Abelian Topology of Multifold Exceptional Points

The interplay between non-Hermiticity and topology induces a variety of unique phenomena. One of the typical examples is the emergence of exceptional points on which two bands touch due to the violation of diagonalizability. This two-band-touching is protected by non-Hermitian topology which is characterized by a winding number[1]. In addition to this theoretical progress, multifold exceptional points where more than three bands touch are reported for metamaterials[2] and open quantum systems[3]. However, their stability and topological protection remain unclear.

In this talk, we elucidate the topology of these multifold exceptional points[4]. Specifically, introducing the resultant winding number, we address the systematic characterization of generic and symmetry-protected multifold exceptional points. The former is stable in the absence of symmetry.