes under heating, electron doping, and photo-excitation. The transition temperature is found ~530K, making this observation
interesting.

In principle the main observation presented in the manuscript is interesting. However, there are some relevant information and discussion are missing, and it is difficult for me to make a judgement based on the current data. I would like to ask authors to present:
Our response: We thank Reviewer #3 for his/her careful reading of our manuscript and giving thoughtful advices and comments to improve our manuscript. To fully respond to the reviewer's request, we have additionally performed STM measurements and characterized our monolayer samples in detail. We have also added several explanations and supplied necessary information to strengthen our main claim. Our point-by-point response to the respective comments from the reviewer is as follows:

Reviewer comment: 1. how the samples were prepared; how monolayer samples were achieved and their STM topographic image or atomically resolved HAADF-STEM image to see how clean the sample is; any surface effects.
Our response: We totally agree with the reviewer that the characterization of the monolayer samples is important to convince readers of our main claim. As described in the Methods section of the previous manuscript, to grow monolayer 1T-TaSe2 and 1T-NbSe2 films, we at first grew bilayer graphene on 6H-SiC, and then co-evaporated Ta (Nb) and Se on the bilayer graphene substrate kept at 560℃ (580℃). This as-grown film was subsequently annealed at 400℃ for 30 min. The growth process was monitored by the reflection high-energy electron diffraction (RHEED). Based on our experience of R5d, and R5e, as Figs. S1a, S1b, Fig. 1d, Fig. 1e, and S3, respectively.

Is there a way to prove that it is indeed a Mott insulator without a magnetic ordering. If yes, please present them. If not, difficulties/challenges in obtaining such data and their implications (e.g., lack of proof on the absence of magnetic ordering) on the final conclusion need to be discussed.
Our response: We thank the reviewer for this important suggestion. At the moment, it is difficult to obtain reliable transport data with our monolayer film, because the film is unstable in the atmosphere and therefore not suitable for performing ex-situ transport measurements. Even when we cover the sample with a protection layer, the electric current will selectively flow through the metallic bilayer graphene substrate (and the protection layer if it is conductive), and consequently, the insulating behavior of the monolayer film cannot be detected. In-situ transport measurements would be also difficult because of the same reason. Even if we find an insulating substrate to grow TaSe2/NbSe2 films, there is no guarantee that the grown film shows exactly the same electronic properties as in the case of bilayer graphene substrate. While both ex-situ and in-situ transport measurements are difficult at the moment, we are able to spectroscopically confirm the insulating nature from the tunneling experiment. As shown in Fig Regarding the magnetic ordering, since the detection of magnetism in monolayer film by standard magnetization measurements (such as SQUID) is difficult, it would be necessary to perform the surface sensitive X-ray magnetic circular dichroism (XMCD) measurement with ultrathin films. Since the XMCD experiment is beyond the scope of present study, we would like to leave it as a future challenge. We have elaborated on these points in the revised manuscript (p. 9, line 225 -p, 10, line 231; p. 5, line 13 from the bottom -p. 6, line 4 of Supplementary note 3).

Authors need to give some convincing arguments (not a full theory, as it is not a theory paper) on how the interaction strength can be renormalized by the hopping processes allowed in 2D vs. 3D.
Our response: We thank the reviewer for this insightful suggestion. It is well-known that the Mott-Hubbard transition occurs when U/W can be tuned above a critical value, where U is the effective onsite Coulomb correlation energy and W is the effective d-electron bandwidth in the material. In the present context of the CDW behavior observed in monolayers of 1T-TaSe2 and 1T-NbSe2, it is important to discuss the independent roles of how U and W are independently affected on going from the bulk 3D structure to the monolayer 2D case. The effective on-site Coulomb correlation energy can be described by the equation U = EI -EA -EPol where, EI is the ionization energy, EA is the electron affinity, and EPol is the polarization energy which arises from screening due to any electronic perturbation such as removing or adding an electron. This screening causes a strong reduction of U Considering the role of screening in monolayer compared to the bulk case, while the intralayer EPol is expected to show negligible changes in the monolayer case, the interlayer EPol would be suppressed as there are no other layers and the interaction with the substrate is weak, resulting in an effective increase in U compared to the bulk.
Similarly, since there is no out-of-plane or inter-layer hopping in the monolayer i.e. the intrinsic bulk interlayer bandwidth Wout is absent, hence the net effective bandwidth W will get reduced. is also expected to reduce due to the structural distortion in the monolayer accompanying the CDW transition. Thus, upon dimensionality reduction from 3D to 2D, both the increase in U and decrease in W are expected to positively work together to efficiently increase U/W. We have revised the discussion part based on this argument (p. 10, line 242 -p. 11, line 258).
We thank again all the reviewers for their useful and constructive comments to improve our manuscript. We believe that the manuscript has been appropriately revised and is now suitable for publication in Nature Communications. Sincerely,

Takafumi Sato
WPI-AIMR and Department of Physics, Tohoku University