A new way to construct topological invariants of non-Hermitian systems with the non-Hermitian skin effect

doi:10.1088/1674-1056/ab5937

中国物理B ›› 2020, Vol. 29 ›› Issue (1): 10302-010302.doi: 10.1088/1674-1056/ab5937

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

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

收稿日期:2019-10-16 修回日期:2019-11-13 出版日期:2020-01-05 发布日期:2020-01-05
通讯作者: C S Liu E-mail:csliu@ysu.edu.cn
基金资助:
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).

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

Received:2019-10-16 Revised:2019-11-13 Online:2020-01-05 Published:2020-01-05
Contact: C S Liu E-mail:csliu@ysu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: non-Hermitian skin effect, Su-Schrieffer-Heeger (SSH) model, bulk-boundary correspondence, topological invariant

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.

Key words: non-Hermitian skin effect, Su-Schrieffer-Heeger (SSH) model, bulk-boundary correspondence, topological invariant

中图分类号: (Phases: geometric; dynamic or topological)

03.65.Vf

05.70.Fh (Phase transitions: general studies) 64.70.Tg (Quantum phase transitions)

刘建森, 韩炎桢, 刘承师. A new way to construct topological invariants of non-Hermitian systems with the non-Hermitian skin effect[J]. 中国物理B, 2020, 29(1): 10302-010302.

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[J]. Chin. Phys. B, 2020, 29(1): 10302-010302.

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A new way to construct topological invariants of non-Hermitian systems with the non-Hermitian skin effect

A new way to construct topological invariants of non-Hermitian systems with the non-Hermitian skin effect

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