Electrons lag behind the nucleus

One of the great successes of 20th-century physics was the quantum mechanical description of solids. This allowed scientists to understand for the first time how and why certain materials conduct electric current and how these properties could be purposefully modified. For instance, semiconductors such as silicon could be used to produce transistors, which revolutionized electronics and made modern computers possible.  

To be able to mathematically capture the complex interplay between electrons and atomic nuclei and their motions in a solid, physicists had to make some simplifications. They assumed, for example, that the light electrons in an atom follow the motion of the much heavier atomic nuclei in a crystal lattice without any delay. For several decades, this Born-Oppenheimer approximation worked well.  

Approximation fails in certain materials 

Now, however, researchers at ETH Zurich and the Max Planck Institute for the Structure and Dynamics of Matter in Hamburg have shown that the electrons in certain materials respond with a delay. Moreover, this delay depends on where the electrons are localized and which energy state they occupy.  

Using experiments with attosecond resolution and theoretical calculations, Ursula Keller and Lukas Gallmann at the Department of Physics at ETH could prove that electrons in flat layered materials, so-called MXenes, respond to the motion of atomic nuclei with an appreciable delay. The researchers recently published their results in the scientific journal Science. These results could help to develop novel opto-electronic devices in the future.  

Interesting effect in graphene-like materials 

Attosecond spectroscopy is used by scientists to study physical events with unimaginable time resolution in the range of billionths of a billionth of a second (10^-18 second). In the past thirty years, ETH researchers have done pioneering work in this field. “Phonons, or lattice vibrations, have not been our main interest as they are relatively slow”, says Sergej Neb, a postdoc in Keller’s group and first author of the paper. While studying phonons in MXenes, however, he and his colleagues discovered the unexpected delay in the motion of electrons.  

MXenes are two-dimensional materials similar to graphene. The MXene studied by the ETH researchers consists of several layers in which titanium, carbon and oxygen atoms bond together to form a lattice. The material was produced by colleagues at the Department of Mechanical and Process Engineering. 

But how can one study lattice vibrations inside such a material? The physicists managed to excite lattice vibrations in the MXene using a short infrared laser pulse. After that, they irradiated the material with an attosecond laser pulse in the extreme ultraviolet and measured how much of the laser light passed through the material. Depending on the wavelength of the pulses, the electrons in the material could be excited to absorb ultraviolet photons and hence to reach higher energy levels. Finally, the researchers repeated the experiment without initially exciting the lattice vibrations. From the difference between the two results they could then infer the motion of the electrons and the atomic nuclei.  

Electrons lag behind 

In particular, by varying the separation in time between the two laser pulses from a few femtoseconds (10^-15 second, or the millionth part of a billionth of a second) up to picoseconds (10^-12 second, or the thousandth part of a billionth of a second), the physicists were able to determine very precisely the delay with which the electrons reacted to the sudden excitation of the lattice vibrations.  

“Obviously, in the standard Born-Oppenheimer approximation we wouldn’t expect any delay at all”, says Neb, “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.” 

Finally, the ETH researchers compared their data to the results of a mathematical model developed by their colleagues in Hamburg. From that comparison they were able to deduce that the vibrations of the atomic nuclei influence the spatial distribution of the electrons, which, in turn, changes the electromagnetic field in the vicinity of the atoms in the lattice. Also, the interactions between the electrons played a big role.  

But there is more: from the data, Neb and his colleagues could even see how the electrons in the vicinity of the different atoms of the MXene behaved. “Such a view of the dynamics between electrons and phonons at the level of single atoms – and even depending on their state, the bonds and their energy – was not possible up to now. This detailed resolution was only made possible by our attosecond technology”, Neb explains.  

The researchers hope that their new insights into the interplay between electrons and lattice vibrations will lead to more precise mathematical models beyond the usual approximations. Practical applications can also be imagined. “Our method allows us to measure the coupling strength between electrons and lattice vibrations. From this, we can predict under what conditions certain electrons contribute more or less strongly to heat conduction”, Neb adds.  

A better understanding of energy and charge transport allows more control over materials and, therefore, new possibilities for opto-electronic devices at the nano-scale. At the same time, the microscopic insights into heat conduction at the atomic level are a starting point for the development of even smaller and more efficient electronic components.

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