Researchers at ETH Zurich have observed, for the first time, that electrons in certain two-dimensional materials do not move in lockstep with atomic nuclei but instead respond with a measurable delay of up to 30 femtoseconds. Published in Science, the discovery challenges a cornerstone assumption of solid-state physics and could open the door to new nano-scale opto-electronic devices.
For decades, physicists have relied on a powerful simplification to understand how solids work. Known as the Born–Oppenheimer approximation, it assumes that lightweight electrons instantly follow the motion of much heavier atomic nuclei in a crystal lattice. This idea underpins much of modern electronics, from silicon transistors to computer processors, and for most materials, it works remarkably well.
Now, a team led by Professor Ursula Keller, professor of physics at ETH Zurich, together with Professor Lukas Gallmann, has shown that this assumption breaks down in a class of atomically thin materials. In these systems, electrons do follow the nuclei—but not immediately.
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Using ultra-precise measurements, the researchers demonstrated that electrons can lag behind lattice vibrations by as much as 30 femtoseconds. In everyday terms, that delay is unimaginably short. But in the realm of attosecond spectroscopy, it is a surprisingly long and physically meaningful timescale.
The experiments focused on MXenes, a family of graphene-like, two-dimensional materials made of layered metals and carbides. The MXene studied at ETH Zurich consists of layers of titanium, carbon, and oxygen atoms arranged in a flat crystal lattice. These materials are already attracting interest for applications ranging from batteries to sensors, but their fundamental physics is still being explored.
To probe electron motion, the team used attosecond spectroscopy, a technique capable of tracking processes on the scale of 10⁻¹⁸ seconds. ETH researchers have played a pioneering role in developing this technology over the past 30 years, and it proved crucial for revealing dynamics that were previously invisible.
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“Phonons, or lattice vibrations, have not been our main interest as they are relatively slow,” said Sergej Neb, the study’s first author and a postdoctoral researcher at ETH Zurich. “But while studying phonons in MXenes, we noticed something unexpected—the electrons didn’t respond instantly.”
In the experiment, the researchers first triggered lattice vibrations in the MXene using a short infrared laser pulse. They then probed the material with an extreme ultraviolet attosecond pulse and measured how much light passed through it. By carefully varying the time delay between the two pulses—from a few femtoseconds to several picoseconds—they reconstructed the motion of both nuclei and electrons with unprecedented resolution.
“Obviously, in the standard Born–Oppenheimer approximation we wouldn’t expect any delay at all,” Neb explained. “But we noticed that the electrons lagged behind the atomic nuclei by up to thirty femtoseconds—in the attosecond world, that’s a very long time.”
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The effect was not uniform. The delay depended on where the electrons were located within the material and which energy states they occupied. This spatial and energetic sensitivity revealed that electron–electron interactions and changes in the local electromagnetic field play a much larger role than previously assumed.
To confirm their findings, the ETH team compared their experimental data with advanced theoretical models developed in collaboration with scientists at the Max Planck Institute for the Structure and Dynamics of Matter in Hamburg. The agreement between theory and experiment strengthened the conclusion that lattice vibrations actively reshape the electronic landscape of the material, rather than electrons merely tagging along.
For the first time, the researchers could even observe how electrons behaved near individual atoms in the lattice. “Such a view of the dynamics between electrons and phonons at the level of single atoms—and even depending on their state and bonding—was not possible up to now,” Neb said. “This detailed resolution was only made possible by our attosecond technology.”
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Beyond rewriting textbooks, the discovery has practical implications. By directly measuring how strongly electrons couple to lattice vibrations, scientists can better predict heat and charge transport in advanced materials. That insight could guide the design of smaller, faster, and more energy-efficient opto-electronic devices, especially at the nano-scale.
The work suggests that future electronics may need theories that go beyond long-standing approximations. As devices shrink and materials become thinner, even a 30-femtosecond delay can matter.
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