  Topological states in non-Hermitian systems are known to exhibit some
anomalous features. Here, we find two new anomalous features of non-Hermitian
topological states. We consider a one dimensional nonreciprocal Hamiltonian and
show that topological robustness can be practically lost for a linear
combination of topological eigenstates in non-Hermitian systems due to the
non-Hermitian skin effect. We consider a two dimensional non-Hermitian Chern
insulator and show that chirality of topological states can be broken at some
parameters of the Hamiltonan. This implies that the topological states are no
longer immune to backscattering in 2D.
