Physicists have long known that electrons can form vortices in quantum materials. What’s new is the proof that these tiny particles create tornado-like structures in momentum space.
In a quantum material called tantalum arsenide (TaAs), electrons form vortices in momentum space. Image credit: Think-Design / Jochen Thamm.
Momentum space is a fundamental concept in physics that describes electron motion in terms of energy and direction, rather than their exact physical position.
Its counterpart, position space, is the realm where familiar phenomena like water vortices or hurricanes occur.
Until now, even quantum vortices in materials had only been observed in position space.
Eight years ago, Dr. Roderich Moessner from the Max Planck Institute for the Physics of Complex Systems and the Würzburg-Dresden Cluster of Excellence ct.qmat theorized that a quantum tornado could also form in momentum space.
At the time, he described the phenomenon as a smoke ring, because, like smoke rings, it consists of vortices.
However, until now, no one knew how to measure them.
To detect the quantum tornado in momentum space, Dr. Moessner and colleagues enhanced a well-known technique called ARPES (angle-resolved photoemission spectroscopy).
“ARPES is a fundamental tool in experimental solid-state physics,” explained Dr. Maximilian Ünzelmann, a researcher with the Experimentelle Physik VII and Würzburg-Dresden Cluster of Excellence ct.qmat at the Universität Würzburg.
“It involves shining light on a material sample, extracting electrons, and measuring their energy and exit angle.”
“This gives us a direct look at a material’s electronic structure in momentum space.”
“By cleverly adapting this method, we were able to measure orbital angular momentum.”
The team’s work appears in the journal Physical Review X.
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T. Figgemeier et al. 2025. Imaging Orbital Vortex Lines in Three-Dimensional Momentum Space. Phys. Rev. X 15, 011032; doi: 10.1103/PhysRevX.15.011032
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