近日，中国科学院物理研究所的胡海平及其研究团队取得一项新进展。经过不懈努力，他们揭示高维均匀光谱中非厄米集肤效应的拓扑起源。相关研究成果已于2024年7月25日在国际知名学术期刊《科学通报》上发表。

本研究采用点能隙视角，揭示了所有空间维度的非厄米集肤效应都源于点能隙。研究人员引入了均匀谱的概念，并揭示了无论晶格几何形状如何，它们的能谱都是由均匀谱给出，尽管它们的集肤模式的表现可能不同。在均匀光谱的基础上，研究人员演示了如何用一般的晶格切割来解释集肤效应，并通过动量基变换建立不同几何形状的趋肤模式之间的联系。这项研究结果凸显了点能隙所起的关键作用，为所有维度的非厄米集肤效应的拓扑起源提供了统一的理解。

据悉，非厄米集肤效应是非厄米系统边界附近特征态聚集的一种标志性现象。虽然在一维上进行了广泛的研究，但理解集肤效应并将非布洛赫带理论扩展到更高的维度遇到了巨大的挑战，主要是由于无限晶格几何或开放边界条件。

附：英文原文

Title: Topological origin of non-Hermitian skin effect in higher dimensions and uniform spectra

Author: Haiping Hu

Issue&Volume: 2024/07/25

Abstract: The non–Hermitian skin effect is an iconic phenomenon characterized by the aggregation of eigenstates near the system boundaries in non–Hermitian systems. While extensively studied in one dimension, understanding the skin effect and extending the non-Bloch band theory to higher dimensions encounters a formidable challenge, primarily due to infinite lattice geometries or open boundary conditions. This work adopts a point-gap perspective and unveils that non-Hermitian skin effect in all spatial dimensions originates from point gaps. We introduce the concept of uniform spectra and reveal that regardless of lattice geometry, their energy spectra are universally given by the uniform spectra, even though their manifestations of skin modes may differ. Building on the uniform spectra, we demonstrate how to account for the skin effect with generic lattice cuts and establish the connections of skin modes across different geometric shapes via momentum-basis transformations. Our findings highlight the pivotal roles point gaps play, offering a unified understanding of the topological origin of non–Hermitian skin effect in all dimensions.

DOI: 10.1016/j.scib.2024.07.022

Source: https://www.sciencedirect.com/science/article/abs/pii/S2095927324005024