Classification of Exceptional Points and Non-Hermitian Topological Semimetals

Exceptional points are universal level degeneracies induced by non-Hermiticity. Whereas past decades witnessed their new physics, the unified understanding has yet to be obtained. Here we present the complete classification of generic topologically stable exceptional points according to two types of complex-energy gaps and fundamental symmetries of charge conjugation, parity, and time reversal. This classification reveals unique non-Hermitian gapless structures with no Hermitian analogs and systematically predicts unknown non-Hermitian semimetals and nodal superconductors; a topological dumbbell of exceptional points in three dimensions is constructed as an illustration. Our work paves the way toward richer phenomena and functionalities of exceptional points and non-Hermitian topological semimetals.