标题： 非厄米霍普夫绝缘体 显示英文标题

标题： Non-Hermitian Hopf insulators

摘要： 霍普夫绝缘体代表了一类独特的拓扑绝缘体，它们仅存在于两能带系统中，并且在引入额外能带时本质上是不稳定的。 同时，最近的研究表明，非厄米性会产生独特的复能隙结构，称为点隙，并产生在厄米系统中没有对应物的关联拓扑相。 然而，霍普夫绝缘体的非厄米对应物仍然 largely 难以捉摸。 在这里，我们根据同伦理论对两能带非厄米系统的拓扑相进行一般分类，并揭示仅在两能带情况下存在的霍普夫型点隙拓扑结构。 具体而言，我们揭示了具有手征对称性的三维系统（类别 AIII）和无对称性的四维系统（类别 A）中的这种霍普夫型点隙拓扑结构。 从厄米霍普夫绝缘体中明确构造出典型模型，我们进一步证明这些非厄米拓扑相会导致光谱上与体能带分离的异常点隙无边界态。 显示英文摘要

摘要： Hopf insulators represent a unique class of topological insulators that exist exclusively in two-band systems and are inherently unstable upon the inclusion of additional bands. Meanwhile, recent studies have shown that non-Hermiticity gives rise to distinctive complex-energy gap structures, known as point gaps, and associated topological phases with no analogs in Hermitian systems. However, non-Hermitian counterparts of Hopf insulators have remained largely elusive. Here, we generally classify topological phases of two-band non-Hermitian systems based on the homotopy theory and uncover Hopf-type point-gap topology present only for two bands. Specifically, we reveal such Hopf-type point-gap topology for three-dimensional systems with chiral symmetry (class AIII) and four-dimensional systems with no symmetry (class A). Explicitly constructing prototypical models from the Hermitian Hopf insulator, we further demonstrate that these non-Hermitian topological phases lead to anomalous point-gapless boundary states spectrally detachable from the bulk bands.