Spectral Riemann Sheet Topology of Gapped Non-Hermitian Systems

TL;DR

This paper explores the topological configurations of complex spectra in gapped non-Hermitian systems, highlighting how exceptional points and branch cuts define distinct topological phases.

Contribution

It introduces a new topological classification based on Riemann sheet configurations and gap closures in non-Hermitian models.

Findings

Exceptional points are linked to topological transitions in spectra.

Gap closing is necessary for tuning between topological configurations.

Protected branch cuts are associated with energy gaps in the spectrum.

Abstract

We show topological configurations of the complex-valued spectra in gapped non-Hermitian systems. These arise when the distinctive EPs in the energy Riemann sheets of such models are annihilated after threading them across the boundary of the Brillouin zone. This results in a non-trivially closed branch cut that is protected by an energy gap in the spectrum. Their presence or absence establishes topologically distinct configurations for fully non-degenerate systems and tuning between them requires a closing of the gap, forming exceptional point degeneracies. We provide an outlook toward experimental realizations in metasurfaces and single-photon interferometry.