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Observation of nodal-line semimetal with ultracold fermions in an optical lattice


The observation of topological phases beyond two dimensions, as widely reported in solid-state systems1,2, has been an open challenge for ultracold atoms. Although many theoretical schemes have been proposed, the experimental complexity in realizing and characterizing the three-dimensional (3D) band structure has acted as a barrier against experiments achieving this. Here, we realize a 3D spin–orbit coupled nodal-line semimetal in an optical Raman lattice filled with ultracold fermions, and observe the bulk line nodes in the band structure. The realized topological semimetal exhibits an emergent magnetic group symmetry. This allows detection of the nodal lines by effectively reconstructing the 3D topological band from a series of measurements of integrated spin textures, which precisely render spin textures on the parameter-tuned magnetic-group-symmetric planes. The detection technique can be applied generally to explore 3D topological states of similar symmetries. Furthermore, we observe the band inversion lines from topological quench dynamics, which are bulk counterparts of Fermi arc states and connect the Dirac points, reconfirming the realized topological band. Our results demonstrate an approach to effectively observe 3D band topology, and open the way to probe exotic topological physics for ultracold atoms in high dimensions.

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Fig. 1: SO coupling in an optical Raman lattice.
Fig. 2: Nodal-line semimetal band structure.
Fig. 3: Measurement of nodal lines in the 3D momentum space.
Fig. 4: Measuring band inversion lines from quantum quench dynamics.

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.


  1. Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).

    ADS  Article  Google Scholar 

  2. Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

    ADS  Article  Google Scholar 

  3. Liu, Z. K. et al. A stable three-dimensional topological dirac semimetal Cd3As2. Nat. Mater. 13, 677–681 (2014).

    ADS  Article  Google Scholar 

  4. Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613–617 (2015).

    ADS  Article  Google Scholar 

  5. Lv, B. Q. et al. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015).

    Google Scholar 

  6. Young, S. M. et al. Dirac semimetal in three dimensions. Phys. Rev. Lett. 108, 140405 (2012).

    ADS  Article  Google Scholar 

  7. Nielsen, H. B. & Ninomiya, M. Absence of neutrinos on a lattice: (I). Proof by homotopy theory. Nucl. Phys. B 185, 20–40 (1981).

    ADS  MathSciNet  Article  Google Scholar 

  8. Fang, C., Chen, Y., Kee, H. Y. & Fu, L. Topological nodal line semimetals with and without spin–orbital coupling. Phys. Rev. B 92, 081201 (2015).

    ADS  Article  Google Scholar 

  9. Bzdušek, T., Wu, Q., Rüegg, A., Sigrist, M. & Soluyanov, A. A. Nodal-chain metals. Nature 538, 75–78 (2016).

    ADS  Article  Google Scholar 

  10. Juan, F., Grushin, A. G., Morimoto, T. & Moore, J. E. Quantized circular photogalvanic effect in Weyl semimetals. Nat. Commun. 8, 15995 (2017).

    ADS  Article  Google Scholar 

  11. Lou, R. et al. Experimental observation of bulk nodal lines and electronic surface states in ZrB2. npj Quantum Mater. 3, 43 (2018).

    ADS  Article  Google Scholar 

  12. Dalibard, J., Gerbier, F., Juzeliūnas, G. & Oehberg, P. Colloquium: Artificial gauge potentials for neutral atoms. Rev. Mod. Phys. 83, 1523–1543 (2011).

    ADS  Article  Google Scholar 

  13. Goldman, N., Juzeliunas, G., Öhberg, P. & Spielman, I. B. Light-induced gauge fields for ultracold atoms. Rep. Prog. Phys. 77, 126401 (2014).

    ADS  Article  Google Scholar 

  14. Zhai, H. Degenerate quantum gases with spin–orbit coupling: a review. Rep. Prog. Phys. 78, 026001 (2015).

    ADS  MathSciNet  Article  Google Scholar 

  15. Zhang, L. & Liu, X. -J. in Synthetic Spin–Orbit Coupling in Cold Atoms (eds Zhang, W. & Sa Melo, C. A. R.) Ch. 1, 1–87 (World Scientific, 2018).

  16. Jotzu, G. et al. Experimental realization of the topological haldane model with ultracold fermions. Nature 515, 237–240 (2014).

    ADS  Article  Google Scholar 

  17. Wu, Z. et al. Realization of two-dimensional spin–orbit coupling for Bose–Einstein condensates. Science 354, 83–88 (2016).

    ADS  Article  Google Scholar 

  18. Liu, X.-J., Law, K. T. & Ng, T. K. Realization of 2D spin–orbit interaction and exotic topological orders in cold atoms. Phys. Rev. Lett. 112, 086401 (2014).

    ADS  Article  Google Scholar 

  19. Li, J.-R. et al. A stripe phase with supersolid properties in spin–orbit-coupled Bose–Einstein condensates. Nature 543, 91–94 (2017).

    ADS  Article  Google Scholar 

  20. Song, B. et al. Observation of symmetry-protected topological band with ultracold fermions. Sci. Adv. 4, eaao4748 (2018).

    Article  Google Scholar 

  21. Xu, Y. & Duan, L. M. Type-II Weyl points in three-dimensional cold-atom optical lattices. Phys. Rev. A 94, 053619 (2016).

    ADS  Article  Google Scholar 

  22. Xu, Y. & Zhang, C. Out-of-equilibrium open quantum systems: a comparison of approximate quantum master equation approaches with exact results. Phys. Rev. A 93, 063606 (2016).

    ADS  Article  Google Scholar 

  23. Wang, Y. & Liu, X.-J. Predicted scaling behavior of bloch oscillation in Weyl semimetals. Phys. Rev. A 94, 031603(R) (2016).

    ADS  Article  Google Scholar 

  24. He, W.-Y., Xu, D.-H., Zhou, B. T., Zhou, Q. & Law, K. T. From nodal-ring topological superfluids to spiral Majorana modes in cold atomic systems. Phys. Rev. A 97, 043618 (2018).

    ADS  Article  Google Scholar 

  25. Wang, B.-Z. et al. Dirac-, Rashba- and Weyl-type spin–orbit couplings: toward experimental realization in ultracold atoms. Phys. Rev. A 97, 011605(R) (2018).

    ADS  Article  Google Scholar 

  26. Dubček, T. et al. Weyl points in three-dimensional optical lattices: synthetic magnetic monopoles in momentum space. Phys. Rev. Lett. 114, 225301 (2015).

    ADS  Article  Google Scholar 

  27. Tran, D. T., Dauphin, A., Grushin, A. G., Zoller, P. & Goldman, N. Probing topology by heating: quantized circular dichroism in ultracold atoms. Sci. Adv. 3, e1701207 (2017).

    ADS  Article  Google Scholar 

  28. Poon, T. F. J. & Liu, X.-J. From a semimetal to a chiral Fulde–Ferrell superfluid. Phys. Rev. B 97, 020501(R) (2018).

    ADS  Article  Google Scholar 

  29. Lin, Y. J., Jiménez-Garca, K. & Spielman, I. B. Spin–orbit-coupled Bose–Einstein condensates. Nature 471, 83–86 (2011).

    ADS  Article  Google Scholar 

  30. Wang, P. et al. Spin–orbit coupled degenerate Fermi gases. Phys. Rev. Lett. 109, 095301 (2012).

    ADS  Article  Google Scholar 

  31. Cheuk, L. W. et al. Spin-injection spectroscopy of a spin–orbit coupled Fermi gas. Phys. Rev. Lett. 109, 095302 (2012).

    ADS  Article  Google Scholar 

  32. Song, B. et al. Spin–orbit-coupled two-electron Fermi gases of ytterbium atoms. Phys. Rev. A 94, 061604 (2016).

    ADS  Article  Google Scholar 

  33. Zhang, L., Zhang, L., Niu, S. & Liu, X.-J. Dynamical classification of topological quantum phases. Sci. Bull. 63, 1385–1391 (2018).

    Article  Google Scholar 

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The authors acknowledge valuable discussions with L. Zhang. This work was supported by the Joint Research Scheme sponsored by the Research Grants Council (RGC) of the Hong Kong and National Natural Science Foundation of China (NSFC) (project nos. N-HKUST601/17 and 11761161003). G.-B.J. acknowledges support from the RGC, the Croucher Foundation (ECS26300014, GRF16300215, GRF16311516, GRF16305317 and C6005-17G-A) and Croucher Innovation grants. G.-B.J also acknowledges partial support (SSTSP grant) from HKUST. X.-J.L. acknowledges support from the National Key R&D Program of China (2016YFA0301604), NSFC (11574008 and 11825401) and the Strategic Priority Research Program of the Chinese Academy of Science (grant no. XDB28000000).

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Authors and Affiliations



B.S., C.H. and Z.R. carried out the experiment and data analysis and helped with numerical calculations. S.N. proved the results of reconstructing the 3D band topology by 2D spin-texture imaging. S.N. and L.Z. performed theoretical modelling and numerical calculations. G.-B.J. and X.-J.L. conceived the project and supervised the research.

Corresponding authors

Correspondence to Xiong-Jun Liu or Gyu-Boong Jo.

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The authors declare no competing interests.

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Supplementary text, Supplementary Figs. 1–8 and Supplementary references.

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Song, B., He, C., Niu, S. et al. Observation of nodal-line semimetal with ultracold fermions in an optical lattice. Nat. Phys. 15, 911–916 (2019).

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