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Title: Topological Chern vectors in three-dimensional photonic crystals
Authors: Liu, Gui-Geng
Gao, Zhen
Wang, Qiang
Xi, Xiang
Hu, Yuan-Hang
Wang, Maoren
Liu, Chengqi
Lin, Xiao
Deng, Longjiang
Yang, Shengyuan A.
Zhou, Peiheng
Yang, Yihao
Chong, Yidong
Zhang, Baile
Keywords: Science::Physics
Issue Date: 2022
Source: Liu, G., Gao, Z., Wang, Q., Xi, X., Hu, Y., Wang, M., Liu, C., Lin, X., Deng, L., Yang, S. A., Zhou, P., Yang, Y., Chong, Y. & Zhang, B. (2022). Topological Chern vectors in three-dimensional photonic crystals. Nature, 609, 925-930.
Project: NRF-CRP23-2019-0007
Journal: Nature
Abstract: The paradigmatic example of a topological phase of matter, the two-dimensional Chern insulator1-5, is characterized by a topological invariant consisting of a single integer, the scalar Chern number. Extending the Chern insulator phase from two to three dimensions requires generalization of the Chern number to a three-vector6,7, similar to the three-dimensional (3D) quantum Hall effect8-13. Such Chern vectors for 3D Chern insulators have never been explored experimentally. Here we use magnetically tunable 3D photonic crystals to achieve the experimental demonstration of Chern vectors and their topological surface states. We demonstrate Chern vector magnitudes of up to six, higher than all scalar Chern numbers previously realized in topological materials. The isofrequency contours formed by the topological surface states in the surface Brillouin zone form torus knots or links, whose characteristic integers are determined by the Chern vectors. We demonstrate a sample with surface states forming a (2, 2) torus link or Hopf link in the surface Brillouin zone, which is topologically distinct from the surface states of other 3D topological phases. These results establish the Chern vector as an intrinsic bulk topological invariant in 3D topological materials, with surface states possessing unique topological characteristics.
ISSN: 0028-0836
DOI: 10.1038/s41586-022-05077-2
Schools: School of Physical and Mathematical Sciences 
Research Centres: Centre for Disruptive Photonic Technologies (CDPT) 
The Photonics Institute 
Rights: © 2022 The Author(s), under exclusive licence to Springer Nature Limited. All rights reserved. This version of the article has been accepted for publication, after peer review and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at:
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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