Non-Hermitian three-dimensional two-band Hopf insulator

The Hopf insulator is a three-dimensional topological insulator outside the standard classification of topological insulators. Here we consider two types of non-Hermitian Hopf insulators, one without and one with the non-Hermitian skin effect. The isolated gapless points of the Hermitian model are broadened into finite regimes in the non-Hermitian models. However, the modulus of the Hopf index remains quantized in the gapped regions. The model...