Hopf exceptional points

Exceptional points at which eigenvalues and eigenvectors of non-Hermitian matrices coalesce are ubiquitous in the description of a wide range of platforms from photonic or mechanical metamaterials to open quantum systems. Here, we introduce a class of Hopf exceptional points (HEPs) that are protected by the Hopf invariants (including the higher-dimensional generalizations) and which exhibit phenomenology sharply distinct from conventional exceptional points. Saliently, owing to their Z_2 ℤ 2 topological invariant related to the Witten anomaly, three-fold HEPs and symmetry-protected five-fold HEPs act as their own . Furthermore, based on higher homotopy groups of spheres, we predict the existence of multifold HEPs and symmetry-protected HEPs with non-Hermitian topology captured by a range of finite groups (such as Z_3 ℤ 3 , Z₁₂ ℤ 12 , or Z₂₄ ℤ 24 ) beyond the periodic table of Bernard-LeClair symmetry classes.