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Experimental discovery of nodal chains

Abstract

Three-dimensional Weyl and Dirac nodal points1 have attracted widespread interest across multiple disciplines and in many platforms but allow for few structural variations. In contrast, nodal lines2,3,4 can have numerous topological configurations in momentum space, forming nodal rings5,6,7,8,9, nodal chains10,11,12,13,14,15, nodal links16,17,18,19,20 and nodal knots21,22. However, nodal lines are much less explored because of the lack of an ideal experimental realization23,24,25. For example, in condensed-matter systems, nodal lines are often fragile to spin–orbit coupling, located away from the Fermi level, coexist with energy-degenerate trivial bands or have a degeneracy line that disperses strongly in energy. Here, overcoming all these difficulties, we theoretically predict and experimentally observe nodal chains in a metallic-mesh photonic crystal having frequency-isolated linear band-touching rings chained across the entire Brillouin zone. These nodal chains are protected by mirror symmetry and have a frequency variation of less than 1%. We use angle-resolved transmission measurements to probe the projected bulk dispersion and perform Fourier-transformed field scans to map out the dispersion of the drumhead surface state. Our results establish an ideal nodal-line material for further study of topological line degeneracies with non-trivial connectivity and consequent wave dynamics that are richer than those in Weyl and Dirac materials.

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Fig. 1: Nodal-chain Hamiltonian and stability.
Fig. 2: Nodal-chain photonic crystal.
Fig. 3: Angle-resolved transmission (ART) measurement of nodal-chain bulk states.
Fig. 4: Fourier-transformed field (FTFS) scan measurement of the drumhead surface state.

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Acknowledgements

We thank Yang He, Chen Fang and Hongming Weng for discussions. The authors were supported by the National Key R&D Program of China under Grant Nos 2017YFA0303800 and 2016YFA0302400 and by NSFC under Project Nos 11721404 (L.L.), 11674189 (Z.Y., Z.W.), 61625502 (H.C.), 61574127 (H.C.), the Top-Notch Young Talents Program (H.C.) and the National Thousand Young Talents Program (L.L.) of China.

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L.L. proposed and led the project. R.L. fabricated the sample. Q.Y. and R.L. made the measurements. Q.Y. processed the data and carried out the calculations. Z.W. and Z.Y. came up with the k.p model and enhanced the theoretical understanding. All authors contributed to the discussion and writing of the manuscript.

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Correspondence to Ling Lu.

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Five figures with additional description and discussions.

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Yan, Q., Liu, R., Yan, Z. et al. Experimental discovery of nodal chains. Nature Phys 14, 461–464 (2018). https://doi.org/10.1038/s41567-017-0041-4

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