Abstract
We report the experimental discovery of orbital vortex lines in the three-dimensional (3D) band structure of a topological semimetal. Combining linear and circular dichroism in soft x-ray angle-resolved photoemission (SX-ARPES) with first-principles theory, we image the winding of atomic orbital angular momentum, thereby revealing - and determining the location of - lines of vorticity in full 3D momentum space. We determine the core of the orbital angular momentum vortex to host an almost movable, twofold, spin-degenerate Weyl nodal line, a topological feature predicted to occur in certain nonsymmorphic crystals. These results establish bimodal dichroism in SX-ARPES as a robust approach to trace 3D orbital textures. Our findings constitute the first imaging of nontrivial quantum-phase winding at line nodes and may pave the way to new orbitronic phenomena in quantum materials.
| Original language | English |
|---|---|
| Article number | 011032 |
| Journal | Physical Review X |
| Volume | 15 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2025 |
| Externally published | Yes |
Funding
D. D. S., G. S., and L. C. thank Chiara Pacella for useful discussions. This work is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through SFB 1170 ToCoTronics, the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter–ct.qmat Project-ID 390858490—EXC 2147, and RE1469/13-2. H. B. acknowledges support from the Research Council of Norway (RCN) through its Centres of Excellence funding scheme, Project No. 262633, “QuSpin,” and RCN Project No. 323766. The research leading to these results has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 897276. We acknowledge DESY (Hamburg, Germany), a member of the Helmholtz Association HGF, for the provision of experimental facilities. Parts of this research were carried out at PETRA III, and we would like to thank Kai Bagschik, Jens Viefhaus, Frank Scholz, Jörn Seltmann, and Florian Trinter for assistance in using Beamline P04. Funding for the photoemission spectroscopy instrument at Beamline P04 (Contract No. 05KS7FK2, No. 05K10FK1, No. 05K12FK1, No. 05K13FK1, and No. 05K19FK4 with Kiel University; No. 05KS7WW1, No. 05K10WW2, and No. 05K19WW2 with Würzburg University) by the Federal Ministry of Education and Research (BMBF) is gratefully acknowledged. J. S. would like to acknowledge Ján Minár for providing a computational cluster at NTC, University of West Bohemia. We gratefully acknowledge the Gauss Centre for Supercomputing e.V. for funding this project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre. J. N. and T. S. acknowledge support from the National Research Foundation, under Grant No. NSF DMR-1606952. The crystal synthesis and characterization was carried out at the National High Magnetic Field Laboratory, which is funded by the National Science Foundation (NSF DMR-2128556) and the State of Florida.