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Chin. Phys. B, 2020, Vol. 29(1): 010302    DOI: 10.1088/1674-1056/ab5937
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A new way to construct topological invariants of non-Hermitian systems with the non-Hermitian skin effect

J S Liu(刘建森), Y Z Han(韩炎桢), C S Liu(刘承师)
Hebei Key Laboratory of Microstructural Material Physics, School of Science, Yanshan University, Qinhuangdao 066004, China
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.
Keywords:  non-Hermitian skin effect      Su-Schrieffer-Heeger (SSH) model      bulk-boundary correspondence      topological invariant  
Received:  16 October 2019      Revised:  13 November 2019      Accepted manuscript online: 
PACS:  03.65.Vf (Phases: geometric; dynamic or topological)  
  05.70.Fh (Phase transitions: general studies)  
  64.70.Tg (Quantum phase transitions)  
Fund: 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).
Corresponding Authors:  C S Liu     E-mail:

Cite this article: 

J S Liu(刘建森), Y Z Han(韩炎桢), C S Liu(刘承师) A new way to construct topological invariants of non-Hermitian systems with the non-Hermitian skin effect 2020 Chin. Phys. B 29 010302

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