Topological classification for intersection singularities of exceptional surfaces in pseudo-Hermitian systems

Abstract

Non-Hermitian systems are known for their intriguing topological properties, which underpin various exotic physical phenomena. Exceptional points, in particular, play a pivotal role in fine-tuning these systems for optimal device functionality and material characteristics. These points can give rise to exceptional surfaces with embedded lower-dimensional non-isolated singularities. Here we introduce a topological classification for non-defective intersection lines of exceptional surfaces, where exceptional surfaces intersect transversally. We achieve this classification by constructing a quotient space of an order-parameter space under equivalence relations of eigenstates. We unveil that the fundamental group of these gapless structures is a non-Abelian group on three generators. This classification not only reveals a unique form of non-Hermitian gapless phases featuring a chain of non-defective intersection lines but also predicts the unexpected existence of topological edge states in one-dimensional lattice models protected by the intersection singularities. Our classification opens avenues for realizing robust topological phases.Non-Hermitian physics expands the range of exotic features that can be explored in non-trivial topological systems and exceptional points play a prominent role. Here, the authors report a topological classification of the intersections of exceptional surfaces and predicted topologically protected edge states that arise from the intersections.