Construction and Observation of Flexibly Controllable High-Dimensional Non-Hermitian Skin Effects

TL;DR

This paper introduces a practical method to construct and observe high-dimensional non-Hermitian skin effects by assembling multiple 1D effects, demonstrated through acoustic metamaterials with controllable localization of sound fields.

Contribution

It proposes a bottom-to-top scheme to predict and synthesize high-dimensional NHSEs from 1D spectral topologies, enabling effective design and manipulation.

Findings

Successful experimental implementation of 2D nonreciprocal acoustic metamaterials

Demonstration of controllable multi-polar NHSEs and hybrid skin-topological effects

Frequency-selective localization of sound fields at desired locations

Abstract

Non-Hermitian skin effect (NHSE) is one of the most fundamental phenomena in non-Hermitian physics. Although it is established that one-dimensional NHSE originates from the nontrivial spectral winding topology, the topological origin behind the higher-dimensional NHSE remains unclear so far. This poses a substantial challenge in constructing and manipulating high-dimensional NHSEs. Here, an intuitive bottom-to-top scheme to construct high-dimensional NHSEs is proposed, through assembling multiple independent one-dimensional NHSEs. Not only the elusive high-dimensional NHSEs can be effectively predicted from the well-defined one-dimensional spectral winding topologies, but also the high-dimensional generalized Brillouin zones can be directly synthesized from the one-dimensional counterparts. As examples, two two-dimensional nonreciprocal acoustic metamaterials are experimentally implemented to demonstrate highly controllable multi-polar NHSEs and hybrid skin-topological effects, where the sound fields can be frequency-selectively localized at any desired corners and boundaries. These results offer a practicable strategy for engineering high-dimensional NHSEs, which could boost advanced applications such as selective filters and directional amplifiers.