The DOI matches its Crossref record; 105 of the 105 references it cites were found in a registry or an index.
Second-Order Topological Phases in Non-Hermitian Systems
Open accessAbstract
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Colloquium : Topological insulators
Hasan, M. Z., & Kane, C. L. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.3045 · Cited by 19,930
Topological insulators and superconductors
Qi, X.-L., & Zhang, S.-C. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.1057 · Cited by 14,394
Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
Bernevig, B. A., Hughes, T. L., & Zhang, S.-C. (2006) · Science · doi:10.1126/science.1133734 · Cited by 7,090
Z 2 Topological Order and the Quantum Spin Hall Effect
Kane, C. L., & Mele, E. J. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.146802 · Cited by 6,460
Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface
Zhang, H., Liu, C.-X., Qi, X.-L., Dai, X., Fang, Z., & Zhang, S.-C. (2009) · Nature Physics · doi:10.1038/nphys1270 · Cited by 6,359
Haldane, F. D. M. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.2015 · Cited by 6,301
(1998) · doi:10.1103/physrevlett.80.5243 · Cited by 6,280
Quantum Spin Hall Insulator State in HgTe Quantum Wells
König, M., Wiedmann, S., Brüne, C., Roth, A., Buhmann, H., Molenkamp, L. W., Qi, X.-L., & Zhang, S.-C. (2007) · Science · doi:10.1126/science.1148047 · Cited by 6,151
Lu, L., Joannopoulos, J. D., & Soljačić, M. (2014) · Nature Photonics · doi:10.1038/nphoton.2014.248 · Cited by 3,655
Making sense of non-Hermitian Hamiltonians
Bender, C. M. (2007) · Reports on Progress in Physics · doi:10.1088/0034-4885/70/6/r03 · Cited by 2,984
Cited by
Exceptional topology of non-Hermitian systems
Bergholtz, E. J., Budich, J. C., & Kunst, F. K. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.015005 · Cited by 1,711
Xie, B., Wang, H.-X., Zhang, X., Zhan, P., Jiang, J.-H., Lu, M., & Chen, Y. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00323-4 · Cited by 543
Non-Hermitian Topological Invariants in Real Space
Song, F., Yao, S., & Wang, Z. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.246801 · Cited by 482
Recent advances in 2D, 3D and higher-order topological photonics
Kim, M., Jacob, Z., & Rho, J. (2020) · Light: Science & Applications · doi:10.1038/s41377-020-0331-y · Cited by 470
Higher-order topological states in photonic kagome crystals with long-range interactions
Li, M., Zhirihin, D., Gorlach, M., Ni, X., Filonov, D., Slobozhanyuk, A., Alù, A., & Khanikaev, A. B. (2020) · Nature Photonics · doi:10.1038/s41566-019-0561-9 · Cited by 448
Metadata
- Authors
- Liu, T., Zhang, Y.-R., Ai, Q., Gong, Z., Kawabata, K., Ueda, M., & Nori, F.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2019-02-20
- Volume
- 122
- Issue
- 7
- Pages
- 076801-076801
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2950613702
- Cited by
- 485
- References
- 105
- FWCI
- 30.00
- Type
- journal article
- Language
- en
- Open access
- green
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Second-Order Topological Phases in Non-Hermitian Systems. https://app.cochat.ai/papers/10.1103/physrevlett.122.076801
- The paper
- Liu, T., Zhang, Y.-R., Ai, Q., Gong, Z., Kawabata, K., Ueda, M., & Nori, F. (2019). Second-Order Topological Phases in Non-Hermitian Systems. Physical Review Letters. https://doi.org/10.1103/physrevlett.122.076801
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
