THz Higher-Order Topological Photonics in Ge-on-Si Heterostructures

I thank the authors for their detailed responses to my comments. However, I am left with the impression that, conceptually, the model and results closely resemble those found in the reference [Xie et al., Phys. Rev. Lett], which shares similar symmetries, topologies, and results including the same type of phase transition. The theoretical added value of the modifications remains unclear to me. While I acknowledge that using different materials and designs can indeed lead to new applications in industry, this suggests that the work may be more suitable for publication in specialized engineering journals.
Two additional points:
1. Despite the correction in Figure 1, my initial concern from the previous report persists. It is unclear how a trivial phase and a non-trivial one can be simply related by lattice translation. This criticism applies to reference 40 as well. Nevertheless, it would be beneficial to clarify this point.

2. As clear from Appendix A, the role of the facet (111) is negligible. It's not clear what is the advantage of including it in the design. One can imagine a large number of small modifications that will turn out to be negligible. I believe that the simplest functional forms (like a perfect square) are preferred at least from a fabrication perspective. Of course, one can ask the question regarding the order of magnitude of perturbations such that the results are not impacted. This question might have a practical relevance in terms of how precise the fabrication process has to be. However, the purpose of the inclusion facet (111) doesn't seem to me to provide an answer to the question.

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This is a theoretical investigation, building on the experimental investigation of Phys. Rev. Applied 16, 064024 (2021), Ref. [37]. The calculations are carried out with the COMSOL Multiphysics applications suite version 6.1.

I have to confess that this investigation is peripheral to my own interests and that I have not reviewed the first version of the manuscript. However, I have the impression that this is more on the level of routine work and thus more suitable for publication in SciPost Physics Core. After all, the physics is single-particle physics and the computations are carried out with a commercial program package.

There is one item concerning content that has been mentioned before (point 1 in Anonymous Report 1 on 2024-2-25), but in my opinion has not been properly addressed yet: The "Compressed" and "Expanded" unit cells of Figs. 2a) and c) are obviously equivalent in the bulk, and indeed the band structures of Figs. 2d) and f) seem to be identical. Accordingly, their symmetry groups must be isomorphic, i.e., only representations can differ. Of course, if one cuts the unit cells in different manners, the edge states can be different. Nevertheless, I find the comments on the bulk properties in Anonymous Report 1 on 2024-2-25 clearer than the corresponding discussion on page 5 of the manuscript. I thus recommend revisiting the discussion on page 5; first focusing on bulk properties and only in a second step introducing boundary states and topological properties might help.

Beyond this, there are some details that I recommend to address, see "Requested changes".

1- The \cite commands after the punctuation marks are sometimes confusing; at least they look strange. While I admit that there seem to be no specific formatting instructions in this respect, I recommend moving the \cite commands before the punctuation marks.
2- The inset of Fig. 1(c) is too small to be readable, at least in my printout. Enlarging the entire figure might help, but to play things safe, I recommend to also revisit the inset.
3- Revisit discussion of "Compressed" and "Expanded" unit cells on page 5, acknowledging that they are equivalent in the bulk.
4- The graphs in Fig. 3b) suggest a small value of $d/a$, but I was not able to find the exact value. I recommend providing this information in the caption of Fig. 3.
5- Figure 3c) contains information that is again too small to be easily visible in a printout. SciPost has no limitation on the length of the manuscript. So, why not use the space it takes for a clear figure?
6- Due to the multiple adjectives, I was not able to make sense of the "opportunely spaced phased dipoles" on lines 189 - maybe reconsider a clearer formulation.
7- Thanks to a comment on line 65, one knows that Fig. 5 belongs to Appendix A. However, Appendix A does not refer to Fig. 5. I recommend adding at least a short comment also at this place.
8- On lines 229-230 there is a reference to Figure S4, but that figure does not seem to exist.
9- I found Fig. 8 a bit confusing since the horizontal axis is reset with each new $k$ point. Maybe a graph with two panels would be clearer: one showing the number of iterations needed and another one the final error, both as a function of $k$.
10- Ref. [16] lacks the article identifier eaat0346 and DOI 10.1126/sciadv.aat0346.
11- Ref. [35]: The "(80-. )." after "Science" looks strange to me.
12- Ref. [38] might be better readable without the URL (i.e., DOI should suffice).
13- The DOI for Ref. [43] is 10.1364/OE.27.016088 - please add.
14- Ref. [49]: upper/lower-casing in the chemical formulas in the title needs to be corrected, same for subscripts (e.g., "YbF$_3$" etc.).

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