# Zak phase and band inversion in dimerized one-dimensional locally resonant metamaterials

## TL;DR

This paper investigates the Zak phase and topological transitions in dimerized one-dimensional locally resonant metamaterials, revealing how band inversion and interface states are influenced by dimerization and singular points in the band structure.

## Contribution

It provides the first detailed analysis of Zak phase and topological phase transitions in locally resonant metamaterials, linking singular points to topological properties and demonstrating interface states experimentally.

## Key findings

- Singular points in the band contribute  to the Zak phase.
- Topological transition occurs with band inversion at a critical dimerization.
- Experimental demonstration of interface states between topologically distinct structures.

## Abstract

Zak phase, which refers to the Berry's phase picked up by a particle moving across the Brillouin zone, characterizes the topological properties of Bloch bands in one-dimensional periodic system. Here the Zak phase in dimerized one-dimensional locally resonant metamaterials is investigated. It is found that there are some singular points in the bulk band across which the Bloch states contribute {\pi} to the Zak phase, whereas while in the rest of the band the contribution is nearly zero. These singular points associated with zero reflection are caused by two different mechanisms: the dimerization-independent anti-resonating of each branch, and the dimerization-dependent destructive interference in multiple backscattering. The structure undergoes a topological transition point in the band structure where the band inverts and the Zak phase, which is determined by the numbers of singular points in the bulk band, changes following a shift in dimerization parameter. Finally, the interface state between two dimerized metamaterial structures with different topological property in the first band gap is demonstrated experimentally. The quasi-one-dimensional configuration of the system allows one to explore topology-inspired new methods and applications in the sub-wavelength scale.

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Source: https://tomesphere.com/paper/1802.08099