Non-Hermitian Hopf insulators

Non-Hermiticity ubiquitously appears in nature and enriches topological phases of matter. Extending beyond the existing $K$-theory framework, the authors reveal here Hopf-type topology requiring exactly two bands, intrinsic to non-Hermitian systems. Explicitly constructing prototypical models, they further demonstrate that these non-Hermitian topological phases support anomalous boundary states detachable from the bulk bands.