Synthetic Kramers pair in phononic elastic plates and helical edge states on a dislocation interface

TL;DR

This paper demonstrates the creation of synthetic helical edge states in a 2D phononic elastic plate with a Kekulé pattern, revealing non-invariant topological properties and experimentally visualizing edge states on a dislocation interface.

Contribution

It introduces a novel phononic platform with a Kekulé-distorted pattern to realize and observe synthetic helical edge states, challenging traditional topological invariants.

Findings

Pseudospin and Chern numbers are not invariant in this system.

Synthetic helical edge states are successfully implemented and visualized.

The $ ext{Z}_2$ number alone is insufficient to predict edge states.

Abstract

In conventional theories, topological band properties are intrinsic characteristics of the bulk material and do not depend on the choice of the reference frame. In this scenario, the principle of bulk-edge correspondence can be used to predict the existence of edge states between topologically distinct materials. In this study, we propose and carefully examine a 2D elastic phononic plate with a Kekul\'e-distorted honeycomb pattern engraved on it. It is found that the pseudospin and the pseudospin-dependent Chern numbers are not invariant properties, and the $\mathbb{Z}_2$ number is no longer a sufficient indicator to examine the existence of the edge state. The distinctive pseudospin texture and the pseudomagnetic field are also revealed. Finally, we successfully devise and experimentally implement the synthetic helical edge states on a dislocation interface connecting two subdomains with bulk pattern identical up to a relative translation. The edge state is also imaged via laser vibrometry.