Topology and observables of the non-Hermitian Chern insulator

Given the rising importance of non-Hermitian theories that describe open lossy systems, significant research has focused on studying non-Hermitian topological invariants. However, recent work suggests that related observables may no longer be quantized. Here, the authors illustrate the underlying structure of the Green's function of non-Hermitian Hamiltonians that precludes the quantization of the Chern-Simons coefficient, resulting in the nonquantization of the Hall response of non-Hermitian Chern insulators. By showing nonquantization across a broad class of non-Hermitian Hamiltonians, the authors demonstrate the disconnect in non-Hermitian systems between a topological invariant, the Chern number, and its associated observable, the Hall conductivity.