A well-known topological material has revealed an unexpected, controllable feature of its electronic structure. Credit: Shutterstock

Scientists have directly observed a subtle geometric property of electrons in a three-dimensional topological insulator.

Electrons moving across the surface of a topological insulator do more than carry electric charge. Their quantum states also possess a geometric structure that can influence how the material behaves. Researchers have now directly observed one measure of that structure, known as the quantum metric, in a three-dimensional topological insulator.

The international team, led by researchers at the University of Geneva (UNIGE), also found that the effect can be controlled electrically. Published in Nature Materials, the results extend previous measurements of the quantum metric to a major class of materials being investigated for future electronics and quantum technologies.

Why Topological Insulators Behave Differently

Topological insulators occupy an unusual middle ground between conductors and conventional insulators. Their interiors resist the flow of electrical current, while electrons can move along their surfaces. This combination arises from the quantum properties of the material’s electronic states rather than simply from differences in electrical resistance.

Those surface electrons are described by quantum states whose geometry can be characterized mathematically. One part of that description is the quantum metric, which measures how rapidly an electron’s quantum state changes as its momentum changes. Accessing that quantity experimentally gives physicists another way to investigate the microscopic behavior of quantum materials.

From Theory to Direct Measurement

Until recently, the quantum metric had largely remained a theoretical concept. In 2025, a team led by Andrea Caviglia, full professor in the Department of Quantum Matter Physics (DQMP), Physics Section, UNIGE Faculty of Science, reported an empirical measurement using a quantum material made from strontium titanate and lanthanum aluminate.

“There are several families of topological insulators,” explains Giacomo Sala, senior research associate in the UNIGE DQMP and lead author of the study. “The material we used in this work consists of antimony and tellurium, two metalloids with properties intermediate between those of metals and non-metals. It is one of the most extensively studied topological insulators to date, and its potential applications are highly promising.”

Electrical Control of Quantum Geometry

The researchers did more than reproduce the earlier observation in another material. Their measurements indicate that quantum metric effects in the topological insulator can be adjusted using electrical control, linking the geometry of electronic quantum states to a practical experimental knob.

“These new results extend and confirm our previous observations, which were obtained using a very different material. Moreover, they show that quantum metric effects can be controlled electrically,” says Andrea Caviglia, who led the research. “The entire scientific community now has a new property to explore in the materials of the future, particularly to investigate how the geometric properties of electrons can reveal the fundamental nature of these materials.”

Reference: “Probing the quantum metric of 3D topological insulators” by Giacomo Sala, Emanuele Longo, Maria Teresa Mercaldo, Stefano Gariglio, Mario Cuoco, Roberto Mantovan, Carmine Ortix and Andrea D. Caviglia, 22 May 2026, Nature Materials.
DOI: 10.1038/s41563-026-02617-3

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