Abstract
The band theory of solids is arguably the most successful theory of condensed-matter physics, providing a description of the electronic energy levels in various materials. Electronic wavefunctions obtained from the band theory enable a topological characterization of metals for which the electronic spectrum may host robust, topologically protected, fermionic quasiparticles. Many of these quasiparticles are analogues of the elementary particles of the Standard Model1,2,3,4,5,6,7,8,9,10, but others do not have a counterpart in relativistic high-energy theories11,12,13,14,15,16,17,18. A complete list of possible quasiparticles in solids is lacking, even in the non-interacting case. Here we describe the possible existence of a hitherto unrecognized type of fermionic excitation in metals. This excitation forms a nodal chain—a chain of connected loops in momentum space—along which conduction and valence bands touch. We prove that the nodal chain is topologically distinct from previously reported excitations. We discuss the symmetry requirements for the appearance of this excitation and predict that it is realized in an existing material, iridium tetrafluoride (IrF4), as well as in other compounds of this class of materials. Using IrF4 as an example, we provide a discussion of the topological surface states associated with the nodal chain. We argue that the presence of the nodal-chain fermions will result in anomalous magnetotransport properties, distinct from those of materials exhibiting previously known excitations.
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Acknowledgements
The crystal structures in Fig. 3 were plotted using VESTA 3. We thank A. Bouhon, C. L. Kane, G. E. Volovik, B. A. Bernevig and R. J. Cava for discussions. T.B., A.R. and M.S. acknowledge financial support through an ETH research grant and the Swiss National Science Foundation. Q.S.W. and A.A.S. acknowledge the support of Microsoft Research and the Swiss National Science Foundation through the National Competence Centres in Research MARVEL and QSIT.
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T.B. initiated the project, carried out the theoretical analysis and determined the suitable space groups. Q.S.W. discovered the IrF4 material class and performed the first-principle studies. T.B. and A.A.S. wrote the manuscript. All authors contributed to the theoretical discussion and the final version of the manuscript.
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Reviewer Information Nature thanks E. Bergholtz, R. Nandkishore and the other anonymous reviewer(s) for their contribution to the peer review of this work.
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This file contains Supplementary Text and Data, Supplementary Figures 1- 8 Supplementary Tables 1- 5 and Supplementary references. (PDF 2158 kb)
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Bzdušek, T., Wu, Q., Rüegg, A. et al. Nodal-chain metals. Nature 538, 75–78 (2016). https://doi.org/10.1038/nature19099
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DOI: https://doi.org/10.1038/nature19099
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