Phononic crystals with non-quantized Zak phases for controlling interface state frequencies

Abstract

Topological interface and edge states have been extensively studied in phononic and photonic crystals with Zak phases quantized at 0 or π. In this work, we design phononic crystals with non-quantized Zak phases ranging from −0.45π to 0.45π by deliberately breaking the symmetry of the unit cell. Through adjustments of the non-quantized Zak phase, we control the phases of waves reflected from the phononic crystals, ensuring that the interface state occurs at a desired frequency. We provide two applications of such frequency control of interface states. The first application focuses on enhancing wave energy localization in the interface state. We identify the frequencies within the band gap at which the reflection coefficient of the phononic crystals is closest to 1, enabling them to function as near-perfect mirrors. We then induce the interface state at that frequency and compare the localized energy with that at other frequencies. The second application involves controlling the frequencies of interface and edge states to achieve their occurrence at the same frequency, revealing a distinctive state characterized by the overlap of these states. This overlap leads to the simultaneous localization of wave energy at both the interface and edges.