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.

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.