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dc.contributor.authorBelopolski, Ilyaen_US
dc.contributor.authorChang, Guoqingen_US
dc.contributor.authorCochran, Tyler A.en_US
dc.contributor.authorCheng, Zi-Jiaen_US
dc.contributor.authorYang, Xian P.en_US
dc.contributor.authorHugelmeyer, Coleen_US
dc.contributor.authorManna, Kaustuven_US
dc.contributor.authorYin, Jia-Xinen_US
dc.contributor.authorCheng, Guangmingen_US
dc.contributor.authorMulter, Danielen_US
dc.contributor.authorLitskevich, Maksimen_US
dc.contributor.authorShumiya, Nanaen_US
dc.contributor.authorZhang, Songtian S.en_US
dc.contributor.authorShekha, Chandraen_US
dc.contributor.authorSchröter, Niels B. M.en_US
dc.contributor.authorChikina, Allaen_US
dc.contributor.authorPolley, Craigen_US
dc.contributor.authorThiagarajan, Balasubramanianen_US
dc.contributor.authorLeandersson, Matsen_US
dc.contributor.authorAdell, Johanen_US
dc.contributor.authorHuang, Shin-Mingen_US
dc.contributor.authorYao, Nanen_US
dc.contributor.authorStrocov, Vladimir N.en_US
dc.contributor.authorFelser, Claudiaen_US
dc.contributor.authorHasan, M. Zahiden_US
dc.identifier.citationBelopolski, 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.
dc.description.abstractQuantum 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.en_US
dc.description.sponsorshipNanyang Technological Universityen_US
dc.description.sponsorshipNational Research Foundation (NRF)en_US
dc.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).en_US
dc.titleObservation of a linked-loop quantum state in a topological magneten_US
dc.typeJournal Articleen
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen_US
dc.description.versionSubmitted/Accepted versionen_US
dc.subject.keywordsTopological Magnetsen_US
dc.subject.keywordsTopological Knoten_US
dc.description.acknowledgementG. Chang acknowledges the support of the National Research Foundation, Singapore under its NRF Fellowship Award (NRF-NRFF13-2021-0010) and the Nanyang Assistant Professorship grant from Nanyang Technological University. T.A.C. acknowledges support by the National Science Foundation Graduate Research Fellowship Program under grant number DGE-1656466. A.C. acknowledges funding from the Swiss National Science Foundation under grant number 200021-165529. We acknowledge synchrotron radiation beamtime at the ADRESS beamline of the Swiss Light Source of the Paul Scherrer Institut in Villigen, Switzerland under proposals 20170898, 20190740 and 20191674. S.-M.H. acknowledges funding by the MOST-AFOSR Taiwan program on Topological and Nanostructured Materials under grant no. 110-2124-M-110-002-MY3. We further acknowledge use of Princeton’s Imaging and Analysis Center, which is partially supported by the Princeton Center for Complex Materials, a National Science Foundation Materials Research Science and Engineering Center (DMR-2011750). This research used resources of the Advanced Photon Source, a US Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under contract number DE-AC02-06CH11357. We acknowledge beamtime at BL25SU of SPring-8 under proposal 2017A1669 and at BL29 of the Advanced Photon Source under proposals 54992 and 60811. K.M. and C.F. acknowledge financial support from the European Research Council Advanced Grant no. 742068 “TOP-MAT”. C.F. acknowledges the DFG through SFB 1143 (project ID. 247310070) and the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat (EXC2147, project ID. 39085490). M.Z.H. acknowledges support from the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Science Center and Princeton University. M.Z.H. acknowledges visiting scientist support at Berkeley Lab (Lawrence Berkeley National Laboratory) during the early phases of this work. Work at Princeton University was supported by the Gordon and Betty Moore Foundation (grant numbers GBMF4547 and GBMF9461; M.Z.H.). The ARPES and theoretical work were supported by the US DOE under the Basic Energy Sciences programme (grant number DOE/BES DE-FG-02-05ER46200; M.Z.H.). Use of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, is supported by the US DOE, Office of Science, Office of Basic Energy Sciences, under contract number DE-AC02-76SF00515. We acknowledge MAX IV Laboratory for time on the BLOCH Beamline under proposal 20210268. Research conducted at MAX IV, a Swedish national user facility, is supported by the Swedish Research council under contract 2018-07152, the Swedish Governmental Agency for Innovation Systems under contract 2018-04969, and Formas under contract 2019-02496. Materials characterization and the study of topological quantum properties were supported by the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Science Center and Princeton Universityen_US
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