Scientists can now measure geometric properties of quantum states in real materials—but they have not photographed an electron’s shape. In one 2025 report, a team detected a quantum-metric signal at an oxide interface through changes in electron trajectories under intense magnetic fields. A separate study reconstructed the quantum geometric tensor in the kagome metal CoSn using advanced photoemission spectroscopy. These experiments reveal different aspects of quantum geometry by different methods.
What “the geometry of electrons” actually means
In a crystal, an electron is described by a quantum state that changes with properties such as its momentum. The quantum geometric tensor (QGT) captures geometric information about how those states vary. It is not a description of an electron’s physical outline.
- Quantum metric: The real part of the QGT. It describes a kind of distance between nearby quantum states.
- Berry curvature: The imaginary part of the QGT. It is associated with geometric phase effects and can contribute to topological responses.
The two quantities are related parts of one mathematical object, but they are not interchangeable. An experiment may detect one, reconstruct both, or study quantum geometry in a different platform.
Two different experiments in solid materials
| Study | Material or system | What researchers measured | How to interpret the result |
|---|---|---|---|
| University of Geneva report, 2025 | Interface between strontium titanate and lanthanum aluminate | A quantum-metric signal inferred from electron-trajectory distortions under intense magnetic fields | An experimentally detected effect attributed to quantum metric, not an image of electrons. University of Geneva identifies the related Science paper by DOI 10.1126/science.adq3255. |
| CoSn study, online 2024; journal volume 21, 2025 | Kagome metal CoSn, which hosts topological flat bands | Researchers used polarization-, spin-, and angle-resolved photoemission spectroscopy to reconstruct the QGT | A momentum- and energy-resolved spectroscopic reconstruction in a crystalline solid. The paper appeared in Nature Physics 21, pages 110–117. Nature Physics paper |
The oxide-interface result
The Geneva team’s approach looked for how quantum metric affects electron motion in the presence of strong magnetic fields. The reported signal is trajectory distortion—not a direct visual rendering of the metric or of individual electrons. The university’s account describes the finding but does not provide a numerical measurement to quote.
Do these 3 things before closing this tab:
1Clear out junk files and repair common Windows errors2Scan for outdated or missing drivers - takes under a minute3Repair Windows errors before they cause bigger problems#1 Best Overall
As Giacomo Sala, the study’s lead author, explained in the University of Geneva account, “Its presence can be revealed by observing how electron trajectories are distorted under the combined influence of quantum metric and intense magnetic fields applied to solids.”
The CoSn photoemission reconstruction
In the separate CoSn experiment, researchers combined polarization, spin, and angle information in angle-resolved photoemission spectroscopy (ARPES) to reconstruct the QGT. ARPES measures electrons emitted from a material after illumination; resolving these additional properties lets researchers infer information about the electronic states and their geometry. The study is reported in Nature Physics. MIT’s account of this CoSn work quotes research leader Riccardo Comin describing the method as “a blueprint for obtaining some completely new information that couldn’t be obtained before.”
Why these are not the same “first”
The Geneva and CoSn studies concern different materials and observables, and they use different experimental approaches: one detects a transport-related trajectory response attributed to quantum metric; the other reconstructs the QGT from photoemission measurements. A third, related result studied quantum metric and nonzero non-Hermitian Berry curvature in a square lattice of radiatively coupled plasmonic nanoparticles. That is an engineered light-based platform, not the same kind of electron-solid experiment. Physical Review Research published that work in 2024.
For that reason, headlines claiming a single, universal first measurement can blur important differences. The useful comparison is the platform, which geometric quantity was accessed, and whether the result was a detected physical effect or a reconstructed tensor.
Free tools Windows power users keep installed
One-click scans. No signup required.
What the measurements could make possible
Quantum geometry gives researchers another way to investigate how electronic states behave in materials. The Geneva group points to possible future relevance for terahertz electronics, superconductivity, and light–matter interactions, but these are research avenues, not demonstrated consumer applications. Andrea Caviglia, director of the University of Geneva’s Department of Quantum Matter Physics, said the findings “open up new avenues for exploring and harnessing quantum geometry” in those areas.
The distinction matters: measuring a property that may influence a material is an advance in understanding and experimental capability. It does not by itself show that a faster device, a new superconductor, or a commercial technology has been built.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.What “direct observation” does—and does not—claim
Here, “direct” refers to experimental access to quantum-geometric properties through measurable effects or spectroscopic signatures. It does not mean ordinary photography. The Geneva result exposes quantum metric through how trajectories respond; the CoSn result reconstructs the tensor from ARPES data. Both connect theory to measurements in real systems, but neither shows a tiny geometric surface around an electron.
Quick Recap
Best Value
Product prices and availability are accurate as of the date/time indicated and are subject to change. Any price and availability information displayed on Amazon at the time of purchase will apply.
Recommended Free Tools
