Classification of exceptional nodal topologies protected by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math> symmetry
Marcus Stålhammar, Emil J. Bergholtz
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.
Topics & Concepts
Eigenvalues and eigenvectorsSymmetry (geometry)MathematicsSimple (philosophy)Network topologyOrder (exchange)Hermitian matrixCombinatoricsTopology (electrical circuits)Discrete mathematicsAlgorithmGeometryPure mathematicsComputer sciencePhysicsQuantum mechanicsOperating systemPhilosophyEpistemologyEconomicsFinanceQuantum Mechanics and Non-Hermitian PhysicsTopological Materials and PhenomenaNonlinear Photonic Systems