Spectra of bulk or edges in topological insulators are often made complex by non-Hermiticity. Here, we show that symmetry protection enables entirely real spectra for both bulk and edges even in non-Hermitian topological insulators. In particular, we demonstrate the entirely real spectra without non-Hermitian skin effects due to a combination of pseudo-Hermiticity and Kramers degeneracy. This protection relies on nonspatial fundamental symmetry and has stability against disorder. As an illustrative example, we investigate a non-Hermitian extension of the Bernevig-Hughes-Zhang model. The helical edge states exhibit oscillatory dynamics due to their nonorthogonality as a unique non-Hermitian feature.

中文翻译：

---

非Hermitian拓扑绝缘体中的实谱

拓扑绝缘体中的体积或边缘的光谱通常会由于非赫米蒂性而变得复杂。在这里，我们表明，即使在非Hermitian拓扑绝缘体中，对称保护也可以使块体和边缘具有完全真实的光谱。尤其是，我们证明了由于伪赫米蒂性和Kramers简并性的组合而没有非赫米特皮肤效应的完全真实的光谱。这种保护依赖于非空间基本对称性，并且对疾病具有稳定性。作为说明性示例，我们研究了Bernevig-Hughes-Zhang模型的非Hermitian扩展。螺旋边缘状态由于其非正交性（作为唯一的非Hermitian特征）而具有振荡动力学。