Research led by Andrea D. Caviglia at the University of Geneva is shedding new light on how electrons move inside quantum materials, revealing that their trajectories can be shaped by an internal geometry that has no classical counterpart. The findings provide experimental evidence for a concept long discussed in theory, showing that the collective behavior of electrons can give rise to geometric effects that resemble how gravity bends the path of light.
Sala, G., Mercaldo, M. T., Domi, K., Gariglio, S., Cuoco, M., Ortix, C., & Caviglia, A. D. (2025). The quantum metric of electrons with spin-momentum locking. Science, 389(6762), 822–825. https://doi.org/10.1126/science.adq3255
The study focuses on quantum materials, a class of systems whose electrical and optical properties are governed by interactions at atomic scales. These materials are of growing interest because of their potential applications in ultra-fast electronics, low-energy computing, and superconducting technologies. However, progress in this area depends on understanding physical effects that emerge only when many particles interact simultaneously.
Andrea D. Caviglia at the University of Geneva stated,
‘‘These discoveries open up new avenues for exploring and harnessing quantum geometry in a wide range of materials, with major implications for future electronics operating at terahertz frequencies (a trillion hertz), as well as for superconductivity and light–matter interactions.”
For decades, physicists have known that electrons in solids are influenced not only by forces such as electric and magnetic fields, but also by the structure of the quantum states they occupy. One such structural property is known as the quantum metric. Unlike conventional geometry, which describes distances in physical space, the quantum metric describes distances between quantum states. Until recently, its role in real materials remained largely speculative.
The research team, working with collaborators from the University of Salerno and the CNR-SPIN Institute in Italy, identified measurable consequences of this quantum geometry at the interface between two oxide materials, strontium titanate and lanthanum aluminate. This interface is known to host a highly mobile electron system that exhibits a range of unusual electronic behaviors.
By applying strong magnetic fields and tracking how electrons responded, the researchers observed deviations in electron motion that could not be explained by existing models alone. These deviations were consistent with the influence of the quantum metric, effectively bending electron trajectories in a manner analogous to how curved spacetime alters the path of light in Einstein’s theory of gravity.
According to the researchers, this observation marks an important step in moving quantum geometry from abstract theory into experimentally accessible physics. The results suggest that the quantum metric is not a rare or engineered feature, but an intrinsic property of many materials, particularly those with strong spin-momentum coupling.
From an engineering perspective, the ability to characterize and eventually control this geometric contribution could improve how materials are designed for high-frequency electronics and optoelectronic devices. Electron transport, optical response, and energy dissipation are all influenced by the underlying quantum structure of a material, and incorporating geometric effects into material models may lead to more accurate predictions and improved performance.
The findings also have implications for superconductivity and light–matter interactions, where subtle changes in electron dynamics can have large macroscopic consequences. As devices continue to shrink and operate at higher frequencies, effects that were once negligible may become central to design considerations.
While practical applications are still some distance away, the study provides experimental tools for probing quantum geometry in solid-state systems. By linking electron motion to measurable geometric properties, the work offers a framework for exploring new regimes of material behavior that lie beyond traditional band theory.
As research into quantum materials advances, understanding how geometry emerges from collective quantum behavior may become as important as understanding forces and interactions. The work from Caviglia and his collaborators shows that even within a solid-state chip, concepts rooted in fundamental physics can play a tangible role in shaping how electrons move and how future electronic systems might function.
Adrian graduated with a Masters Degree (1st Class Honours) in Chemical Engineering from Chester University along with Harris. His master’s research aimed to develop a standardadised clean water oxygenation transfer procedure to test bubble diffusers that are currently used in the wastewater industry commercial market. He has also undergone placments in both US and China primarely focused within the R&D department and is an associate member of the Institute of Chemical Engineers (IChemE).
