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

Area of Science:

• Condensed Matter Physics
• Quantum Materials Science
• Topological Matter

Background:

• Topological invariants classify quantum phases, crucial for understanding diverse phenomena like superfluids and topological insulators.
• Knot theory, a branch of mathematics, offers tools to describe complex topological structures.

Purpose of the Study:

• To identify and characterize a new topological invariant in quantum matter using knot theory.
• To experimentally observe and determine the linking number of electronic band crossing loops in a magnetic material.

Main Methods:

• Utilized state-of-the-art spectroscopic methods to probe the electronic band structure.
• Analyzed the topology of intertwined degeneracy loops in the bulk Brillouin zone.
• Drew link diagrams to determine the linking number invariant.

Main Results:

• Observed three intertwined degeneracy loops in a mirror-symmetric ferromagnet.
• Determined a linking number invariant of (2, 2, 2) for these loops.
• Predicted and observed Seifert boundary states protected by the bulk linked loops, demonstrating a bulk-boundary correspondence.

Conclusions:

• Established a novel linking-number invariant for quantum phases, analogous to knot theory.
• Demonstrated the direct experimental determination of topological invariants from spectroscopic data.
• Highlighted the potential of knot theory in exploring magnetic and superconducting quantum matter.