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Volume 10
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10.3390/photonics10090992
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Article

The Topological Origin of Boundary Charges at Edges of One-Dimensional Crystals without Inversion Symmetry

by
Pengdong Shi
1,
Xingchao Qi
2,
Yufu Liu
1,
Xianjun Wang
1,
Langlang Xiong
2 and
Xunya Jiang
1,*
1
Department of Illuminating Engineering and Light Sources, School of Information Science and Engineering, Fudan University, Shanghai 200433, China
2
Institute of Future Lighting, Academy for Engineering and Technology, Fudan University, Shanghai 200433, China
*
Author to whom correspondence should be addressed.
Photonics 2023, 10(9), 992; https://doi.org/10.3390/photonics10090992
Submission received: 3 August 2023 / Revised: 24 August 2023 / Accepted: 29 August 2023 / Published: 30 August 2023
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Abstract

We report the edge states and non-zero boundary charges in one-dimensional photonic crystals (1D PhCs) without inversion symmetry. In contrast to common 1D systems, we show that edge states corresponding to non-zero boundary charges do exist in these asymmetric 1D PhCs even if we cannot obtain non-integral topological invariants. Moreover, an edge state could be observed in the interface between the PhC without inversion symmetry and the well-defined trivial PhC. Finally, the origin of the non-quantized boundary charges is unveiled by the non-central Wannier center. Not only exact solutions of photonic systems, but the above topological phenomena can also be found in the tight-binding models. This work proposes a way to study the 1D symmetries-broken systems and provides models to show the topological origin of boundary charges, which is suitable for both classic systems and quantum systems.
Keywords: photonic crystal; boundary charge; edge state; inversion symmetry photonic crystal; boundary charge; edge state; inversion symmetry

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MDPI and ACS Style

Shi, P.; Qi, X.; Liu, Y.; Wang, X.; Xiong, L.; Jiang, X. The Topological Origin of Boundary Charges at Edges of One-Dimensional Crystals without Inversion Symmetry. Photonics 2023, 10, 992. https://doi.org/10.3390/photonics10090992

AMA Style

Shi P, Qi X, Liu Y, Wang X, Xiong L, Jiang X. The Topological Origin of Boundary Charges at Edges of One-Dimensional Crystals without Inversion Symmetry. Photonics. 2023; 10(9):992. https://doi.org/10.3390/photonics10090992

Chicago/Turabian Style

Shi, Pengdong, Xingchao Qi, Yufu Liu, Xianjun Wang, Langlang Xiong, and Xunya Jiang. 2023. "The Topological Origin of Boundary Charges at Edges of One-Dimensional Crystals without Inversion Symmetry" Photonics 10, no. 9: 992. https://doi.org/10.3390/photonics10090992

APA Style

Shi, P., Qi, X., Liu, Y., Wang, X., Xiong, L., & Jiang, X. (2023). The Topological Origin of Boundary Charges at Edges of One-Dimensional Crystals without Inversion Symmetry. Photonics, 10(9), 992. https://doi.org/10.3390/photonics10090992

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