  Topological stability is an important property for topological materials.
However, the non-Hermitian effects may change this situation. Here, we
investigate the robustness of edge states in the non-Hermitian Kitaev chain
with imbalanced tunneling term and superconducting pairing term. By defining
the similarity of Majorana zero modes (MZMs) and magnetic factor, the
coalescing phase diagram of the MZMs and corresponding spin polarization phase
diagram are provided. Because of the non-Hermitian coalescence effect and
non-Hermitian suppression effect induced by the breakdown of sublattice
symmetry and particle-hole symmetry, the system emergence very interesting
phenomenons, such as defective MZMs, number-anomalous bulk-boundary
correspondence, coalescing of many-body ground states, the magnetic phase
crossover without gap closing. Those novel non-Hermitian effects offer fresh
insights into MZMs and topological physics.
