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

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.