Author
Listed:
- Ilya Belopolski
(Princeton University
RIKEN Center for Emergent Matter Science (CEMS))
- Guoqing Chang
(Nanyang Technological University)
- Tyler A. Cochran
(Princeton University)
- Zi-Jia Cheng
(Princeton University)
- Xian P. Yang
(Princeton University)
- Cole Hugelmeyer
(Princeton University)
- Kaustuv Manna
(Max Planck Institute for Chemical Physics of Solids
Indian Institute of Technology Delhi)
- Jia-Xin Yin
(Princeton University)
- Guangming Cheng
(Princeton University)
- Daniel Multer
(Princeton University)
- Maksim Litskevich
(Princeton University)
- Nana Shumiya
(Princeton University)
- Songtian S. Zhang
(Princeton University)
- Chandra Shekhar
(Max Planck Institute for Chemical Physics of Solids)
- Niels B. M. Schröter
(Swiss Light Source, Paul Scherrer Institut)
- Alla Chikina
(Swiss Light Source, Paul Scherrer Institut)
- Craig Polley
(Lund University)
- Balasubramanian Thiagarajan
(Lund University)
- Mats Leandersson
(Lund University)
- Johan Adell
(Lund University)
- Shin-Ming Huang
(National Sun Yat-sen University)
- Nan Yao
(Princeton University)
- Vladimir N. Strocov
(Swiss Light Source, Paul Scherrer Institut)
- Claudia Felser
(Max Planck Institute for Chemical Physics of Solids)
- M. Zahid Hasan
(Princeton University
Princeton University
Lawrence Berkeley National Laboratory
Quantum Science Center)
Abstract
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.
Suggested Citation
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 & , 2022.
"Observation of a linked-loop quantum state in a topological magnet,"
Nature, Nature, vol. 604(7907), pages 647-652, April.
Handle:
RePEc:nat:nature:v:604:y:2022:i:7907:d:10.1038_s41586-022-04512-8
DOI: 10.1038/s41586-022-04512-8
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Citations
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Cited by:
- Xian P. Yang & Yueh-Ting Yao & Pengyu Zheng & Shuyue Guan & Huibin Zhou & Tyler A. Cochran & Che-Min Lin & Jia-Xin Yin & Xiaoting Zhou & Zi-Jia Cheng & Zhaohu Li & Tong Shi & Md Shafayat Hossain & She, 2024.
"A topological Hund nodal line antiferromagnet,"
Nature Communications, Nature, vol. 15(1), pages 1-10, December.
- Jing Wang & Deshan Liang & Jing Ma & Yuanyuan Fan & Ji Ma & Hasnain Mehdi Jafri & Huayu Yang & Qinghua Zhang & Yue Wang & Changqing Guo & Shouzhe Dong & Di Liu & Xueyun Wang & Jiawang Hong & Nan Zhang, 2023.
"Polar Solomon rings in ferroelectric nanocrystals,"
Nature Communications, Nature, vol. 14(1), pages 1-9, December.
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