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Title: Observation of a linked-loop quantum state in a topological magnet
Authors: Belopolski, Ilya
Chang, Guoqing
Cochran, Tyler A.
Cheng, Zi-Jia
Yang, Xian P.
Hugelmeyer, Cole
Manna, Kaustuv
Yin, Jia-Xin
Cheng, Guangming
Multer, Daniel
Litskevich, Maksim
Shumiya, Nana
Zhang, Songtian S.
Shekha, Chandra
Schröter, Niels B. M.
Chikina, Alla
Polley, Craig
Thiagarajan, Balasubramanian
Leandersson, Mats
Adell, Johan
Huang, Shin-Ming
Yao, Nan
Strocov, Vladimir N.
Felser, Claudia
Hasan, M. Zahid
Keywords: Science::Physics
Issue Date: 2022
Source: Belopolski, I., Chang, G., Cochran, T. A., Cheng, Z., Yang, X. P., Hugelmeyer, C., Manna, K., Yin, J., Cheng, G., Multer, D., Litskevich, M., Shumiya, N., Zhang, S. S., Shekha, C., Schröter, N. B. M., Chikina, A., Polley, C., Thiagarajan, B., Leandersson, M., ...Hasan, M. Z. (2022). Observation of a linked-loop quantum state in a topological magnet. Nature, 604, 647-652.
Project: NRF-NRFF13-2021-0010
Journal: Nature 
Abstract: Quantum phases can be classified by topological invariants, which take on discrete values capturing global information about the quantum state. Over the past decades, these invariants have come to play a central role in describing matter, providing the foundation for understanding superfluids, magnets, the quantum Hall effect, topological insulators, Weyl semimetals and other phenomena. Here we report an unusual linking-number (knot theory) invariant associated with loops of electronic band crossings in a mirror-symmetric ferromagnet. Using state-of-the-art spectroscopic methods, we directly observe three intertwined degeneracy loops in the material’s three-torus, T3, bulk Brillouin zone. We find that each loop links each other loop twice. Through systematic spectroscopic investigation of this linked-loop quantum state, we explicitly draw its link diagram and conclude, in analogy with knot theory, that it exhibits the linking number (2, 2, 2), providing a direct determination of the invariant structure from the experimental data. We further predict and observe, on the surface of our samples, Seifert boundary states protected by the bulk linked loops, suggestive of a remarkable Seifert bulk–boundary correspondence. Our observation of a quantum loop link motivates the application of knot theory to the exploration of magnetic and superconducting quantum matter.
ISSN: 0028-0836
DOI: 10.1038/s41586-022-04512-8
Rights: © 2022 The Author(s), under exclusive licence to Springer Nature Limited. All rights reserved. This paper was published in Nature and is made available with permission of The Author(s).
Fulltext Permission: embargo_20221105
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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