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

Abstract

Exceptional degeneracies, at which both eigenvalues and eigenvectors coalesce, and parity-time ($\mathcal{P}\mathcal{T}$) 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 $\mathcal{P}\mathcal{T}$ 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.

Including supplementary material

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