Realization of a non-Hermitian Haldane model in circuits

Abstract

The Haldane model is the simplest yet most powerful topological lattice model exhibiting various phases, including the Dirac semimetal phase and the anomalous quantum Hall phase (also known as the Chern insulator). Although considered unlikely to be physically directly realizable in condensed matter systems, it has been experimentally demonstrated in other physical settings such as cold atoms, where Hermiticity is usually preserved. Extending this model to the non-Hermitian regime with energy non-conservation can significantly enrich topological phases that lack Hermitian counterparts; however, such exploration remains experimentally challenging due to the lack of suitable physical platforms. Here, based on electric circuits, we report the experimental realization of a genuine non-Hermitian Haldane model with asymmetric next-nearest-neighbor hopping. We observe two previously uncovered phases: a non-Hermitian Chern insulator and a non-Hermitian semimetal phase, both exhibiting boundary-dependent amplifying or dissipative chiral edge states. Our work paves the way for exploring non-Hermiticity-induced unconventional topological phases in the Haldane model.

Graphical abstract

Keywords

Haldane model / Chern insulator / non-Hermitian / topological circuit / semimetal

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Declarations

The authors declare that they have no competing interests and there are no conflicts.

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Electronic supplementary materials

The online version contains supplementary material available at https://doi.org/10.15302/frontphys.2025.044204.

Acknowledgements

The authors thank fruitful discussions with Baile Zhang and Yihao Yang. R.L., W.W., and X.K. were sponsored by the National Key Research and Development Program of China (Grant No. 2022YFA1404902), the National Natural Science Foundation of China (Grant No. 12104353), the Fundamental Research Funds for the Central Universities (Grant No. QTZX25086), and the Open Foundation of the State Key Laboratory of Modern Optical Instrumentation. B.L. was sponsored by the National Natural Science Foundation of China (Grant No. 61901133), the Fundamental Research Funds for the Central Universities (No. 3072024XX2504), the Forward Design Technology Special Fund Project of Harbin Engineering University (Nos. KYWZ220242504, KYW220240807, and KYWZ220240807). P.L. was sponsored by the National Natural Science Foundation of China (Grant No. 11805141) and Basic Research Program of Shanxi Province (No. 202203021222250). Y.L. was sponsored by the National Natural Science Foundation of China (Grant No. 62271366) and the 111 Project.

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