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Topological interface modes in aperiodic subwavelength resonator chains

by H. Ammari and J. Qiu and A. Uhlmann

(Report number 2025-30)

Abstract
We consider interface modes in block disordered subwavelength resonator chains in one dimension. Based on the capacitance operator formulation, which provides a first-order approximation of the spectral properties of dimer-type block resonator systems in the subwavelength regime, we show that a two-fold topological characterization of a block disordered resonator chain is available if it is of dominated type. The topological index used for the characterization is a generalization of the Zak phase associated with one-dimensional chiral-symmetric Hamiltonians. As a manifestation of the bulk-edge correspondence principle, we prove that a localized interface mode occurs whenever the system consists of two semi-infinite chains with different topological characters. We also illustrate our results from a dynamic perspective, which provides an explicit geometric picture of the interface modes, and finally present a variety of numerical results to complement the theoretical results.

Keywords: one-dimensional aperiodic chain, dimer-type block disordered system, topologically protected interface eigenmode, bandgap, uniform hyperbolicity, quasi-periodic system, Zak phase

@Techreport{AQU25_1151,
  author = {H. Ammari and J. Qiu and A. Uhlmann},
  title = {Topological interface modes in aperiodic subwavelength resonator chains},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2025-30},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2025/2025-30.pdf },
  year = {2025}
}

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