Non-Hermitian skin effect (NHSE) is one of the most fundamental phenomena in non-Hermitian physics. It is established that 1D NHSE originates from the nontrivial spectral winding topology. However, the topological origin behind the higher-dimensional NHSE remains unclear, which 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 1D NHSEs. Not only the elusive high-dimensional NHSEs can be effectively predicted from the well-defined 1D spectral winding topologies, but also the high-dimensional generalized Brillouin zones can be directly synthesized from the 1D counterparts. As examples, two 2D 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 can boost advanced applications such as selective filters and directional amplifiers.

中文翻译：

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灵活可控高维非厄米集肤效应的构建与观测


非厄米趋肤效应（NHSE）是非厄米物理学中最基本的现象之一。已确定一维 NHSE 源自非平凡的谱缠绕拓扑。然而，高维 NHSE 背后的拓扑起源仍不清楚，这对构建和操纵高维 NHSE 提出了巨大的挑战。在这里，通过组装多个独立的一维 NHSE，提出了一种直观的自下而上的方案来构造高维 NHSE。不仅可以从明确定义的一维谱缠绕拓扑中有效预测难以捉摸的高维 NHSE，而且可以从一维对应物直接合成高维广义布里渊区。例如，通过实验实现了两种 2D 非互易声学超材料，以展示高度可控的多极 NHSE 和混合皮肤拓扑效应，其中声场可以频率选择性地定位在任何所需的角落和边界。这些结果为设计高维 NHSE 提供了一种可行的策略，可以促进选择性滤波器和定向放大器等高级应用。