Topological interface modes in aperiodic subwavelength resonator chains

TL;DR

This paper investigates topological interface modes in disordered one-dimensional subwavelength resonator chains, demonstrating their existence through a topological index based on a generalized Zak phase, supported by theoretical and numerical analysis.

Contribution

It introduces a two-fold topological characterization for disordered resonator chains using a generalized Zak phase, linking topological properties to localized interface modes.

Findings

Localized interface modes occur at boundaries between chains with different topological indices.

The topological index is a generalization of the Zak phase for chiral-symmetric Hamiltonians.

Numerical results support the theoretical predictions of interface mode existence.

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.