A new way to construct topological invariants of non-Hermitian systems with the non-Hermitian skin effect**Project supported by Hebei Provincial Natural Science Foundation of China (Grant Nos. A2012203174 and A2015203387) and the National Natural Science Foundation of China (Grant Nos. 10974169 and 11304270).

Abstract

The non-Hermitian skin effect breaks the conventional bulk–boundary correspondence and leads to non-Bloch topological invariants. Inspired by the fact that the topological protected zero modes are immune to perturbations, we construct a partner of a non-Hermitian system by getting rid of the non-Hermitian skin effect. Through adjusting the imbalance hopping, we find that the existence of zero-energy boundary states still dictate the bulk topological invariants based on the band-theory framework. Two non-Hermitian Su–Schrieffer–Heeger (SSH) models are used to illuminate the ideas. Specially, we obtain the winding numbers in analytical form without the introduction of the generalized Brillouin zone. The work gives an alternative method to calculate the topological invariants of non-Hermitian systems.