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

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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.


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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).

Author information

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.

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

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

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