Classification of Exceptional Nodal Topologies Protected by $\mathcal{PT}$ Symmetry

TL;DR

This paper completes the topological classification of exceptional nodal degeneracies protected by $ ext{PT}$ symmetry in up to three dimensions, revealing new complex topologies like knotted surfaces and high-order points in non-Hermitian photonic systems.

Contribution

It provides a comprehensive classification and introduces new models with previously unrecognized topological features such as knotted surfaces and high-order degeneracies.

Findings

Classified all $ ext{PT}$-protected exceptional nodal degeneracies in 3D.

Discovered new topologies including knotted surfaces and high-order points.

Provided simple models demonstrating these complex topologies.

Abstract

Exceptional degeneracies, at which both eigenvalues and eigenvectors coalesce, and parity-time ($\mathcal{PT}$) symmetry, reflecting balanced gain and loss in photonic systems, are paramount concepts in non-Hermitian systems. We here complete the topological classification of exceptional nodal degeneracies protected by $\mathcal{PT}$ symmetry in up to three dimensions and provide simple example models whose exceptional nodal topologies include previously overlooked possibilities such as second-order knotted surfaces of arbitrary genus, third-order knots and fourth-order points.