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

by Ian Colombo, Pietro Minazzi, Emiliano Bonera, Fabio Pezzoli, and Jacopo Pedrini

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Submission summary

Authors (as registered SciPost users): Ian Colombo · Jacopo Pedrini · Fabio Pezzoli
Submission information
Preprint Link: scipost_202311_00045v3  (pdf)
Date accepted: 2024-06-03
Date submitted: 2024-05-20 16:03
Submitted by: Pedrini, Jacopo
Submitted to: SciPost Physics Core
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Computational
  • Quantum Physics
Approach: Computational


We design germanium-based higher-order topological cavities for terahertz applications by breaking the symmetry of a two-dimensional photonic crystal following the Su-Schrieffer-Heeger model. Calculations demonstrate the parity inversion of the electric field in differently deformed unit cells. The interface between domains of opposite topology presents edge and corner modes. The former are chiral, locking light propagation to its helicity. The latter prove that Ge-based structures can be used as high-order topological photonic crystals. These findings can accelerate the development of Si-photonic components working in a spectral range of high technological interest.

Author comments upon resubmission

Dear editor-in-charge,

Thank you for your effort of finding a second referee and for providing us with a complete Referee report. The remarks from both referees were overall positive and asked for minor revisions, which we provided to the best of our ability. We believe that both referees helped to better our work with their scrutiny. Unfortunately, we are sorry to read that both referees decided to not accept our work for publication on SciPost Physics, but to redirect it towards SciPost Physics Core.
Nevertheless, we accept their decision and we are thus resubmitting the work for publication on SciPost Physics Core. Since the work has already been thoroughly reviewed, and both referees suggest acceptance with minor revisions, we ask for direct publication without another round of revision, if possible.

Kind regards,
Jacopo Pedrini

List of changes

1. We added the following paragraph to the text, starting at line 137:
"It is worth noting that the definition of the unit cells does not affect the eigenvalues of the system, i.e., the photonic bandstructure: the compressed and expanded cells generate the same bulk (infinite) structure. In other words, when the PC has no boundaries, the compressed and expanded cells can be mapped one into the other, and the choice of the repeating unit does not yield differences in light propagation. Yet the eingenfunctions, i.e., the electromagnetic field distribution associated to a given eigenvalue, can differ. More specifically, the degree of freedom that changes between the two structures is the parity of Ez, which is reflected by the change in the Zak phase from (0,0) in the compressed cell to (π,π) in the expanded cell. While this property does not manifest itself in the bulk, it has a physical consequence when an interface is realized between the two topologically distinct domains. Indeed, the presence of a junction that acts as a boundary implies a closing gap to connect the states having the same parity [58].
This is one of the fingerprints of a topological transition and is generally referred to as bulk-edge correspondence, i.e., the emergence of spatially confined guided modes at the boundary between two domains with different band topology."

2. We added the following sentence to line 65: "[...] but they were included in the computational model for the sake of accurately simulating the results of fabrication."

3. We added the following sentence to line 194: "The resonator introduced in this work is an initial demonstration of a topological device utilizing group-IV semiconductors, which shows promise for use in high-quality factor emitters that are directly integrated into the Si platform."

4. We inverted the citation numbers with punctuation marks throughout the text.

5. We changed the inset of Fig. 1(c) and increased the size of the figure.

6. We added "(d=0.3a)" in the caption of Fig. 3.

7. We changed the design of Fig. 3.

8. We removed "opportunely spaced" from a sentence in line 189.

9. We added "Fig. 5 shows that [...]" at the beginning of the sentence starting on line 213.

10. We removed a reference to Fig. S4 from line 229.

11. We changed the design of Fig. 8.

12. We added the DOI and identifier to Ref. [16]

13. We corrected a typo in Ref. [35]

14. We removed the URL from Ref. [38]

15. We added the DOI to Ref. [43]

16. We corrected the formatting to Ref. [49]

17. We added Ref. [58]

Published as SciPost Phys. Core 7, 039 (2024)

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