• Photonics Research
  • Vol. 12, Issue 3, 491 (2024)
Jun Li1、2、3、*, Yaping Yang1、4、*, and C.-M. Hu2、5、*
Author Affiliations
  • 1MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
  • 2Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
  • 3e-mail: jli_phys@tongji.edu.cn
  • 4e-mail: yang_yaping@tongji.edu.cn
  • 5e-mail: hu@physics.umanitoba.ca
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    DOI: 10.1364/PRJ.509746 Cite this Article Set citation alerts
    Jun Li, Yaping Yang, C.-M. Hu. Multichannel coupling induced topological insulating phases with full multimerization[J]. Photonics Research, 2024, 12(3): 491 Copy Citation Text show less

    Abstract

    We propose and experimentally realize a class of quasi-one-dimensional topological lattices whose unit cells are constructed by coupled multiple identical resonators, with uniform hopping and inversion symmetry. In the presence of coupling-path-induced effective zero hopping within the unit cells, the systems are characterized by complete multimerization with degenerate -1 energy edge states for open boundary condition. Su–Schrieffer–Heeger subspaces with fully dimerized limits corresponding to pairs of nontrivial flat bands are derived from the Hilbert spaces. In particular, topological bound states in the continuum (BICs) are inherently present in even multimer chains, manifested by embedding the topological bound states into a continuous band assured by bulk-boundary correspondence. Moreover, we experimentally demonstrate the degenerate topological edge states and topological BICs in radio-frequency circuits.
    Hn=(0κκκ0κκκ0)n×n,

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    Hn(k)=(0κκ+κeikaκ0κκ+κeikaκ0)n×n,

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    ωn,o(k)=(2n/31(A++i3A)/2n/31(A+i3A)/20n/31+A+)κ,

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    ωn,e(k)=(2n/21n2/4+1+ncoska0n/21+(n2/4+1+ncoska)κ,

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    U4=12(1010101001010101),

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    H4BD(k)=(12+eika002+eika100001eika00eika1)κ,

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    J(ω)=1iω[(nLω2C)I+H]

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    H=(01/L1/L1/L01/L1/L1/L0)s×s,

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    S11=ZR0Z+R0,(A1)

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    Z=1+S111S11R0.(A2)

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    I=1RV,I=CdVdt,dIdt=1LV,(B1)

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    ZR(ω)=R,ZC(ω)=1iωC,ZL(ω)=iωL.(B2)

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    Ij(ω)=Ij0+k=1nIjk=Vj(ω)ZC(ω)+k=1nVj(ω)Vk(ω)ZL(ω),(B3)

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    I(ω)=J(ω)V(ω),(B4)

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    J(ω)=1iω[(nLω2C)I+H].(B5)

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    H=(01/L1/L0001/L01/L0001/L1/L01/L00001/L01/L1/L0001/L01/L0001/L1/L0)24×24,(B6)

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    H=(01/L1/L1/L00001/L01/L1/L00001/L1/L01/L01/L001/L1/L1/L01/L0000001/L01/L1/L1/L001/L01/L01/L1/L00001/L1/L01/L00001/L1/L1/L0)24×24,(B7)

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    U5=12(1/201/2011/201/201101000101001010),(C1)

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    H3×3=(1/2+22+1+K+1/22+1+K121+K1/221+K+1/22)κ(C2)

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    H2×2=(1eikaeika1)κ.(C3)

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    Ho1=(X+Y++K+(n3)/4Y++K(n3)/2Y+K(n3)/4Y+K+X)κ,(C4)

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    Ho2=(1eikaeika1)κ,(C5)

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    He1=(n/21n/2+eikan/2+eikan/21)κ,(C6)

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    He2=(1eikaeika1)κ.(C7)

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    Jun Li, Yaping Yang, C.-M. Hu. Multichannel coupling induced topological insulating phases with full multimerization[J]. Photonics Research, 2024, 12(3): 491
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