The DOI matches its Crossref record; 41 of the 41 references it cites were found in a registry or an index.
Photonic topological insulator with broken time-reversal symmetry
Open accessAbstract
Significance: Topological insulators are first discovered in electronic systems. A key factor is the Kramers doublet for the spin-1/2 electrons under fermionic time-reversal symmetry T f 2 = − 1 . Unlike electrons, photons are massless bosons with spin-1. Therefore, the Kramers degeneracy theorem cannot readily apply to photons under the bosonic time-reversal symmetry. So far, there has been no coherent physical explanation for the symmetry protection mechanism behind the photonic topological insulator. Here, we design a photonic topological insulator that violates the bosonic time-reversal symmetry but complies with a fermionic-like pseudo time-reversal symmetry. The analyses and results, through comprehensive investigations on the properties of edge states, validate that the topological edge states are, in fact, protected by the fermionic-like pseudo time-reversal symmetry T p ( T p 2 = − 1 ).
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
Klitzing, K. V., Dorda, G., & Pepper, M. (1980) · Physical Review Letters · doi:10.1103/physrevlett.45.494 · Cited by 7,119
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
Quantized Hall Conductance in a Two-Dimensional Periodic Potential
Thouless, D. J., Kohmoto, M., Nightingale, M. P., & den Nijs, M. (1982) · Physical Review Letters · doi:10.1103/physrevlett.49.405 · Cited by 6,973
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
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
Two-Dimensional Magnetotransport in the Extreme Quantum Limit
Tsui, D. C., Stormer, H. L., & Gossard, A. C. (1982) · Physical Review Letters · doi:10.1103/physrevlett.48.1559 · Cited by 4,788
Metamaterials and Negative Refractive Index
Smith, D. R., Pendry, J. B., & Wiltshire, M. C. K. (2004) · Science · doi:10.1126/science.1096796 · Cited by 4,541
Cited by
Ozawa, T., Price, H. M., Amo, A., Goldman, N., Hafezi, M., Lu, L., Rechtsman, M. C., Schuster, D., Simon, J., Zilberberg, O., et al. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.015006 · Cited by 3,722
Experimental demonstration of anomalous Floquet topological insulator for sound
Peng, Y.-G., Qin, C.-Z., Zhao, D.-G., Shen, Y.-X., Xu, X.-Y., Bao, M., Jia, H., & Zhu, X.-F. (2016) · Nature Communications · doi:10.1038/ncomms13368 · Cited by 461
Zhang, X., Xiao, M., Cheng, Y., Lu, M.-H., & Christensen, J. (2018) · Communications Physics · doi:10.1038/s42005-018-0094-4 · Cited by 357
Self-citationA second wave of topological phenomena in photonics and acoustics
Zhang, X., Zangeneh-Nejad, F., Chen, Z.-G., Lu, M.-H., & Christensen, J. (2023) · Nature · doi:10.1038/s41586-023-06163-9 · Cited by 240
Self-citationTopological phononic insulator with robust pseudospin-dependent transport
Xia, B.-Z., Liu, T.-T., Huang, G.-L., Dai, H.-Q., Jiao, J.-R., Zang, X.-G., Yu, D.-J., Zheng, S.-J., & Liu, J. (2017) · Physical Review B · doi:10.1103/physrevb.96.094106 · Cited by 166
Metadata
- Authors
- He, C., Sun, X.-C., Liu, X.-P., Lu, M.-H., Chen, Y., Feng, L., & Chen, Y.-F.
- Venue
- Proceedings of the National Academy of Sciences
- Published
- 2016-04-18
- Volume
- 113
- Issue
- 18
- Pages
- 4924-4928
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- OpenAlex
- W2338277331
- Cited by
- 257
- References
- 41
- FWCI
- 15.88
- Type
- journal article
- Language
- en
- Open access
- bronze
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: Photonic topological insulator with broken time-reversal symmetry. https://app.cochat.ai/papers/10.1073/pnas.1525502113
- The paper
- He, C., Sun, X.-C., Liu, X.-P., Lu, M.-H., Chen, Y., Feng, L., & Chen, Y.-F. (2016). Photonic topological insulator with broken time-reversal symmetry. Proceedings of the National Academy of Sciences. https://doi.org/10.1073/pnas.1525502113
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.