Floquet hybrid skin-topological effects in checkerboard lattices with large Chern numbers

Yi-Ling Zhang; Li-Wei Wang; Yang Liu; Zhao-Xian Chen; Jian-Hua Jiang

doi:10.1364/PRJ.550282

Journals >Photonics Research >Volume 13 >Issue 5 >Page 1321 > Article

Photonics Research
Vol. 13, Issue 5, 1321 (2025)

Floquet hybrid skin-topological effects in checkerboard lattices with large Chern numbers

Yi-Ling Zhang¹, Li-Wei Wang², Yang Liu¹, Zhao-Xian Chen³, and Jian-Hua Jiang^1,4,5,*

Author Affiliations

¹School of Physical Science and Technology, and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China

²School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China

³National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, and College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China

⁴School of Biomedical Engineering, Division of Life Sciences and Medicine, University of Science and Technology of China, Hefei 230026, China

⁵Suzhou Institute for Advanced Research, University of Science and Technology of China, Suzhou 215123, China

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DOI: 10.1364/PRJ.550282 Cite this Article Set citation alerts

Yi-Ling Zhang, Li-Wei Wang, Yang Liu, Zhao-Xian Chen, Jian-Hua Jiang, "Floquet hybrid skin-topological effects in checkerboard lattices with large Chern numbers," Photonics Res. 13, 1321 (2025) Copy Citation Text

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Abstract

Non-Hermitian topology provides an emergent research frontier for studying unconventional topological phenomena and developing new materials and applications. Here, we study the non-Hermitian Chern bands and the associated non-Hermitian skin effects in Floquet checkerboard lattices with synthetic gauge fluxes. Such lattices can be realized in a network of coupled resonator optical waveguides in two dimensions or in an array of evanescently coupled helical optical waveguides in three dimensions. Without invoking nonreciprocal couplings, the system exhibits versatile non-Hermitian topological phases that support various skin-topological effects. Remarkably, the non-Hermitian skin effect can be engineered by changing the symmetry, revealing rich non-Hermitian topological bulk-boundary correspondences. Our system offers excellent controllability and experimental feasibility, making it appealing for exploring diverse non-Hermitian topological phenomena in photonics.

H (z) = H_{SSH} + H_{loss - potential} (z) + H_{inter - SSH} (z),

(1)

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H_{SSH} = \sum_{i, j} t_{1} (a_{i, j}^{†} b_{i, j} + d_{i, j}^{†} c_{i, j} + b_{i, j}^{†} d_{i, j} + a_{i, j}^{†} c_{i, j}) + \sum_{i, j} t_{2} (a_{i + 1, j}^{†} b_{i, j} + d_{i + 1, j}^{†} c_{i, j} + b_{i, j + 1}^{†} d_{i, j} + a_{i, j + 1}^{†} c_{i, j}) + h .c.,

(2)

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H_{loss - potential} (z) = \sum_{i, j} (V_{i, j} (z) - i γ) ξ_{i, j}^{†} ξ_{i, j} .

(3)

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H_{eff} = i / T \log (U),

(4)

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i \partial_{z} | ψ (z) ⟩ = H (z) | ψ (z) ⟩ .

(A1)

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i \partial_{z} | ϕ (z) ⟩ = H^{'} (z) | ϕ (z) ⟩,

(A2)

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H^{'} (z) = \sum_{i, j} t_{1} (a_{i, j}^{†} b_{i, j} + d_{i, j}^{†} c_{i, j} + b_{i, j}^{†} c_{i, j} + a_{i, j}^{†} d_{i, j}) + \sum_{i, j} t_{2} (a_{i + 1, j}^{†} b_{i, j} + d_{i + 1, j}^{†} c_{i, j} + b_{i, j + 1}^{†} c_{i, j} + a_{i, j + 1}^{†} d_{i, j}) + \sum_{i, j} (G_{1} (z) (e_{i, j}^{†} a_{i, j}) + G_{2} (z) (e_{i, j}^{†} b_{i, j})) + \sum_{i, j} (G_{3} (z) (e_{i, j}^{†} c_{i, j}) + G_{4} (z) (e_{i, j}^{†} d_{i, j}) + i γ (ξ_{i, j}^{†} ξ_{i, j})) + h .c .

(A3)

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H_{n} = \sum_{i, j} t_{1} (a_{i, j}^{†} b_{i, j} + d_{i, j}^{†} c_{i, j} + b_{i, j}^{†} c_{i, j} + a_{i, j}^{†} d_{i, j}) + \sum_{i, j} t_{2} (a_{i + 1, j}^{†} b_{i, j} + d_{i + 1, j}^{†} c_{i, j} + b_{i, j + 1}^{†} c_{i, j} + a_{i, j + 1}^{†} d_{i, j}) + \sum_{i, j} g_{m} e^{i n θ_{m}} ((e_{i, j}^{†} a_{i, j}) + (e_{i, j}^{†} b_{i, j}) + (e_{i, j}^{†} c_{i, j}) + (e_{i, j}^{†} d_{i, j})) + \sum_{i, j} i γ (ξ_{i, j}^{†} ξ_{i, j}) + h .c .

(A4)

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H_{eff} = H_{0} + \frac{(H_{- 1}, H_{1})}{ω} + O (\frac{1}{ω^{2}}) = \sum_{i, j} t_{1} (a_{i, j}^{†} b_{i, j} + d_{i, j}^{†} c_{i, j} + b_{i, j}^{†} c_{i, j} + a_{i, j}^{†} d_{i, j}) + \sum_{i, j} t_{2} (a_{i + 1, j}^{†} b_{i, j} + d_{i + 1, j}^{†} c_{i, j} + b_{i, j + 1}^{†} c_{i, j} + a_{i, j + 1}^{†} d_{i, j}) + \frac{1}{ω} \sum_{i, j} (g_{1} e^{i θ_{1}} (e_{i, j}^{†} a_{i, j}) + g_{2} e^{i θ_{2}} (e_{i, j}^{†} b_{i, j})) + \frac{1}{ω} \sum_{i, j} (g_{3} e^{i θ_{3}} (e_{i, j}^{†} c_{i, j}) + g_{4} e^{i θ_{4}} (e_{i, j}^{†} d_{i, j})) + \sum_{i, j} i γ (ξ_{i, j}^{†} ξ_{i, j}) + h .c .

(A5)

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| ψ (t, n) ⟩ = U (t) | ψ (t_{0}, n) ⟩,

(C1)

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| ψ (t, k) ⟩ = \sum_{n = 1}^{N} | ψ (t, n) ⟩ e^{- i k x_{n}} .

(C2)

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| ψ (t, k) ⟩ = \sum_{j} c_{j} (t, k) | ϕ_{j, R} (k) ⟩, c_{j} (t, k) = ⟨ ϕ_{j, L} (k) | ψ (t, k) ⟩,

(C3)

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⟨ ϕ_{i, L} (k) | ϕ_{j, R} (k) ⟩ = δ_{i, j} .

(C4)

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| ψ (t, k) ⟩ = \sum_{j} ⟨ ϕ_{j, L} (k) | ψ (t_{0}, k) ⟩ \exp (- i E_{j} t) | ϕ_{j, R} (k) ⟩ = \sum_{j} c_{j} (t, k) e^{- i Re (E_{j}) t} e^{Im (E_{j}) t} | ϕ_{j, R} (k) ⟩ .

(C5)

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Yi-Ling Zhang, Li-Wei Wang, Yang Liu, Zhao-Xian Chen, Jian-Hua Jiang, "Floquet hybrid skin-topological effects in checkerboard lattices with large Chern numbers," Photonics Res. 13, 1321 (2025)

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