Student or educator? Sign up with your school email and get 6 months of Pro free.
Cited by 167

The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.

Dimensional hierarchy of higher-order topology in three-dimensional sonic crystals

Open access
Zhang, Xiujuan, Xie, Bi-Ye, Wang, Hong-Fei, Xu, Xiangyuan, Tian, Yuan, Jiang, Jian-Hua, Lu, Ming-Hui, Chen, Yan-Feng·2019·Nature Communications

Abstract

Wave trapping and manipulation are at the heart of modern integrated photonics and acoustics. Grand challenges emerge on increasing the integration density and reducing the wave leakage/noises due to fabrication imperfections, especially for waveguides and cavities at subwavelength scales. The rising of robust wave dynamics based on topological mechanisms offers possible solutions. Ideally, in a three-dimensional (3D) topological integrated chip, there are coexisting robust two-dimensional (2D) interfaces, one-dimensional (1D) waveguides and zero-dimensional (0D) cavities. Here, we report the experimental discovery of such a dimensional hierarchy of the topologically-protected 2D surface states, 1D hinge states and 0D corner states in a single 3D system. Such an unprecedented phenomenon is triggered by the higher-order topology in simple-cubic sonic crystals and protected by the space group $${P}_{m\bar{3}m}$$Pm3 ¯m. Our study opens up a new regime for multidimensional wave trapping and manipulation at subwavelength scales, which may inspire future technology for integrated acoustics and photonics.

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.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1038/s41467-019-13333-9

Cites

11 of 11 references verified0 citation errors · 0 not checkable

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.

A few free checks a day · papers already verified open instantly · results are public

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

Show all 11 references

Cited by

See all 167

Metadata

Authors
Zhang, X., Xie, B.-Y., Wang, H.-F., Xu, X., Tian, Y., Jiang, J.-H., Lu, M.-H., & Chen, Y.-F.
Venue
Nature Communications
Published
2019-11-25
Volume
10
Issue
1
Pages
5331-5331
ISSN
2041-1723 (ISSN-L)
OpenAlex
W2989598084
Cited by
167
References
11
FWCI
8.00
Type
journal article
Language
en
Open access
gold

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: Dimensional hierarchy of higher-order topology in three-dimensional sonic crystals. https://app.cochat.ai/papers/10.1038/s41467-019-13333-9
The paper
Zhang, X., Xie, B.-Y., Wang, H.-F., Xu, X., Tian, Y., Jiang, J.-H., Lu, M.-H., & Chen, Y.-F. (2019). Dimensional hierarchy of higher-order topology in three-dimensional sonic crystals. Nature Communications. https://doi.org/10.1038/s41467-019-13333-9

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.