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

• URL: http://arxiv.org/abs/2106.04582v3
• Date: Mon, 15 Nov 2021 17:04:25 GMT
• Title: Classification of Exceptional Nodal Topologies Protected by $\mathcal{PT}$ Symmetry
• Authors: Marcus St{\aa}lhammar, Emil J. Bergholtz
• Abstract summary: We classify exceptional nodal degeneracies protected by $mathcalPT$ symmetry in up to three dimensions. These exceptional nodal topologies include previously overlooked possibilities such as second-order knotted surfaces of arbitrary genus, third-order knots and fourth-order points.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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