Acoustic Tunneling Study for Hexachiral Phononic Crystals Based on Dirac-Cone Dispersion Properties
Round 1
Reviewer 1 Report
The manuscript entitled “Acoustic tunneling study for hexachiral phononic crystal based on Dirac-cone dispersions properties” by L. Chen and Y. Liu is clearly written, original, and well-organized. It will be of great interest to the audience beyond the field of phononic crystals and its applications. In this manuscript, the authors theoretically study essential properties of phononic crystals in Dirac cones.
Specifically, the authors study theoretically the influence of geometric parameters on opening the Dirac cone states and directional band gaps by analyzing the linear dispersions for accidental degeneracy of the Bloch eigenstates in the hexachiral phononic crystals. The authors clearly defined a 2D hexachiral phononic crystal theory, described their main characteristics including the band structure. The band gaps and acoustic transmission tunneling are analyzed in detail near double Dirac cone frequency region. Finally, the obtained results will be of high importance for the field of topological insulators in the scope of hexachiral phononic crystals.
Minor comments to address/incorporate:
The authors did a good job by reviewing the literature in the introduction section; however, they also can additionally discuss relevant computational (https://pubs.acs.org/doi/abs/10.1021/acs.jpcc.6b08250) and experimental studies (https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.7b01324) in the field of phononic crystals.
This manuscript is subject to minor revisions.
Author Response
Detailed Response to Reviewers
No.: crystals-1509688
Title: Optimization study of bandgaps properties for two-dimensional chiral phononic crystals base on lightweight design
Reviewer:1
The manuscript entitled “Acoustic tunneling study for hexachiral phononic crystal based on Dirac-cone dispersions properties” by L. Chen and Y. Liu is clearly written, original, and well-organized. It will be of great interest to the audience beyond the field of phononic crystals and its applications. In this manuscript, the authors theoretically study essential properties of phononic crystals in Dirac cones.
Specifically, the authors study theoretically the influence of geometric parameters on opening the Dirac cone states and directional band gaps by analyzing the linear dispersions for accidental degeneracy of the Bloch eigenstates in the hexachiral phononic crystals. The authors clearly defined a 2D hexachiral phononic crystal theory, described their main characteristics including the band structure. The band gaps and acoustic transmission tunneling are analyzed in detail near double Dirac cone frequency region. Finally, the obtained results will be of high importance for the field of topological insulators in the scope of hexachiral phononic crystals.
Minor comments to address/incorporate:
The authors did a good job by reviewing the literature in the introduction section; however, they also can additionally discuss relevant computational (https://pubs.acs.org/doi/abs/10.1021/acs.jpcc.6b08250) and experimental studies (https:// pubs.acs.org/doi/abs/10.1021/acs.nanolett.7b01324) in the field of phononic crystals.
This manuscript is subject to minor revisions.
Response: At first, thank you for your time and thoughtful comments concerning our manuscript titled “Optimization study of bandgaps properties for two-dimensional chiral phononic crystals base on lightweight design” (ID: crystals-1509688). Those comments are all valuable and very helpful for revising and improving my manuscript. I have studied comments carefully and have made corrections which I hope meet with approval.
In the revised manuscript, this article has been checked carefully and the language has been polished by other colleagues who are good at English, and the grammar or syntax errors are corrected. Revised portions are marked in red in the paper.
In the revised manuscript, some useful references were added, such as Bolmatov, et al. J. Phys. Chem. C. 2016 and Bolmatov, et al. Nano Lett. 2017.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Manuscript: Acoustic tunneling study for hexachiral phononic crystal based on Dirac-cone dispersions properties
- The scientific and professional quality of the manuscript is a good form in generally.
- The section 2.1. can be further elaborated about cylindrical scatterers, connection ligaments, filler matrixs.
- Can experimental analysis of the study be make besides simulations? Please add if possible, if not, explain why.
- In the conclusion, the novelty of the researched subject to the literature can be explained in more detail, please explain more.
- Pleas improve the introduction part by adding novel studies related with subject such as;
https://doi.org/10.1007/s00419-021-02057-2
Author Response
Detailed Response to Reviewers
No.: crystals-1509688
Title: Optimization study of bandgaps properties for two-dimensional chiral phononic crystals base on lightweight design
Reviewer:2
Manuscript: Acoustic tunneling study for hexachiral phononic crystal based on Dirac-cone dispersions properties
- The scientific and professional quality of the manuscript is a good form in generally.
Response: At first, thank you for your time and thoughtful comments concerning our manuscript titled “Optimization study of bandgaps properties for two-dimensional chiral phononic crystals base on lightweight design” (ID: crystals-1509688). Those comments are all valuable and very helpful for revising and improving my manuscript. I have studied comments carefully and have made corrections which I hope meet with approval.
In the revised manuscript, this article has been checked carefully and the language has been polished by other colleagues who are good at English, and the grammar or syntax errors are corrected. Revised portions are marked in red in the paper.
- The section 2.1. can be further elaborated about cylindrical scatterers, connection ligaments, filler matrixs.
Response: In the revised manuscript, some description about cylindrical scatterers, connection ligaments, filler matrixs are rewritten, and the revised portions are marked in red in the paper.
- Can experimental analysis of the study be make besides simulations? Please add if possible, if not, explain why.
Response: In the Dirac cone properties and acoustic tunneling study for the phononic crystals, the model experiment is of great significance. However, in order to obtain a accurate experimental results, nice experimental environment, highly accurate sample manufactured process and high sensitive experiment platforms, are necessary. It means long experimental time and large experimental cost. Therefore, only numerical analysis are carried out in the present work at this stage. The experimental verification for numerical analysis results will be implemented in the future work.
- In the conclusion, the novelty of the researched subject to the literature can be explained in more detail, please explain more.
Response: In the revised manuscript, the conclusion part is rewritten and give a more clear overview of the research content for the present work. The conclusion " In this work, the Dirac cone and dispersion properties are systematically investigated for the hexachiral phononic crystal. The formation and breaking of four-fold accidental degenerate Dirac cone for phononic crystal are determined while the lattice constant is kept unchanged. The influences of design parameters such as coating thickness, ligament thickness, and cylindrical scatterer diameter on the acoustic topological phase transition are taken into account. Finally, the Dirac cone properties of hexachiral phononic crystal are unambiguously demonstrated by acoustic transmission calculation, and the tunneling effect is verified. The following conclusion are obtained by calculation data: (1) Due to the introduction of chirality properties, the acoustic manipulation ability of phononic crystal is significantly strengthened; (2) Variations in the geometric parameters break the corresponding Dirac cone, yielding the directional or complete band gaps; (3) In the double Dirac cone frequency region, the relationship between the design parameters and the directional band gaps width is approximately linear, while the ligaments thickness is insensitive in contrast to the other parameters; (4) According to the acoustic transmission calculation, an acoustic transmission tunneling effect is existing in the double Dirac cone frequency, and it provides a new idea for the application of metamaterials in acoustic transmission. Some conclusions in this work can provides technical support for design and application of innovative acoustic metamaterials.” had been modified as “The Dirac cone and dispersion properties are systematically investigated for the hexachiral phononic crystal in this study. The influences of design parameters such as coating thickness, ligament thickness, and cylindrical scatterer diameter on the acoustic topological phase transition are taken into account. The four-fold accidental degenerate Dirac cone of phononic crystal are emerged and disappeared by variations in the geometric parameters while the lattice constant is kept unchanged, and the band inversion process are occurred at the Dirac point. Finally, the Dirac cone properties of hexachiral phononic crystal are unambiguously demonstrated by acoustic transmission calculation, and the tunneling effect is verified. The following conclusion are obtained by numerical analysis: (1) By introduction of chirality properties, the acoustic transmission manipulation ability of hexachiral phononic crystal are significantly strengthened; (2) In the double Dirac cone frequency region, the relationship between the design parameters and the directional band gaps width is approximately linear, and the frequency linear dispersion properties is verified; (3) According to the acoustic transmission calculation, an acoustic transmission tunneling effect is existing in the double Dirac cone frequency; (4) The transmission acoustic wave and the incident acoustic wave will be consistent in acoustic pressure amplitude and phase corresponding to the double Dirac point state, the tunneling effect at Dirac point is further verified. Some conclusions in this work can provides technical support for design and application of innovative acoustic metamaterials.”.
- Pleas improve the introduction part by adding novel studies related with subject such as; https://doi.org/10.1007/s00419-021-02057-2
Response: In the revised manuscript, some useful references were added, such as Kaçın, et al. J. Arch. Appl. Mech. 2021.
Author Response File: Author Response.pdf
