When repulsion turns into attraction

Materials can take on completely different properties depending on temperature, pressure, electrical voltage or other physical quantities. In theoretical solid-state physics, state-of-the-art computer models are used to understand these properties in detail. Sometimes it works well, but sometimes weird effects occur that still seem puzzling, such as phenomena related to high temperature superconductivity.

A few years ago, scientists from TU Wien had already been able to mathematically clarify where the boundary is between the area that follows the known rules and the area where unusual effects play an important role. Now, with the help of complex supercomputer calculations, it was possible for the first time to explain exactly what happens when this boundary is crossed: the repulsion between the electrons is suddenly countered by an additional attractive force that allows for completely counterintuitive effects.

Similarly to the way water molecules combine to form droplets, electrons can then join at certain points, as if they are partially stuck together. The results, obtained in an international collaboration between TU Wien, the University of Würzburg, the University of L’Aquila and the Georgetown University of Washington DC, have now been published in the journal Physical Review Letters.

To infinity and beyond

“The electrons are negatively charged, they repel each other. Therefore, the electrons moving through the material are scattered by other electrons,” says prof. Alessandro Toschi of the Institute of Solid State Physics of the TU Wien. “However, this dispersion is not always as strong. It is possible that the repulsion between the electrons is shielded in the material. This depends on many factors, such as the chemical composition of the material.”

Exactly at the border where unusual effects begin to appear, the diffusion processes between electrons theoretically become infinitely strong due to the lack of shielding. This is known as “divergence” and these divergences present a major research challenge. “For a long time there has been a very controversial discussion: do these differences actually have real physical significance?” says Patrick Chalupa, who is studying this problem as part of his dissertation in Alessandro Toschi’s group. “We were able to answer this question: Yes, these divergences are not just a mathematical curiosity, but the key to a better understanding of important material effects,” says Matthias Reitner, who wrote his dissertation on this topic. .

As you approach the mathematical limit, the repulsion grows stronger and stronger. At the limit, the corresponding dispersion between the electrons becomes infinitely large, but if the limit is exceeded, something surprising happens: the repulsion suddenly causes an additional attraction. This effective attraction forces the electrons to gather at certain points in a confined space, as if they are partially stuck together. This drastic change in behavior is closely related to the occurrence of differences.

Phase transition, similar to water vapor

“The result is a situation reminiscent of liquid water and water vapor,” says Alessandro Toschi, “under certain conditions there is an attraction between the water molecules. They bond together and create a mixture of liquid droplets and gaseous vapor. However, the origin of this attraction is completely different in the two cases “.

For the first time it was possible to get a detailed picture of what happens in such situations from a materials science perspective at the microscopic level. “This means that it is now possible to understand exactly why some mathematical approaches, the so-called perturbative methods, did not produce the correct result,” says Patrick Chalupa.

This new microscopic insight may be a missing piece of the puzzle for the theoretical understanding of so-called unconventional superconductors. These are iron, copper or nickel based materials that can be superconducting under certain conditions up to incredibly high temperatures. “Perhaps we will finally be able to answer some of the essential questions that have remained unanswered since the discovery of these mysterious materials 40 years ago,” hopes Matthias Reitner.