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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The data that support the findings of this study are available from the corresponding authors upon reasonable request.
Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).
Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
Liu, Z. K. et al. A stable three-dimensional topological dirac semimetal Cd3As2. Nat. Mater. 13, 677–681 (2014).
Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613–617 (2015).
Lv, B. Q. et al. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015).
Young, S. M. et al. Dirac semimetal in three dimensions. Phys. Rev. Lett. 108, 140405 (2012).
Nielsen, H. B. & Ninomiya, M. Absence of neutrinos on a lattice: (I). Proof by homotopy theory. Nucl. Phys. B 185, 20–40 (1981).
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).
Bzdušek, T., Wu, Q., Rüegg, A., Sigrist, M. & Soluyanov, A. A. Nodal-chain metals. Nature 538, 75–78 (2016).
Juan, F., Grushin, A. G., Morimoto, T. & Moore, J. E. Quantized circular photogalvanic effect in Weyl semimetals. Nat. Commun. 8, 15995 (2017).
Lou, R. et al. Experimental observation of bulk nodal lines and electronic surface states in ZrB2. npj Quantum Mater. 3, 43 (2018).
Dalibard, J., Gerbier, F., Juzeliūnas, G. & Oehberg, P. Colloquium: Artificial gauge potentials for neutral atoms. Rev. Mod. Phys. 83, 1523–1543 (2011).
Goldman, N., Juzeliunas, G., Öhberg, P. & Spielman, I. B. Light-induced gauge fields for ultracold atoms. Rep. Prog. Phys. 77, 126401 (2014).
Zhai, H. Degenerate quantum gases with spin–orbit coupling: a review. Rep. Prog. Phys. 78, 026001 (2015).
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).
Jotzu, G. et al. Experimental realization of the topological haldane model with ultracold fermions. Nature 515, 237–240 (2014).
Wu, Z. et al. Realization of two-dimensional spin–orbit coupling for Bose–Einstein condensates. Science 354, 83–88 (2016).
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).
Li, J.-R. et al. A stripe phase with supersolid properties in spin–orbit-coupled Bose–Einstein condensates. Nature 543, 91–94 (2017).
Song, B. et al. Observation of symmetry-protected topological band with ultracold fermions. Sci. Adv. 4, eaao4748 (2018).
Xu, Y. & Duan, L. M. Type-II Weyl points in three-dimensional cold-atom optical lattices. Phys. Rev. A 94, 053619 (2016).
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).
Wang, Y. & Liu, X.-J. Predicted scaling behavior of bloch oscillation in Weyl semimetals. Phys. Rev. A 94, 031603(R) (2016).
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).
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).
Dubček, T. et al. Weyl points in three-dimensional optical lattices: synthetic magnetic monopoles in momentum space. Phys. Rev. Lett. 114, 225301 (2015).
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).
Poon, T. F. J. & Liu, X.-J. From a semimetal to a chiral Fulde–Ferrell superfluid. Phys. Rev. B 97, 020501(R) (2018).
Lin, Y. J., Jiménez-Garca, K. & Spielman, I. B. Spin–orbit-coupled Bose–Einstein condensates. Nature 471, 83–86 (2011).
Wang, P. et al. Spin–orbit coupled degenerate Fermi gases. Phys. Rev. Lett. 109, 095301 (2012).
Cheuk, L. W. et al. Spin-injection spectroscopy of a spin–orbit coupled Fermi gas. Phys. Rev. Lett. 109, 095302 (2012).
Song, B. et al. Spin–orbit-coupled two-electron Fermi gases of ytterbium atoms. Phys. Rev. A 94, 061604 (2016).
Zhang, L., Zhang, L., Niu, S. & Liu, X.-J. Dynamical classification of topological quantum phases. Sci. Bull. 63, 1385–1391 (2018).
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).
The authors declare no competing interests.
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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). https://doi.org/10.1038/s41567-019-0564-y
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