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Abstract

Exceptional points of order n (EPns) appear in non-Hermitian systems as points where the eigen- values and eigenvectors coalesce. Whereas EP2s generically appear in two dimensions (2D), higher- order EPs require a higher-dimensional parameter space to emerge. In this work, we provide a complete characterization the appearance of symmetry-induced higher-order EPs in 2D parameter space. We find that besides EP2s only EP3s, EP4s, and EP5s can be stabilized in 2D. Moreover, these higher-order EPs must always appear in pairs with their dispersion determined by the sym- metries. Upon studying the complex spectral structure around these EPs, we find that depending on the symmetry, EP3s are accompanied by EP2 arcs, and 2- and 3-level open Fermi structures. Similarly, EP4s and closely related EP5s, which arise due to multiple symmetries, are accompanied by exotic EP arcs and open Fermi structures. For each case, we provide an explicit example. We also comment on the topological charge of these EPs, and discuss similarities and differences between symmetry-protected higher-order EPs and EP2s.