近日，韩国基础科学研究所教授Moon Jip Park团队研究了多频带非厄米系统中的伪厄米拓扑。这一研究成果于2025年4月9日发表在《物理评论A》杂志上。

非厄米系统的复本征能和非正交本征态表现出厄米系统中无法出现的独特拓扑现象。代表性的例子是非厄米皮肤效应和例外点。在二维参数空间中，可以通过调用置换群来建立多带非埃尔米特系统中不可分带的拓扑分类，其中置换的乘积表示由于空间中的异常点引起的状态交换。

研究组在这项工作中揭示了伪厄米线在多带非厄米拓扑中的作用。特别是，在二维空间中，非埃尔米特多带的不可分离性在拓扑上可以是非平凡的，没有异常点。作为伪厄米线作用的物理说明，他们研究了具有损耗材料的光子晶体系统的多频带结构。该工作建立在对非厄米多频带系统的基本和全面理解的基础上，还提供了非厄米系统的通用应用和实现，而不需要考虑异常点。

附：英文原文

Title: Pseudo-Hermitian topology in multiband non-Hermitian systems

Author: Jung-Wan Ryu, Jae-Ho Han, Chang-Hwan Yi, Hee Chul Park, Moon Jip Park

Issue&Volume: 2025/04/09

Abstract: The complex eigenenergies and nonorthogonal eigenstates of non-Hermitian systems exhibit unique topological phenomena that cannot appear in Hermitian systems. Representative examples are the non-Hermitian skin effect and exceptional points. In a two-dimensional parameter space, topological classifications of nonseparable bands in multiband non-Hermitian systems can be established by invoking a permutation group, where the product of the permutation represents state exchange due to exceptional points in the space. We unveil in this work the role of pseudo-Hermitian lines in non-Hermitian topology for multiple bands. In particular, the nonseparability of non-Hermitian multibands can be topologically nontrivial without exceptional points in two-dimensional space. As a physical illustration of the role of pseudo-Hermitian lines, we examine a multiband structure of a photonic crystal system with lossy materials. Our work builds on the fundamental and comprehensive understanding of non-Hermitian multiband systems and also offers versatile applications and realizations of non-Hermitian systems without the need to consider exceptional points.

DOI: 10.1103/PhysRevA.111.042205

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.111.042205