Peer review of: Switching of band inversion and topological surface states by charge density wave (2020)

Reviewers' comments: 
 
Reviewer #1 (Remarks to the Author): 
 
This manuscript provides a comprehensive characterization (both experimental and theoretical) of the 
evolution in the electronic structure of the transition-metal dichalcogenide (TMD) VTe2 through its 
structural/CDW transition. This compound has been known to display a peculiar structural transition 
from the octahedral 1T configuration to a trimerized distorted phase at around 475 K. The nature of 
the distorted phase is interesting, first, because it is associated with a dimensional crossover from 2D 
to a more 1D-like electronic behavior arising from the quasi-1D trimerized chains of the transition 
metal ions. Second, the origin of the instability is related to the concept of "hidden nesting" seen in 
other closely related TMDs, as well as in the so-called purple bronzes, but which remains largely 
unexplored. Finally, it is a Weyl semimetal in the 1T phase whose fate upon the structural transition is 
given particular scrutiny here. 
 
The fact that the authors study different samples of the family V_{1-x}Ti_{x}Te_{2} is quite 
important as it allows them to acquire the ARPES spectra on either of the 1T and 1T' phases on 
different samples, as well as probing the two phases on the same sample. This supports the 
assumption that the ARPES spectrum of the pristine compound VTe2 will essentially be the same as 
the one shown in Fig. 2c. 
 
In addition to providing a very careful and comprehensive analysis of all the ARPES data as a function 
of doping and temperature, the manuscript provides also a careful analysis on the underlying 
microscopic changes taking place through the transition. This analysis is anchored on equally detailed 
DFT calculations performed for both 1T and 1T' phases, as well as for doped and undoped samples. I 
find the various aspects of this discussion and interpretation very compelling and clear. 
 
In my view, these are experimental and theoretical results of very good quality and the manuscript 
conveys a very consistent picture of the underlying physics. The possibility of manipulating 
topologically non-trivial electronic states on-demand is an exciting prospect, which this manuscripts 
initiates by demonstrating one explicit example where that occurs due to a structural transition that 
can be induced with external perturbations. It therefore shows that the goal of achieving tunable 
topological states (at least as far as suppressing them) via tunable structural transitions is quite 
realistic. I therefore think that the manuscript meets in principle the criteria for publication in Nature 
Communications. 
 
Notwithstanding, the authors should clarify/correct the following points in a revised version. 
 
 
1) Page 5, line 6 -- "It is characterized by the circular and triangular hole Fermi surfaces around Γ and 
K, respectively". The topmost band in Fig. 2a intersects Ef 3 times along ΓK (or ΓM). This means that 
the statement that there is a hole pocket centered at Γ is, strictly speaking, not accurate (in fact, from 
Fig. 2a one could say there is a tiny electron pocket at Γ). Likewise, the energy contour at kz=0 in Fig. 
2b should show an additional tiny circle centered at Γ. Why is it not there and, instead of 3, we have 
only 2 contours in Fig. 2b. 
Is it a matter of resolution? I understand this is a somewhat minor aspect that has no impact on the 
conclusions and interpretation of the underlying picture, but it would be good to clarify what currently 
looks like a small inconsistency. 
 
 
2) Page 9, line 18/19 -- When discussing the hidden nesting scenario, I suggest that the authors refer 
not only to TMDs but also to the case of purple bronzes, where that hidden nesting is crucial to 
describe the electronic structure and ARPES measurements. In this regard, the authors could cite, in 
addition to reference 23, the following additional references: 
 
- M. H. Whangbo et al., Hidden fermi surface nesting and charge density wave instability in low-
dimensional metals. Science 252, 96 (1991). 
 
- D. Mou et al., Discovery of an Unconventional Charge Density Wave at the Surface of K0.9Mo6O17. 
Phys. Rev. Lett. 116, 196401 (2016). 
 
- L. Su, C.-H. Hsu, H. Lin, V. M. Pereira, Charge Density Waves and the Hidden Nesting of Purple 
Bronze K0.9Mo6O17. Phys. Rev. Lett. 118, 257601 (2017). 
 
 
3) Page 12, line 10 -- Please add a citation to the relevant references describing the "virtual crystal 
approximation". 
 
 
4) Neither the main text nor supplementary sections S10, S11 explain how were the DFT calculations 
performed for the 1T' distorted phase. Were the distorted positions fixed "by hand" or allowed to relax 
in a supercell? If they were fixed, were experimental values used for that or, if not, how were the 
distorted equilibrium positions obtained? Please include a brief statement describing that procedure in 
the "Methods - Band Calculations" section, and provide additional details in Supplementary section 
S10. 
 
 
5) Supplementary section S11, line 5 -- Replace "reproduce the ARPES results" by "reproduce the 
ARPES results for a single domain region" to emphasize that the comparison is meaningful only in the 
case of a single-domain region. 
 
 
6) Supplementary section S11, line 6 -- "the surface state observed in ARPES measurement (Fig. 4b) 
does not appear in this bulk calculation". I understand that the theoretical results shown in Fig. S11 
represent the unfolded spectral function of the bulk system and, consequently, surface states cannot 
appear there. However, as the authors do not show nor mention it anywhere in the main or 
supplementary texts, it is still unclear whether the calculations for the pristine 1T' case reveal (or not) 
a band inversion and the corresponding surface states, if one calculates a *slab* projection of the 
spectral function analogously to what is done in Fig. 3c (main text). In other words, Figs. 3a-c show 
both the band inversion and surface state in the calculation done for the 13% doped case. The 
question is what is the result of the same calculation for the undoped 1T' case? Is there a surface 
state and Weyl point near M1, or do all 3 equivalent Weyl points disappear? Does the result depend on 
the doping level used in the calculations? The authors should clarify this point because, if all the Weyl 
points disappear in the calculation of pristine 1T', that would be in contrast with the experimental 
result (where the Weyl point at M1 remains), and must be carefully justified. 
 
 
 
Reviewer #2 (Remarks to the Author): 
 
The manuscript by Mitsuishi et al. reports an extensive ARPES investigation of the Charge Density 
Wave (CDW) transition in the VxTi1-xTe2 (x=0; 0.1) transition metal dichalcogenide. Such material 
hosts topological surface states (TSS) and the authors investigate the interplay between the CDW 
transition and the topology of the material, with a particular focus on its band inversion. This is a very 
interesting point because it would open the possibility to manipulate the topological phase of materials 
by means of CDW. The presented results are interesting, the quality of the performed research is of 
high level, the presentation is clear and the paper very well written. However, the presented 
interpretation is not conclusive in that sense. The authors states that some of the TSS are destroyed 
by the CDW order as it is shown by the ARPES investigation (fig. 4.b-e and fig 5.d). Moreover, the 
Spin-ARPES in the supplementary (section S8) shows that the remaining Dirac cone (across the M1 
high symmetry point) preserves its typical spin texture. As the topology of a material is a property of 
the system as a whole, the data seems to demonstrate that the topology is conserved across the CDW 
transition and that the reorganisation of the Dirac cones occurs to follow the changed structural 
symmetry (C3 symmetry is lifted in the monoclinic 1T” phase). 
This is ‘the’ focal point/question of the paper and needs to be addressed more convincingly, or it 
should be much more elaborated. 
 
Moreover, some further points need clarification, namely: 
1. why the t2g orbitals (dxy dyz dxz) are discussed mostly to explain the removal of band inversion in 
the CDW phase. Looking at fig.3.a it seems that the band inversion mainly involves the px-py Te 
orbitals and the dx2-y2-dxy orbitals of V (or I’m confused by the similar colour code red-pink?). 
According to the authors the dxy orbital is unaffected by the CDW transition, I therefore think that a 
discussion of the effects of CDW on the dx2-y2 V and px-py orbitals should be included. 
 
2. In the text and figures three coordinate systems are chosen: crystal directions, the global xyz and 
XYZ centred on the V atom of the VTe6 octahedron. I found confusing for the reader the presence of 
both xyz and XYZ, tough. It would be possible to adopt only one coordinate system? Otherwise, I 
would suggest to indicate both the systems e.g. in fig.5.a. 
 
3. Transport data fig. S2.b Are these data necessary? I found them a bit confusing when compared 
with the rich ARPES dataset. For example, looking at x=0.1 transport curve, the anomaly occurs at 
~400K while from the ARPES data (fig. 2, fig. 3 and supplementary section S5) it is stated that the 
CDW transition starts at ~250K as stated in the main text. Can the authors comment a bit more on 
this? Another point not completely clear to me is the apparent discrepancy between transport and 
ARPES data in the CDW phase: ARPES spectra show strong localisation of the electronic bands (across 
the M2 high symmetry point) and the arise of almost 1D electronic state, while the transport shows 
metallic behaviour with localisation only for very low temperature (<20K). Can the authors clarify this 
point? 
 
4. Spin-ARPES data fig. S8.d As the signal is faint, I would suggest to avoid the arb. units and to 
indicate the counts of the Iy+,- spectra. 
 
A curiosity on the transport data: I am wondering why the anomaly is fainter for higher x values. Is it 
due to disorder introduced by the doping or it depends on the hole concentration introduced by the Ti-
doping? 
 
 
 
Reviewer #3 (Remarks to the Author): 
 
The manuscript by Mitsuishi et al. reports changes in topological surface states in doped VTe2, due to 
large changes in the crystal structure due to the formation of a 3x1 CDW. In principle, this is quite an 
interesting finding, although the way the paper is initially presented, it seems to imply (incorrectly) 
that the CDW transitions completely changes the topological character of the material which is not the 
case. Instead, some of the DSSes are removed due to CDW formation, while other DSSes remain 
present (in the ungapped parts of the Fermi surface). This is still an interesting finding, although not 
as remarkable as if the entire topological character of the material changed. 
 
The presentation of the data showing the DSSes themselves is not particularly clear, particularly in 
Figures 4g-h, and Figures 3g-h. I actually found that some of the data in the SI (Figs S5 and S7) seem 
to show the DSSes much more clearly. I do believe that the authors' main identification of the DSSes 
in both the 1T and 1T' phases. In addition, there is some discussion of the spin-resolved results even 
in the abstract, yet none of the spin-resolved measurements actually show up in the main manuscript, 
only the supplemental Figure S8; authors should consider moving this to the main text. Granted, the 
spin-resolved data is not of the best quality, although the results from the lower branch of the DSS 
seem relatively clear. 
 
Furthermore, the DFT calculations in Figure 3a-c in the normal state structure appear to indicate band 
inversion, supported by the appearance of a DSS in the slab calculation in 3c. This seems to be 
sensible and consistent with the ARPES data in the normal state. What about the DFT calculations for 
a 3x1 supercell in the 1T' phase? Do they likewise support the author's observations of a DSS at 
certain k-points and absence on the gapped parts of the FS? I see in the SI that they have produced 
DFT calculations of the 1T' phase but am surprised that they have not produced a similar analysis. 
Also (a more minor question), why is a Ti doping of 13% selected (as it does not appear to correspond 
to any of the doping used), nor is a supercell used in the calculation? 
 
The organization and presentation of the paper is jumbled, disorganized, and confusing. There is a lot 
of switching back and forth between different data sets (single domain, domain-averaged, different 
photon energies, etc...). It would be much more clear-cut to just have all the data taken for single 
domain, since the domains appear to be rather large (many hundreds of microns - this is not a 
technically challenging experiment). As mentioned earlier, it is not evident until quite late in the 
manuscript (end of pg 7, beginning of pg 8) that only some DSSes disappear and others remain 
unchanged - this should be made clear at the outset. 
 
In summary, I think that the report of changes in the topological DSSes due to CDW transition in 
doped VTe2 is certainly an interesting one, potentially worthy of publication in Nature Communications, 
and I do believe the authors' identification of this phenomenon. In its current state, however, I do not 
think the manuscript is ready for publication unless the authors make significant changes and 
improvements.