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Topologically protected refraction of robust kink states in valley photonic crystals

Nature Physics volume 14, pages 140–144 (2018)Cite this article

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Abstract

Recently discovered1,2 valley photonic crystals (VPCs) mimic many of the unusual properties of two-dimensional (2D) gapped valleytronic materials3,4,5,6,7,8,9. Of the utmost interest to optical communications is their ability to support topologically protected chiral edge (kink) states3,4,5,6,7,8,9 at the internal domain wall between two VPCs with opposite valley-Chern indices. Here we experimentally demonstrate valley-polarized kink states with polarization multiplexing in VPCs, designed from a spin-compatible four-band model. When the valley pseudospin is conserved, we show that the kink states exhibit nearly perfect out-coupling efficiency into directional beams, through the intersection between the internal domain wall and the external edge separating the VPCs from ambient space. The out-coupling behaviour remains topologically protected even when we break the spin-like polarization degree of freedom (DOF), by introducing an effective spin–orbit coupling in one of the VPC domains. This also constitutes the first realization of spin–valley locking for topological valley transport.

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Figure 1: Topological valley photonic crystal and its bulk band structure.
Figure 2: Symmetry-protected topological valley kink states.
Figure 3: Topologically protected refraction of kink states into an empty waveguide region.
Figure 4: Topologically protected refraction of spin–valley-locked kink states.

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Acknowledgements

This work was sponsored by Nanyang Technological University for NAP Start-up Grants, Singapore Ministry of Education under Grants No. MOE2015-T2-1-070, MOE2015-T2-2-008, MOE2016-T3-1-006 and Tier 1 RG174/16 (S). K.L., Y.Y. and G.S. acknowledge the support of the Air Force Office of Scientific Research under a Grant No. FA9550-15-1-0075, and the Army Research Office under a Grant No. W911NF-16-1-0319.

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Author notes

  1. Fei Gao and Haoran Xue: These authors contributed equally to this work.

Authors and Affiliations

  1. Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore

    Fei Gao, Haoran Xue, Zhaoju Yang, Xiao Lin, Yidong Chong & Baile Zhang

  2. School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA

    Kueifu Lai, Yang Yu & Gennady Shvets

  3. Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA

    Kueifu Lai

  4. Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore

    Yidong Chong & Baile Zhang

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  1. Fei Gao
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Contributions

All authors contributed extensively to this work. F.G., H.X. and Z.Y. fabricated structures and performed measurements. F.G., Z.Y., Y.Y. and X.L. performed simulation. F.G. and Z.Y. provided major theoretical analysis. K.L. designed part of the unidirectional excitation experiment. Y.C., G.S., and B.Z. supervised the project.

Corresponding authors

Correspondence to Zhaoju Yang, Gennady Shvets or Baile Zhang.

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The authors declare no competing financial interests.

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Gao, F., Xue, H., Yang, Z. et al. Topologically protected refraction of robust kink states in valley photonic crystals. Nat. Phys. 14, 140–144 (2018). https://doi.org/10.1038/nphys4304

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