Scientists 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 – a finding that has now been confirmed experimentally. This achievement was led by Dr. Maximilian Ünzelmann, a group leader at ct.qmat – Complexity and Topology in Quantum Matter – at the Universities of Würzburg and Dresden. Demonstrating this quantum phenomenon marks a major milestone in quantum materials research. The team hopes that the vortex-like behavior of electrons in momentum space could pave the way for new quantum technologies, such as orbitronics, which would use electrons’ orbital torque to transmit information in electronic components instead of relying on electrical charge, potentially slashing energy losses.

Momentum Space vs. Position Space 

Momentum space is a fundamental concept in physics that describes electron motion in terms of energy and direction, rather than their exact physical position. Position space (its “counterpart”) 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. A few years ago, another ct.qmat research team made waves worldwide when they captured the first-ever three-dimensional image of a vortex-like magnetic field in a quantum material’s position space (Nature Nanotechnology 17 (2022) 250–255).

Theory Confirmed

Eight years ago, Roderich Moessner theorized that a quantum tornado could also form in momentum space. At the time, the Dresden-based ct.qmat co-founder 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. The breakthrough experiments revealed that the quantum vortex is created by orbital angular momentum – electrons’ circular motion around atomic nuclei. “When we first saw signs that the predicted quantum vortices actually existed and could be measured, we immediately reached out to our Dresden colleague and launched a joint project,” recalls Ünzelmann.

Quantum Tornado Discovered by Refining a Standard Method 

To detect the quantum tornado in momentum space, the Würzburg team enhanced a well-known technique called ARPES (angle-resolved photoemission spectroscopy). “ARPES is a fundamental tool in experimental solid-state physics. 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,” explains Ünzelmann. “By cleverly adapting this method, we were able to measure orbital angular momentum. I’ve been working with this approach since my dissertation.”

ARPES is rooted in the photoelectric effect, first described by Albert Einstein and taught in high school physics. Ünzelmann had already refined the method in 2021, gaining international recognition for detecting orbital monopoles in tantalum arsenide. Now, by integrating a form of quantum tomography, the team has taken the technique a step further to detect the quantum tornado – another major milestone. “We analyzed the sample layer by layer, similar to how medical tomography works. By stitching together individual images, we were able to reconstruct the three-dimensional structure of the orbital angular momentum and confirm that electrons form vortices in momentum space,” Ünzelmann explains.

Würzburg-Dresden Network: A Global Collaboration 

“The experimental detection of the quantum tornado is a testament to ct.qmat’s team spirit,” says Matthias Vojta, Professor of Theoretical Solid-State Physics at TU Dresden and ct.qmat’s Dresden spokesperson. “With our strong physics hubs in Würzburg and Dresden, we seamlessly integrate theory and experiment. Additionally, our network fosters teamwork between leading experts and early-career scientists – an approach that fuels our research into topological quantum materials. And, of course, almost every physics project today is a global effort – this one included.”

The tantalum arsenide sample was grown in the US and analyzed at PETRA III, a major international research facility at the German Electron Synchrotron (DESY) in Hamburg. A scientist from China contributed to the theoretical modeling, while a researcher from Norway played a key role in the experiments.

Looking ahead, the ct.qmat team is exploring whether tantalum arsenide could be used in the future to develop orbital quantum components.

Publication

T. Figgemeier, M. Ünzelmann, et al., "Imaging Orbital Vortex Lines in Three-Dimensional Momentum Space", Physical Review X 15, 011032 (2025)
https://journals.aps.org/prx/abstract/10.1103/PhysRevX.15.011032

Scientific Contact

Dr. Maximilian Ünzelmann
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Cluster of Excellence ct.qmat

The Cluster of Excellence ct.qmat – Complexity and Topology in Quantum Matter has been jointly run by Julius-Maximilians-Universität (JMU) Würzburg and Technische Universität (TU) Dresden since 2019. Over 300 scientists from more than thirty countries and four continents study topological quantum materials that reveal surprising phenomena under extreme conditions such as ultra-low temperatures, high pressure, or strong magnetic fields. ct.qmat is funded through the German Excellence Strategy of the Federal and State Governments and is the only Cluster of Excellence in Germany to be based in two different federal states.