Braid Protected Topological Band Structures with Unpaired Exceptional Points

We demonstrate the existence of topologically stable unpaired exceptional points (EPs), and construct simple non-Hermitian (NH) tight-binding models exemplifying such remarkable nodal phases. While Fermion doubling, i.e. the necessity of compensating the topological charge of a stable nodal point by an anti-dote, rules out a direct counterpart of our findings in the realm of Hermitian semimetals, here we derive how non-commuting braids of complex energy levels may stabilize unpaired EPs. Drawing on this insight, we reveal the occurrence of a single, unpaired EP, manifested as a non-Abelian monopole in the Brillouin zone of a minimal three-band model. This third-order degeneracy cannot be fully gapped by any local perturbation. Instead, it may split into simpler (second-order) degeneracies that can only gap out by pairwise annihilation after having moved around inequivalent large circles of the Brillouin zone. Our results imply the incompleteness of a topological classification based on winding numbers, due to non-Abelian representations of the braid group intertwining three or more complex energy levels.