What an Electron Really Looks Like

Measuring the Electron QGT in Kagome Solids

Quantum Visualization Breakthrough: International Teams Unveil Electron's Geometry for First Time

In a groundbreaking achievement that marks a significant leap forward in quantum physics, an international collaboration led by MIT researchers has successfully measured the geometric "shape" of electrons in solid materials for the first time. This discovery, published in the November 25, 2024 issue of Nature Physics, has opened up entirely new avenues for understanding and manipulating quantum properties of materials that were previously inaccessible to experimental observation.

From Theory to Observation

While scientists have long been able to measure the energies and velocities of electrons in crystalline materials, their quantum geometry—how electrons are distributed and behave in space as they move through solids—remained theoretical until now. Using highly specialized techniques, the MIT team successfully measured the Quantum Geometric Tensor (QGT) [see sidebar] in kagome metals, a class of quantum materials with a distinctive basket-weave atomic structure [see sidebar], providing the first direct experimental confirmation of quantum geometry in solid-state physics.

"This work represents the culmination of years of theoretical development and experimental refinement," explains Riccardo Comin, MIT's Associate Professor of Physics who led the research. "We've essentially created a blueprint for accessing completely new information about quantum materials that could dramatically accelerate development in fields ranging from quantum computing to energy-efficient electronics."

Global Scientific Impact

The breakthrough has attracted attention from quantum materials research centers worldwide. At the Max Planck-UBC-UTokyo Center for Quantum Materials, a collaboration between German, Canadian, and Japanese institutions, scientists are already exploring potential applications of this new measurement technique to their own cutting-edge research on quantum phenomena and materials.

Meanwhile, researchers at Southern University of Science and Technology (SUSTech) in China, in partnership with Princeton University, have been advancing parallel work on kagome materials, exploring the rich emergent phenomena resulting from the quantum interactions between geometry, topology, spin, and electron correlation effects.

Technological Applications

The implications of this discovery extend far beyond fundamental physics. At Florida State University, researchers have demonstrated how kagome metals like cesium vanadium antimonide (CsV₃Sb₅) can enhance nano-optics by generating unique plasmon polaritons, potentially advancing optical communication and sensing technologies.

European researchers at the Würzburg-Dresden Cluster of Excellence ct.qmat in Germany have made complementary discoveries showing that kagome metals exhibit superconductivity through a unique wave-like distribution of electron pairs, which could lead to the development of novel superconducting quantum devices.

Further research at RMIT University in Australia and the High Magnetic Field Laboratory in China has demonstrated the first electronic control of superconductivity and the quantum Hall effect in kagome metals, potentially enabling dramatic reductions in the energy costs of computing.

The Heart of the Discovery: ARPES Technique

The key to the MIT team's breakthrough was their innovative application of angle-resolved photoemission spectroscopy (ARPES). This technique works by directing high-energy light at a material to eject electrons, then analyzing the angles and velocities of these ejected electrons to create detailed maps of their geometric structure.

The team specifically directed this technique at a cobalt-tin alloy, a kagome metal with an intricate lattice structure resembling the traditional Japanese kagome basket-weaving pattern. The measurements provided researchers with the first direct observation of the QGT in a solid, allowing them to infer the complete quantum geometry of electrons in the metal.

"This is truly a global achievement," notes Mingu Kang, first author of the Nature Physics paper and now a Kavli Postdoctoral Fellow at Cornell University. "The pandemic actually facilitated international collaboration in unexpected ways, connecting theorists and experimentalists across continents in a remarkable example of science transcending borders."

Looking Forward

As quantum materials research continues to advance worldwide, the new ability to directly measure quantum geometry opens up exciting possibilities for materials engineering and quantum technologies. The Max Planck Institute for the Science of Light in Germany is already using this new understanding to investigate the effects of electronic correlations in the AV₃Sb₅ family of kagome superconductors, potentially enabling breakthroughs in energy-efficient electronics.

At the Max Planck Institute for Solid State Research, scientists have synthesized new complex iridium oxides with hyper-kagome lattices that exhibit semi-metallic states produced by competition between molecular orbital splitting and strong spin-orbit coupling, further expanding the frontiers of quantum materials research.

With these international collaborations accelerating, the future of quantum materials science looks exceptionally bright, promising new technologies that could transform computing, energy production, and electronic devices in the coming decade.

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SIDEBAR: Understanding the Quantum Geometric Tensor (QGT)

What Is the QGT?

The Quantum Geometric Tensor (QGT) is a central mathematical object in modern physics that encodes complete information about the geometry of quantum states. Its imaginary part is the well-known Berry curvature, which plays a fundamental role in topological magnetoelectric and optoelectronic phenomena.

Why It Matters

Think of the QGT as providing a map of the "landscape" that electrons navigate in quantum materials. Just as geographic maps help us understand how objects move across terrain, the QGT reveals how electrons behave as they move through solids, including their unusual quantum effects that have no classical analog.

Two Important Components

The QGT has two parts:

1. The imaginary part (Berry curvature): This functions like a "magnetic field" in momentum space, bending electron trajectories in ways that enable phenomena like the quantum Hall effect and other topological behaviors in electronic materials.

2. The real part (quantum metric): This measures "distances" between quantum states, revealing how electron wavefunctions change when system parameters are slightly modified, crucial for understanding properties like superconductivity.

In Everyday Terms

If traditional electron measurements only tell us how fast electrons move (energy) and in which direction (momentum), the QGT reveals the full terrain they're traversing—the hills, valleys, and obstacles that shape their journey through a material.

Global Research Impact

The Max Planck Institute in Germany is using QGT measurements to investigate exotic electronic correlations in kagome superconductors, while Chinese researchers at SUSTech are exploring how the QGT relates to quantum magnetism and topology.

At the University of Tokyo, part of the Max Planck-UBC-UTokyo collaboration, scientists are combining QGT measurements with studies of strongly correlated electron systems to understand complex quantum behaviors in new materials.

The MIT breakthrough is significant because it's the first time scientists have directly measured the QGT in solid materials rather than just theorizing about it—like moving from drawing imaginary maps to actually surveying the territory.

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Kagome Basket Weave (Kagome Metals)

SIDEBAR: Kagome Metals - A Global Quantum Playground

What Are Kagome Metals?

Named after a traditional Japanese basket-weaving pattern, kagome metals are quantum materials whose atoms arrange in corner-sharing triangles with hexagonal voids, creating a unique electronic environment that hosts exotic quantum phenomena including flat bands, Dirac fermions, and topological states.

Extraordinary Electronic Properties

The kagome lattice's geometric frustration gives rise to three remarkable features:

1. Flat Bands: These energy bands where electrons behave with nearly infinite effective mass have been observed in materials like CoSn with extraordinarily narrow bandwidths below 0.02 eV, making them ideal platforms for studying strong electron correlations.

2. Dirac Cones: These linear band crossings host electrons that behave like massless relativistic particles, enabling high electron mobility and topological effects that persist even at room temperature in some kagome magnets.

3. Van Hove Singularities: Points where the density of states spikes dramatically, enhancing electron interactions and potentially driving exotic phenomena like superconductivity and charge density waves.

Global Research Landscape

European scientists at the Würzburg-Dresden Cluster have discovered that kagome metals exhibit superconductivity through wave-like distribution of electron pairs, a phenomenon termed "sublattice-modulated superconductivity," with significant implications for quantum computing.

Researchers at Southern University of Science and Technology in China, in collaboration with Princeton University, have demonstrated the connection between kagome geometry and emergent quantum phenomena, including topological magnetism and unconventional superconductivity.

At Florida State University, scientists have shown how kagome metals like CsV₃Sb₅ can generate unique plasmon polaritons for advanced optical technologies, while minimizing energy losses typically encountered in conventional metals.

The Max Planck Institute for Solid State Research has synthesized complex iridium oxides with hyper-kagome lattices, demonstrating how spin-orbit coupling can induce semi-metallic states, further expanding the frontiers of kagome physics.

Synthesis Methods

Thin films of kagome metals like FeSn can be grown via molecular beam epitaxy (MBE) on substrates such as LaAlO₃(111), enabling precise layer-by-layer growth under ultra-high vacuum conditions for fundamental research and potential device applications.

Single crystals of materials like YCr₆Ge₆ are typically grown using flux methods, where precise mixtures of elements are heated to temperatures around 1100°C and slowly cooled to allow crystal formation, often using tin or other metals as flux media.

Researchers at multiple institutions have also employed magnetron sputtering to create continuous, epitaxial thin films of kagome metals on various substrates, sometimes using ferromagnetic buffer layers to improve film quality and explore spintronic applications.

International Collaboration

The Max Planck-UBC-UTokyo Center for Quantum Materials represents a premier global collaboration between German, Canadian, and Japanese institutions, advancing research on kagome metals and other quantum materials through joint research programs and scientist exchanges.

Research on kagome materials in the United States is supported by the National Quantum Initiative Act, with institutions like the University of Pennsylvania exploring the intricate relationship between superconductivity, topology, and correlation in these materials.

These global efforts highlight how kagome metals have become central to the worldwide quest to understand and harness quantum phenomena for future technologies.

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Sources

For Main Story and Both Sidebars

1. Kang, M., Kim, S., Qian, Y., Neves, P.M., Ye, L., Jung, J., Puntel, D., Mazzola, F., Fang, S., Jozwiak, C., Bostwick, A., Rotenberg, E., Fuji, J., Vobornik, I., Park, J.H., Checkelsky, J.G., Yang, B.J., & Comin, R. (2024). Measurements of the quantum geometric tensor in solids. Nature Physics. DOI: 10.1038/s41567-024-02678-8 https://www.nature.com/articles/s41567-024-02678-8

2. Yin, J.X., Lian, B., & Hasan, M.Z. (2022). Rise of Kagome Physics. Southern University of Science and Technology. https://phy.sustech.edu.cn/news/detail/3460.html?lang=en-us

3. SciTechDaily. (2024, August 25). Kagome Metals Unlocked: A New Dimension of Superconductivity. https://scitechdaily.com/kagome-metals-unlocked-a-new-dimension-of-superconductivity/

4. SciTechDaily. (2024, August 3). Weaving Light: Unraveling the Quantum Lattice of Kagome Metals. https://scitechdaily.com/weaving-light-unraveling-the-quantum-lattice-of-kagome-metals/

5. Max Planck-UBC-UTokyo Center for Quantum Materials. https://www.fkf.mpg.de/mpg-ubc

6. Max Planck Institute for Solid State Research. Takayama - Takagi: Spin-orbit coupling induced semi-metallic state in the hyper-kagome Na3Ir3O8. https://www.fkf.mpg.de/5246920/I_01_Takayama

7. ScienceDaily. (2023, May 10). Destroying the superconductivity in a kagome metal: Electronic control of quantum transitions in candidate material for future low-energy electronics. https://www.sciencedaily.com/releases/2023/03/230303105219.htm

8. Brookhaven National Laboratory. (2023). Scientists Study Atomic Vibrations in a Kagome Metal. https://www.bnl.gov/newsroom/news.php?a=221687

9. Laxmeesha, P.M., Tucker, T.D., Rai, R.K., Li, S., Yoo, M.W., Stach, E.A., Hoffmann, A., & May, S.J. (2024). Epitaxial growth and magnetic properties of kagome metal FeSn/elemental ferromagnet heterostructures. Journal of Applied Physics, 135(8), 085302. https://pubs.aip.org/aip/jap/article/135/8/085302/3267318/Epitaxial-growth-and-magnetic-properties-of-kagome

10. University of British Columbia. UBC, Max Planck joined by UTokyo in quantum materials collaboration. https://science.ubc.ca/news/ubc-max-planck-joined-utokyo-quantum-materials-collaboration

11. Max Planck Institute for the Science of Light. (2024). Contradictions of the Kagome metal AV₃Sb₅. https://www.mpsd.mpg.de/841750/2024-02-kagome-guo

12. Wu, L., et al. (2024). New discoveries in kagome metals. Penn Today. https://penntoday.upenn.edu/news/penn-engineering-discoveries-kagome-metals

    
    

“Now We Finally See It”: Historic Quantum Physics Breakthrough Reveals What an Electron Really Looks Like for the First Time Ever - Sustainability Times