Classification of exceptional nodal topologies protected by PT symmetry

Abstract

Exceptional degeneracies, at which both eigenvalues and eigenvectors coalesce, and parity-time (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 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.