Second-Order Topological Phases in Non-Hermitian Systems

A d-dimensional second-order topological insulator (SOTI) can host topologically protected (d-2)-dimensional gapless boundary modes. Here, we show that a 2D non-Hermitian SOTI can host zero-energy modes at its corners. In contrast to the Hermitian case, these zero-energy modes can be localized only...

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Published inPhysical review letters Vol. 122; no. 7; p. 076801
Main Authors Liu, Tao, Zhang, Yu-Ran, Ai, Qing, Gong, Zongping, Kawabata, Kohei, Ueda, Masahito, Nori, Franco
Format Journal Article
LanguageEnglish
Published United States 22.02.2019
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Summary:A d-dimensional second-order topological insulator (SOTI) can host topologically protected (d-2)-dimensional gapless boundary modes. Here, we show that a 2D non-Hermitian SOTI can host zero-energy modes at its corners. In contrast to the Hermitian case, these zero-energy modes can be localized only at one corner. A 3D non-Hermitian SOTI is shown to support second-order boundary modes, which are localized not along hinges but anomalously at a corner. The usual bulk-corner (hinge) correspondence in the second-order 2D (3D) non-Hermitian system breaks down. The winding number (Chern number) based on complex wave vectors is used to characterize the second-order topological phases in 2D (3D). A possible experimental situation with ultracold atoms is also discussed. Our work lays the cornerstone for exploring higher-order topological phenomena in non-Hermitian systems.
ISSN:1079-7114
DOI:10.1103/PhysRevLett.122.076801