Non-Hermitian Topology of Exceptional Points

Kohei Kawabata, Takumi Bessho, Masatoshi Sato

Published 2019-02-22Version 1

We present a general theory on topology of exceptional points. On the basis of two distinct complex-energy gaps, a point-like or line-like vacant region in the complex-energy plane, we reveal that gapless points in non-Hermitian systems are categorized into two: the one around which only a point-like gap is open and the other around which both gaps are open. Whereas the latter has counterparts to conventional Hermitian systems, the former is unique to non-Hermitian systems, characterizing exceptional points. Based on this observation, we complete classification of topologically stable symmetry-protected exceptional points at generic momentum points for each type of complex-energy gaps. This theory clarifies that exceptional points possess multiple topological structures identified by a couple of independent topological charges. Moreover, our classification theory predicts unknown exceptional points; an exceptional point in three dimensions is constructed as an illustration.