First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals
Open accessAbstract
By using the $\stackrel{\ensuremath{\rightharpoonup}}{k}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightharpoonup}}{p}$ method, we propose a first-principles theory to study the linear dispersions in phononic and photonic crystals. The theory reveals that only those linear dispersions created by doubly degenerate states can be described by a reduced Hamiltonian that can be mapped into the Dirac Hamiltonian and possess a Berry phase of $\ensuremath{-}\ensuremath{\pi}$. Linear dispersions created by triply degenerate states cannot be mapped into the Dirac Hamiltonian and carry no Berry phase, and, therefore should be called Dirac-like cones. Our theory is capable of predicting accurately the linear slopes of Dirac and Dirac-like cones at various symmetry points in a Brillouin zone, independent of frequency and lattice structure.
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The Berry phase is zero, caused by the existence of the longitudinal flat band.
“From the above analysis, we can see that the Berry phase is equal to zero, which is caused by the existence of the longitudinal flat band.This result is consistent with the discussion shown in [77].”
From Dirac Dispersion in Two-Dimensional Photonic Crystals (2012) · cites this paper as [77]
The emergence of linear bands as a consequence of accidental degeneracy at k=0 can also be obtained using multiple scattering theory or k·p perturbation.
“We note that the emergence of linear bands as a consequence of accidental degeneracy at k = 0 can also be obtained using multiple scattering theory [66] or k • p perturbation [76,77].”
From Dirac Dispersion in Two-Dimensional Photonic Crystals (2012) · cites this paper as [77]
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Dirac Dispersion in Two-Dimensional Photonic Crystals
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Self-citation
- Authors
- Mei, J., Wu, Y., Chan, C. T., & Zhang, Z.-Q.
- Affiliations
- Hong Kong University of Science and Technology (HK)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2012-07-24
- Volume
- 86
- Issue
- 3
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W2223459153
- Cited by
- 314
- References
- 9
- Citations by year
- 2026: 16 · 2025: 18 · 2024: 26 · 2023: 21 · 2022: 25 · 2021: 22 · 2020: 31 · 2019: 35 · 2018: 18 · 2017: 34 · 2016: 27 · 2015: 17 · 2014: 14 · 2013: 4 · 2012: 5
- FWCI
- 6.62
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Rare & Special e-Zone (The Hong Kong University of Science and Technology) (submittedVersion)
- King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Natural Science Foundation of China (10804086)
- Ministry of Education of the People's Republic of China (200804861018)
- King Abdullah University of Science and Technology
- Fundamental Research Funds for the Central Universities
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Engineering › Biomedical Engineering › Acoustic Wave Phenomena Research
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Photonic Crystals and Applications
- Keywords
- Dirac cones, phononic crystals, photonic crystals, Berry phase, linear dispersion, Dirac Hamiltonian, degenerate states, Brillouin zone, first-principles theory
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