Homotopy characterization of non-Hermitian Hamiltonians

There has been much recent interest in understanding topological band theory of non-Hermitian systems. Most work has focused on the Chern number in these systems, although interesting phenomena related to an eigenvalue winding number has also been reported. Here, the authors give a complete topological classification using homotopy theory. They find that the Chern number can be reduced modulo 2 depending on the winding number, and this is interpreted in terms of braiding of Weyl points and exceptional nodal rings.