A Unified Symmetry-Constrained Framework for Band Inversions in Photonic Crystals with $C_n$ Symmetry
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911147775492096 |
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| author | Tao, Ze Liu, Fujun |
| author_facet | Tao, Ze Liu, Fujun |
| contents | The lack of a unified theoretical framework for characterizing band inversions across different crystal symmetries hinders the rapid development of topological photonic band engineering. To address this issue, we have constructed a framework constrained by symmetry $k \cdot p$ that universally models bands near high-symmetry points for symmetric photonic crystals $C_6$, $C_4$, $C_3$, and $C_2$. This framework enables a coefficient-free quantitative diagnosis of band topology. We have demonstrated the power of this framework by systematically engineering band inversions. In $C_6$ crystals, we induce a reopening of the linear gap at $Γ$. In $C_4$ systems, mirror symmetry enforces a characteristic quadratic coupling leading to distinct spectral features. Our analysis further reveals that a lone $E$ doublet prevents inversion at the $Γ$ point in $C_3$ symmetry, while $C_2$ symmetry facilitates a unique inversion of $Y$ pointsints with anisotropic gap. This symmetry-first, fit-free approach establishes a direct link between experimental band maps and the extraction of fundamental topological parameters. It offers a universal tool for inversion and coupling-order identification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08620 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Unified Symmetry-Constrained Framework for Band Inversions in Photonic Crystals with $C_n$ Symmetry Tao, Ze Liu, Fujun Optics Materials Science Mathematical Physics Computational Physics The lack of a unified theoretical framework for characterizing band inversions across different crystal symmetries hinders the rapid development of topological photonic band engineering. To address this issue, we have constructed a framework constrained by symmetry $k \cdot p$ that universally models bands near high-symmetry points for symmetric photonic crystals $C_6$, $C_4$, $C_3$, and $C_2$. This framework enables a coefficient-free quantitative diagnosis of band topology. We have demonstrated the power of this framework by systematically engineering band inversions. In $C_6$ crystals, we induce a reopening of the linear gap at $Γ$. In $C_4$ systems, mirror symmetry enforces a characteristic quadratic coupling leading to distinct spectral features. Our analysis further reveals that a lone $E$ doublet prevents inversion at the $Γ$ point in $C_3$ symmetry, while $C_2$ symmetry facilitates a unique inversion of $Y$ pointsints with anisotropic gap. This symmetry-first, fit-free approach establishes a direct link between experimental band maps and the extraction of fundamental topological parameters. It offers a universal tool for inversion and coupling-order identification. |
| title | A Unified Symmetry-Constrained Framework for Band Inversions in Photonic Crystals with $C_n$ Symmetry |
| topic | Optics Materials Science Mathematical Physics Computational Physics |
| url | https://arxiv.org/abs/2509.08620 |