Topological States in Twisted Pillared Phononic Plates

Abstract

In recent years, the advances in topological insulator in the fields of condensed matter have been extended to classical wave systems such as acoustic and elastic waves. However, the quantitative robustness study of topological states which is indispensable in practical realization is rarely reported. In this work, we proposed topologically protected edge states with zigzag, bridge and armchair interfaces in a new twisted phononic plate. The robustness of non-trivial band gap in bulk structure is clearly presented versus twisted angles, revealing a threshold of 5 degrees which is the key fundamental information for the robustness of topological edge states. We further defined a localized displacement ratio as an efficient parameter to characterize edge states. Due to the different orientation of the three interfaces, zigzag and bridge edge states show higher quantitative robustness in their localized displacement ratio. A map of robustness as a function of both frequency and twisted angle highlights the better performance of the topological zigzag edge state. Robustness is evaluated for twisted angle and for all possible types of interfaces for the first time, which benefits for the design and fabrication of solid functional devices with great potential applications.