Topological Chern vectors in three-dimensional photonic crystals

Gui-Geng Liu, Zhen Gao, Qiang Wang, Xiang Xi, Yuan-Hang Hu, Maoren Wang, Chengqi Liu, Xiao Lin, Longjiang Deng, Shengyuan A. Yang, Peiheng Zhou (), Yihao Yang (), Yidong Chong () and Baile Zhang ()
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Gui-Geng Liu: Nanyang Technological University
Zhen Gao: Southern University of Science and Technology
Qiang Wang: Nanyang Technological University
Xiang Xi: Southern University of Science and Technology
Yuan-Hang Hu: University of Electronic Science and Technology of China
Maoren Wang: University of Electronic Science and Technology of China
Chengqi Liu: University of Electronic Science and Technology of China
Xiao Lin: Zhejiang University
Longjiang Deng: University of Electronic Science and Technology of China
Shengyuan A. Yang: Singapore University of Technology and Design
Peiheng Zhou: University of Electronic Science and Technology of China
Yihao Yang: Zhejiang University
Yidong Chong: Nanyang Technological University
Baile Zhang: Nanyang Technological University

Nature, 2022, vol. 609, issue 7929, 925-930

Abstract: 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.

Date: 2022
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DOI: 10.1038/s41586-022-05077-2

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