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

Journal Article · · Nature (London)
ORCiD logo [1]; ORCiD logo [2];  [3];  [3]; ORCiD logo [3];  [3]; ORCiD logo [4]; ORCiD logo [3];  [3];  [3]; ORCiD logo [3];  [3];  [3]; ORCiD logo [5]; ORCiD logo [6];  [6];  [7];  [7];  [7];  [7] more »; ORCiD logo [8]; ORCiD logo [3]; ORCiD logo [6]; ORCiD logo [5]; ORCiD logo [9] « less
  1. Princeton Univ., NJ (United States); RIKEN Center for Emergent Matter Science (CEMS), Wako (Japan)
  2. Nanyang Technological Univ. (Singapore)
  3. Princeton Univ., NJ (United States)
  4. Max Planck Institute for Chemical Physics of Solids, Dresden (Germany); Indian Inst. of Technology (IIT), New Delhi (India)
  5. Max Planck Institute for Chemical Physics of Solids, Dresden (Germany)
  6. Paul Scherrer Inst. (PSI), Villigen (Switzerland). Swiss Light Source
  7. Lund Univ. (Sweden)
  8. National Sun Yat-sen University, Kaohsiung City (Taiwan)
  9. Princeton Univ., NJ (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Quantum Science Center (QSC)
+ Show Author Affiliations

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. Here 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.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); Argonne National Laboratory (ANL), Argonne, IL (United States). Advanced Photon Source (APS); SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP); National Research Foundation, Singapore; National Science Foundation (NSF); Swiss National Science Foundation (SNSF); MOST-AFOSR; European Research Council (ERC); Gordon and Betty Moore Foundation (GBMF)
Grant/Contract Number:
AC02-05CH11231; AC02-06CH11357; AC02-76SF00515; FG02-05ER46200; NRF-NRFF13-2021-0010; DGE-1656466; 200021-165529; 110-2124-M-110-002-MY3; DMR-2011750; 742068 “TOP-MAT”; GBMF4547; GBMF9461; 2018-07152
OSTI ID:
1958529
Journal Information:
Nature (London), Vol. 604, Issue 7907; ISSN 0028-0836
Publisher:
Nature Publishing GroupCopyright Statement
Country of Publication:
United States
Language:
English

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Figures / Tables (15)

FIG. 1(p. 18)figure FIG. 1
FIG. 2(p. 19)figure FIG. 2
FIG. 3(p. 20)figure FIG. 3
FIG. 4(p. 21)figure FIG. 4
FIG. 5(p. 22)figure FIG. 5
Extended Data Fig. 1(p. 23)figure Extended Data Fig. 1
Extended Data Fig. 2(p. 24)figure Extended Data Fig. 2
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Extended Data Fig. 4(p. 26)figure Extended Data Fig. 4
Extended Data Fig. 5(p. 27)figure Extended Data Fig. 5
Extended Data Fig. 6(p. 29)figure Extended Data Fig. 6
Extended Data Fig. 7(p. 30)figure Extended Data Fig. 7
Extended Data Fig. 8(p. 31)figure Extended Data Fig. 8
Extended Data Fig. 9(p. 32)figure Extended Data Fig. 9
Extended Data Fig. 10(p. 33)figure Extended Data Fig. 10

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