Topological Classificaton of Non-Hermitian Gapless Phases: Exceptional Points and Bulk Fermi Arcs

TL;DR

This paper classifies gapless phases in non-Hermitian systems based on complex-energy gaps, highlighting the topological nature of exceptional points and bulk Fermi arcs, and providing illustrative examples.

Contribution

It introduces a classification scheme for non-Hermitian gapless phases using point and line gaps, emphasizing the topological characterization of exceptional points and Fermi arcs.

Findings

Exceptional points are characterized by topological charges of point gaps.

Bulk Fermi arcs are topologically protected due to real line gap charges.

The classification scheme is demonstrated with specific examples.

Abstract

We provide classification of gapless phases in non-Hermitian systems according to two types of complex-energy gaps: point gap and line gap. We show that exceptional points, at which not only eigenenergies but also eigenstates coalesce, are characterized by gap closing of point gaps with nontrivial topological charges. Moreover, we find that bulk Fermi arcs accompanying exceptional points are robust because of topological charges for real line gaps. On the basis of the classification, some examples are also discussed.