Observation of a linked-loop quantum state in a topological magnet

Ilya Belopolski, Guoqing Chang, Tyler A. Cochran, Zi Jia Cheng, Xian P. Yang, Cole Hugelmeyer, Kaustuv Manna, Jia Xin Yin, Guangming Cheng, Daniel Multer, Maksim Litskevich, Nana Shumiya, Songtian S. Zhang, Chandra Shekhar, Niels B.M. Schröter, Alla Chikina, Craig Polley, Balasubramanian Thiagarajan, Mats Leandersson, Johan AdellShin Ming Huang, Nan Yao, Vladimir N. Strocov, Claudia Felser, M. Zahid Hasan

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


Quantum phases can be classified by topological invariants, which take on discrete values capturing global information about the quantum state1–13. Over the past decades, these invariants have come to play a central role in describing matter, providing the foundation for understanding superfluids5, magnets6,7, the quantum Hall effect3,8, topological insulators9,10, Weyl semimetals11–13 and other phenomena. Here we report an unusual linking-number (knot theory) invariant associated with loops of electronic band crossings in a mirror-symmetric ferromagnet14–20. 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.

Original languageEnglish (US)
Pages (from-to)647-652
Number of pages6
Issue number7907
StatePublished - Apr 28 2022

All Science Journal Classification (ASJC) codes

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