Topological phase transition independent of system non-Hermiticity

Non-Hermiticity can vary the topology of system, induce topological phase transitions, and even invalidate the conventional bulk-boundary correspondence. Here, we show the introduction of non-Hermiticity without affecting the topological properties of the original chiral symmetric Hermitian systems. Conventional bulk-boundary correspondence holds; the topological phase transition and the (non)existence of edge states are unchanged even though the energy bands are inseparable due to non-Hermitian phase transitions. The Chern number for energy bands of the generalized non-Hermitian system in two dimensions is proved to be unchanged and favorably coincides with the simulated topological charge pumping. Our findings provide insights into the interplay between non-Hermiticity and topology. A topological phase transition independent of the non-Hermitian phase transition is a unique feature that is beneficial for future applications of non-Hermitian topological materials.