Anomalous topological edge states in non-Hermitian piezophononic media

TL;DR

This paper explores non-Hermitian topological phenomena in piezophononic media, revealing unconventional edge and bulk vibrational states influenced by nonreciprocity and gain/loss effects, with potential applications in ultrasonics.

Contribution

It demonstrates the existence of non-Hermitian skin effects and unconventional topological edge states in piezophononic media using numerical simulations, highlighting their dependence on electrical bias and boundary conditions.

Findings

Bulk bands are highly sensitive to crystal termination.

Reversing electrical bias switches edge and bulk vibrational localization.

In-gap edge states can delocalize despite skin effects.

Abstract

The bulk-boundary or bulk-edge correspondence is a principle relating surface confined states to the topological classification of the bulk. By combining non-Hermitian ingredients in terms of gain or loss with media that violate reciprocity, an unconventional non-Bloch bulk-boundary correspondence leads to unusual localization of bulk states at boundaries$-$a phenomenon coined non-Hermitian skin effect. Here we \textcolor{black}{numerically} employ the acoustoelectric effect in electrically biased and layered piezophononic media as a solid framework for non-Hermitian and nonreciprocal topological mechanics in the MHz regime. Thanks to a non-Hermitian skin effect for mechanical vibrations, we find that the bulk bands of finite systems are highly sensitive to the type of crystal termination, which indicates a failure of using traditional Bloch bands to predict the wave characteristics. More surprisingly, when reversing the electrical bias, we unveil how topological edge and bulk vibrations can be harnessed either at the same or opposite interface. Yet, while bulk states are found to display this unconventional skin effect, we further discuss how in-gap edge states in the same instant, counterintuitively are able to delocalize along the entire layered medium. We foresee that our predictions will stimulate new avenues in echo-less ultrasonics based on exotic wave physics.