Non-Hermitian Topological Invariants in Real Space

The topology of non-Hermitian systems is drastically shaped by the non-Hermitian skin effect, which leads to the generalized bulk-boundary correspondence and non-Bloch band theory. The essential part in formulations of bulk-boundary correspondence is a general and computable definition of topologica...

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Bibliographic Details
Published in:Physical review letters 2019-12, Vol.123 (24), p.246801-246801, Article 246801
Main Authors: Song, Fei, Yao, Shunyu, Wang, Zhong
Format: Article
Language:English
Subjects:
Band theory
Bloch band
Brillouin zones
Invariants
Skin effect
Topology
Wave functions
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Summary:The topology of non-Hermitian systems is drastically shaped by the non-Hermitian skin effect, which leads to the generalized bulk-boundary correspondence and non-Bloch band theory. The essential part in formulations of bulk-boundary correspondence is a general and computable definition of topological invariants. In this Letter, we introduce a construction of non-Hermitian topological invariants based directly on real-space wave functions, which provides a general and straightforward approach for determining non-Hermitian topology. As an illustration, we apply this formulation to several representative models of non-Hermitian systems, efficiently obtaining their topological invariants in the presence of non-Hermitian skin effect. Our formulation also provides a dual picture of the non-Bloch band theory based on the generalized Brillouin zone, offering a unique perspective of bulk-boundary correspondence.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.123.246801