Measurements of Electronic Band Structure in CeCoGe₃ by Angle-Resolved Photoemission Spectroscopy

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In the article the authors present the results of electronic structure (ARPES+XPS) study on a CeCoGe3 crystal. This is a non-centrosymmetric, heavy fermion material, believed to show interesting physical properties including unconventional superconductivity. The crystal is synthesized by solution growth method and investigated at well established MERLIN ARPES end-station. The results are compared with theoretical data and also discussed in relation to the other work presenting ARPES results obtained for the same system (ref 10).

In general, the article contains a lot of experimental data and might be useful for readers, however I would suggest to consider the following improvements:

1. Fig. 1 shows the crystallographic structure and the Brillouin Zone (BZ) sketch. The BZ sketch is very important and could serve as a guide for analyzing the presented ARPES data. Please add some more information on it like measurement planes, maybe also projected BZs.
2. While the ARPES data are the essential part of this manuscript I find it quite difficult to follow them. 
   1. Fig 3. shows very small ARPES maps that are low resolution what makes it impossible to see some minor features. Consider adding the measured kz planes to the sketch Fig.1 (b).
   2. Also in Fig. 3 Please consider superimposing the calculated data on the experimental results.
   3. I am not sure if I properly localized the X-shaped bands on Fig.3.
   4. In Fig. 4a. b. there is k// label. Please add this GXZ plane on BZ sketch or at least show this direction on Fermi surface maps. This will also facilitate the identification of the discussed surface states on the Fermi maps.
   5. In Fig. 4a. I indeed see some vertical features but I suggest adding some marks to point on them.
3. Figure 5. shows the surface-like features that is supposed to cross the Fermi level at 0.44 1/A, what is apparent but the bottom of this band is not visible there. At least in this fig 5 in the presented k range can see it down to about -0.55 eV. Is it visible elsewhere? Why it is claimed to extend down to -0.6 eV and not more?
4. Please improve the synthesis description included in the first paragraph of sec. 2. I suppose in the current form it might be clear for those familiar with such methods but please consider adding the information like how the temperature was measured, and what is the reason to include Bi and explain better how it was removed.

Minor suggestions:

m1. Please unify the plots style/fonts for better readability. For example In Fig. 2 the labels are very small. Also in Fig. 1. there is (a) and (b) and later a. notation is used.

m2. The resolution of ARPES data (also in supplementary) is quite low.

m3. Figure 6 has very small label fonts and does not use the same notation as other figures indicating used here LCP and photon energy.

Author Response

We thank the referee for taking the time to offer constructive suggestions which have improved the readability of the manuscript.

Comment 1: Fig. 1 shows the crystallographic structure and the Brillouin Zone (BZ) sketch. The BZ sketch is very important and could serve as a guide for analyzing the presented ARPES data. Please add some more information on it like measurement planes, maybe also projected BZs.
Response 1: Measurement planes, color matched to later figures, have been added to the Brillouin zone.

Comment 2: While the ARPES data are the essential part of this manuscript I find it quite difficult to follow them. 

Comment 2.1: Fig 3. shows very small ARPES maps that are low resolution what makes it impossible to see some minor features. Consider adding the measured kz planes to the sketch Fig.1 (b).
Response 2.1: The measurement planes have been added to 1(b).

Comment 2.2: Also in Fig. 3 Please consider superimposing the calculated data on the experimental results.
Response 2.2: Superimposed calculations are shown in the supplements (Fig. S4).  We have left them off in the main text because superimposing makes it more difficult to see dimmer spectral features.

Comment 2.3: I am not sure if I properly localized the X-shaped bands on Fig.3.
Response 2.3: To aid in visualizing that feature, we show an example zoomed spectrum in Fig. S5 of the supplements.  When zoomed in, the raw data shows that feature pretty clearly.  But to aid further in visualization we also show a ‘sharpened’ spectrum using data processing techniques from the recent literature.

Comment 2.4: In Fig. 4a. b. there is k// label. Please add this GXZ plane on BZ sketch or at least show this direction on Fermi surface maps. This will also facilitate the identification of the discussed surface states on the Fermi maps.
Response 2.4: we have added this sentence to the caption to clarify this notation: “k_{||}$ label on x-axis denotes momentum parallel to sample surface, which for panels (a)-(b) is along the $\Gamma-X$ line.”  To facilitate connection between features in panel a and panels (c)-(g), we have also added labels of high symmetry points in the latter where applicable.

Comment 2.5: In Fig. 4a. I indeed see some vertical features but I suggest adding some marks to point on them.
Response 2.5: An arrow has been added to indicate these features in 4a.

Comment 3: Figure 5. shows the surface-like features that is supposed to cross the Fermi level at 0.44 1/A, what is apparent but the bottom of this band is not visible there. At least in this fig 5 in the presented k range can see it down to about -0.55 eV. Is it visible elsewhere? Why it is claimed to extend down to -0.6 eV and not more?
Response 3: Thank you for pointing this out.  The 42 eV data does not have enough momentum span to reach the band bottom and all of the other spectra were cropped in to match the x-axis and avoid a different confusion.  While the -0.6 eV band bottom is accurate, it is not supported by the data as shown, so we have removed that statement. Interested readers may peruse the raw data which will be posted upon publication.

Comment 4: Please improve the synthesis description included in the first paragraph of sec. 2. I suppose in the current form it might be clear for those familiar with such methods but please consider adding the information like how the temperature was measured, and what is the reason to include Bi and explain better how it was removed.
Response 4: We thank the referee for this comment. The Bi was added because it was previously reported that it is a good flux for this synthesis, i.e. it can dissolve Ce, Co and Ge without forming unwanted compounds. We cite ref. [18] (https://doi.org/10.1143/JPSJ.74.1858 ) for this. Due to it's low melting point, and high boiling point, Bi is a common flux to use for solution growth (Canfield 1992, https://doi.org/10.1080/13642819208215073 ). The temperature is measured by a thermocouple inside an alumina tube positioned near the ampoule and that is part of the furnace used.  General details about the solution growth method including the centrifugation can be found in the following work: https://doi.org/10.1142/9789811219375_0003. Additional details about the removal of Bi by centrifugation can be found in:
https://doi.org/10.1080/14786435.2015.1122248

https://doi.org/10.1002/zaac.202500007
These references have been added to the text.

 

Minor suggestions:

m1. Please unify the plots style/fonts for better readability. For example In Fig. 2 the labels are very small. Also in Fig. 1. there is (a) and (b) and later a. notation is used.
Our response: The panel letters have been made consistent, and labels in Fig 2 and other figures were made bigger.

m2. The resolution of ARPES data (also in supplementary) is quite low.
Our response: It is not clear whether this statement is about the data itself or the figures.  This material tends to cleave poorly and spectra are weak at E_F, as discussed in the text, and spectral quality is about as good as it gets in this compound right now.  The figure resolution has been improved via the format of source files in tex document.

m3. Figure 6 has very small label fonts and does not use the same notation as other figures indicating used here LCP and photon energy.

Our response: This has been corrected.

Reviewer 2 Report

Comments and Suggestions for Authors

The article presents Angle-resolved photoemission spectroscopy (ARPES) study of CeCoGe3, the noncentrosymmetric system of particular interest due to a possibility of inducing superconductivity, magnetic phase transitions and the presence of 4f electrons with increased masses.

Although the first ARPES data have already been published for this system, the article delivers new information, namely surface states are identified and a proposal of band-folding is made. In my opinion the manuscript can be published in Condensed Matter after a revision is made. I recommend to consider the following comments:

1. When I was analyzing Figures 3, 4 and 5, I got confused by photon energies and colors of theoretical band structure. In Fig. 3, the solid lines are in red for hv=90 eV, yellow for 82 eV, violet for 78 eV, green for 70 eV and cyan for 66 eV. In contrast, in the Fig. 4 analogical solid lines correspond to increasing photon energy, also in Fig. 5.

Maybe providing photon energies corresponding to selected k-perpendicular in Figure. 4 would make the situation clearer.

2. According to the authors the obtained dispersions for nodal lines presented in Fig. 6 show “splitting and re-joining”, what would indicate directly Weyl crossing. However, the data for LC MDC (dotted) at Fermi energy and at -0.1 eV are of weak quality and do not indicate where the peaks actually are. Hence, I do not see any evidence of band crossing. I propose to use the statements like “is consistent”, or “band splitting is detected”, which reflexes the data quality. The quality of the data is too weak to show band crossing.
3. The discussion of the possible ordering vector has to be clarified. Currently it is written that “The presumed unit cell doubling is consistent with ground state bulk magnetic order”, “the magnetic ordering vector is (0, 0, 2/3)”, “We do not fully rule out this ordering vector but our data slightly favor (0, 0, 1/2)”

In my opinion the sequence of these statements is not logical. This should be written more clearly. As I understand, the data give some indications for (0, 0, 1/2) ordering (spectra at Gamma and Z). However, other features of the data (more complex Fermi surface in same regions of BZ would be consistent with another modulation, possibly related to magnetic ordering…).

4. “Yellow dots” for high symmetry points, as stated in the caption of Fig. 4 are not visible in the figure.
5. In conclusions it is written that the electronic structure agrees in large part with quantum oscillation experiments. However, I do not find a proper discussion of this fact in the text.

Author Response

The article presents Angle-resolved photoemission spectroscopy (ARPES) study of CeCoGe3, the noncentrosymmetric system of particular interest due to a possibility of inducing superconductivity, magnetic phase transitions and the presence of 4f electrons with increased masses.

 

Although the first ARPES data have already been published for this system, the article delivers new information, namely surface states are identified and a proposal of band-folding is made. In my opinion the manuscript can be published in Condensed Matter after a revision is made. I recommend to consider the following comments:
We thank the referee for their supportive summary and the helpful suggestions for improving the manuscript.

Comment 1: When I was analyzing Figures 3, 4 and 5, I got confused by photon energies and colors of theoretical band structure. In Fig. 3, the solid lines are in red for hv=90 eV, yellow for 82 eV, violet for 78 eV, green for 70 eV and cyan for 66 eV. In contrast, in the Fig. 4 analogical solid lines correspond to increasing photon energy, also in Fig. 5.  Maybe providing photon energies corresponding to selected k-perpendicular in Figure. 4 would make the situation clearer.
Response 1: Photon energies have been added to the FS maps in Fig. 4 (c)-(g).

 

Comment 2: According to the authors the obtained dispersions for nodal lines presented in Fig. 6 show “splitting and re-joining”, what would indicate directly Weyl crossing. However, the data for LC MDC (dotted) at Fermi energy and at -0.1 eV are of weak quality and do not indicate where the peaks actually are. Hence, I do not see any evidence of band crossing. I propose to use the statements like “is consistent”, or “band splitting is detected”, which reflexes the data quality. The quality of the data is too weak to show band crossing.
Response 2: We appreciate the referee’s careful reading.  We have changed the statements to ‘consistent with' and other weaker statements than originally used

Comment 3: The discussion of the possible ordering vector has to be clarified. Currently it is written that “The presumed unit cell doubling is consistent with ground state bulk magnetic order”, “the magnetic ordering vector is (0, 0, 2/3)”, “We do not fully rule out this ordering vector but our data slightly favor (0, 0, 1/2)”  In my opinion the sequence of these statements is not logical. This should be written more clearly. As I understand, the data give some indications for (0, 0, 1/2) ordering (spectra at Gamma and Z). However, other features of the data (more complex Fermi surface in same regions of BZ would be consistent with another modulation, possibly related to magnetic ordering…).
Response 3: thank you for helping us improve the clarity in our argument.  That section of the discussion has been revised as follows:
“The other new experimental observation is the additional band features shown in Fig. 3 and 4 which show strong similarity with bands that are half a BZ away in kz for most cuts where they are observed. These extra features are interpreted as originating from a reconstruction of the unit cell from some incipient order. The discussion below assumes a c-axis reconstruction because known magnetic orders in this material are along c [ 8, 18 ,36 ]. The evidence for this ordering wavevector (q = (0, 0, 1 / 2)) in our data is 1) strong mixing of Γ-plane and Z-plane spectra, 2) the ΓZ/ 2 periodicity of FS maps in Fig.4(b), as well as 3) large discrepancies between calculation and experiment in the N − P plane, where bands would cross and hybridize under a doubled unit cell. The presumed unit cell doubling has the same periodicity as the ground state bulk magnetic order [36 ]. One might argue that the highest-temperature magnetic order may be most relevant at the measurement temperature of 30K. Below TN1 = 21K, the magnetic ordering vector is q = (0, 0, 2 / 3), and we do not fully rule out this ordering vector. The aspect of the data that more favors a q = (0, 0, 2 / 3) order is the observation that many of the FS maps outside of the Γ and Z planes in Fig. 4(c)-(g) show strong Z-plane features of a square inside of a diamond (c1, d1, e2). A q = (0, 0, 2 / 3) order would repeat Z-plane spectra more times along kz even before considering the effects of perpendicular momentum resolution. Perpendicular momentum uncertainty/broadening originates from a short IMFP, and this can both broaden spectra and oversample extremal momenta of a dispersing band [37, 38]. In the present experiments, momentum uncertainty is estimated to be ∆k⊥ = 1 /IMFP ≈ 0.2 Å−1, or ≈ 17% of the BZ height. This amount of perpendicular momentum broadening could partially convolve spectra comparatively nearby to each other in kz, such as those originating from a q = (0, 0, 2/3) reconstruction.”

 

Comment 4: “Yellow dots” for high symmetry points, as stated in the caption of Fig. 4 are not visible in the figure.
Response 4: Thank you for noticing this figure change that didn’t propagate to the text.  The dots are back and text has been changed to reflect this.

 

Comment 5: In conclusions it is written that the electronic structure agrees in large part with quantum oscillation experiments. However, I do not find a proper discussion of this fact in the text.

Response 5: Thank you for pointing out this inconsistency.  We have omitted reference to quantum oscillations in the conclusions, since it is not the main point of the paper, but in the first paragraph of the discussion, we reference the quantum oscillation study [ref 9] in the context of how our measurements of electronic structure in full BZ correspond to prior studies.