Einstein in a Chip: Hidden Geometry Bends Electrons Like Gravity

Scientists are exploring quantum materials to enable ultra-fast computing and lossless electricity, but doing so requires understanding atomic-scale effects that are still largely mysterious. A new study reveals an elusive “quantum geometry” that subtly bends electron paths inside materials, echoing how gravity curves light. Credit: SciTechDaily.com A team at UNIGE has uncovered a geometric structure once thought to be purely theoretical at the core of quantum materials, opening the door to major advances in future electronics. How can information be processed almost instantly, or electrical current flow without energy loss? To reach these goals, researchers in both academia and industry are increasingly focused on quantum materials, which operate according to the rules of physics at the smallest scales. Creating these materials demands a deep understanding of atomic-level behavior, an area that is still far from fully understood. Researchers from the University of Geneva (UNIGE), working with colleagues at the University of Salerno and the CNR-SPIN Institute (Italy), have now made a significant advance by identifying a hidden form of geometry that was previously only predicted by theory. This geometry alters the paths followed by electrons in a way that resembles how gravity curves the path of light. Their findings, published in Science, point to new possibilities for quantum electronics. The technologies of the future rely on materials with extraordinary capabilities rooted in quantum physics. This shift is driven by the study of matter at microscopic scales, which lies at the core of quantum science. Over the last century, investigating how atoms, electrons, and photons behave inside materials led to the invention of transistors and eventually to modern computers. Today, scientists continue to uncover quantum effects that challenge long-standing theoretical models. Recent research indicates that, in some materials, a form of geometry can emerge when large numbers of particles are considered together. This geometric structure appears to influence how electrons move through a material, in a way that echoes Einstein’s description of gravity shaping the trajectory of light. From theory to observation Known as quantum metric, this geometry reflects the curvature of the quantum space in which electrons move. It plays a crucial role in many phenomena at the microscopic scale of matter. Yet detecting its presence and effects remains a major challenge. ‘‘The concept of quantum metric dates back about 20 years, but for a long time it was regarded purely as a theoretical construct. Only in recent years have scientists begun to explore its tangible effects on the properties of matter,’’ explains Andrea Caviglia, full professor and director of the Department of Quantum Matter Physics at the UNIGE Faculty of Science. Thanks to recent work, the team led by the UNIGE researcher, in collaboration with Carmine Ortix, associate professor in the Department of Physics at the University of Salerno, has detected quantum metric at the interface between two oxides — strontium titanate and lanthanum aluminate — a well-known quantum material. ‘‘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,’’ explains Giacomo Sala, research associate in the Department of Quantum Matter Physics at the UNIGE Faculty of Science and lead author of the study.

Unlocking Future Technologies Observing this phenomenon makes it possible to characterize a material’s optical, electronic, and transport properties with greater precision. The research team also demonstrates that quantum metric is an intrinsic property of many materials — contrary to previous assumptions. ‘‘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,’’ concludes Andrea Caviglia. Reference: “The quantum metric of electrons with spin-momentum locking” by Giacomo Sala, Maria Teresa Mercaldo, Klevis Domi, Stefano Gariglio, Mario Cuoco, Carmine Ortix and Andrea D. Caviglia, 21 August 2025, Science. DOI: 10.1126/science.