In one sentence
The GreenNP project, led by Jean Paul Nery at the Physics Department of the University of Liège, aims to study the role of nonperturbative electron-phonon effects in electronic properties of solids.
One paragraph summary
Solids are made of electrons and atoms. The atoms vibrate constantly, and these vibrations — known as phonons — interact with the electrons in ways that govern many of the most important properties of solids: the colors they absorb or emit, how they conduct electricity, and whether they become superconductors. The standard tool for studying how electronic energies are modified by phonons is perturbation theory, a framework that works well when atomic vibrations produce modest changes in electronic behavior. GreenNP instead uses a rigorous nonperturbative approach: rather than assuming small effects, it directly explores the full range of atomic configurations that actually occur in a crystal at a given temperature. A key example is hydrogen: being the lightest element, quantum mechanics dictates that its atomic vibrations are particularly large, causing dramatic shifts in the energy barrier electrons must overcome to conduct electricity. Hydrogen-rich compounds have attracted enormous interest in recent years and are among the most promising candidates for high-temperature superconductivity, yet in these materials the perturbative approach cannot reliably describe the distribution of electronic energies. To this end, the project will develop open-source tools within a first-principles framework, meaning the calculations rely solely on the fundamental equations of quantum mechanics rather than experimental data. Ultimately, this work aims to provide a clear picture of when nonperturbative methods are necessary to describe the effect of phonons on electronic properties, and what they reveal that standard approaches miss.
Additional details for the curious
Solid-state physics studies the properties of solids at the atomic and quantum mechanical level. Its connections to technology run deep: the transistor, the building block of every modern processor, was a direct product of fundamental solid-state research. One of the field’s central ambitions is to predict the complex material properties that arise from a vast number of interacting electrons, using a first-principles approach: building directly from the fundamental equations of quantum mechanics, and minimizing experimental input. To advance this effort, this project will develop new theoretical methods and release the resulting computational tools as open-source software.
A fundamental question at the heart of this effort is how electrons in a solid really behave. The answer is complicated by the fact that atoms in a crystal are never perfectly still; they vibrate constantly, and those vibrations propagate through the material as waves called phonons. Electrons and phonons interact continuously, and these electron-phonon interactions are responsible for many important phenomena: the colors materials absorb or emit, how their electrical resistance changes with temperature, and whether they become superconductors. The standard approach for studying how atomic vibrations modify electronic energies uses perturbation theory, a framework that works well when the coupling is weak. In many materials of great scientific interest, however, vibrations alter the electronic behavior dramatically, and perturbation theory breaks down.
This project focuses on such cases, with particular attention to how electron-phonon interactions affect the distribution of electronic energies — how those energies shift, how well-defined the energy levels remain, and how the energy barrier electrons must overcome to conduct electricity changes with temperature. Rather than assuming that the effect of atomic vibrations is small, the approach directly explores the actual range of atomic arrangements that occur in a crystal at a given temperature. This includes capturing purely quantum effects: even at absolute zero temperature, quantum mechanics dictates that atoms do not sit perfectly still. These vibrations are particularly pronounced for hydrogen, the lightest element, causing very large shifts in its electronic properties, thus playing a fundamental role in explaining how it becomes metallic under high pressure. Hydrogen-rich compounds are among the most promising known candidates for high-temperature superconductivity, and accurately describing their electronic properties requires going beyond standard perturbation theory. Diamond serves as an important complementary case: its electronic properties change measurably with temperature, and since it is widely studied, it provides a rigorous test of the new methods before they are applied to less well-understood materials, where reliable predictions matter most. Finally, because the standard approach for studying electron-phonon interactions also assumes that atomic vibrations behave like ideal springs, a parallel line of work in the project goes beyond this assumption by using a complementary nonperturbative treatment.
The project’s main objectives are:
- Implementation of the nonperturbative method for first-principles calculations of electronic properties, integrated into ABINIT, one of the world’s leading open-source codes.
- Study of electron-phonon effects in diamond and hydrogen, both of which show some of the largest known shifts in the electronic band gap (the energy barrier mentioned earlier) with temperature. For hydrogen, we will develop a machine learning potential, which will reproduce first-principles results at a fraction of the computational cost, and will allow us to incorporate the effects of anharmonic vibrations.
- First-principles calculation of how the spatial distribution of electrons in silicon changes with temperature, a computationally demanding problem addressed here using a novel perturbative implementation, comparing the results against a nonperturbative approach. This includes the study of quasi-forbidden reflections: subtle experimental signals that symmetry almost completely cancels.
Among the results already emerging: the standard perturbation approach breaks down near the edges of the electronic energy bands — precisely the regions that determine whether a material conducts electricity — yielding qualitatively wrong predictions. By the end of the project, through systematic study of elemental semiconductors and insulators, the aim is to reach a clear understanding of when perturbation theory is reliable and when nonperturbative methods are essential.
Advisor: Prof. Matthieu Verstraete, elected fellow of the American Physical Society, chair of the steering committee of the European Theoretical Spectroscopy Facility, and member of the international advisory committee of ABINIT [abinit.org].
Analogy
Imagine a classroom where students sit in assigned seats, arranged so nobody ends up next to their friends. When the teacher is around, everyone behaves: students barely shift in their chairs, hardly talk to each other. Then the teacher walks out. Suddenly students are leaning over, turning around, dragging chairs across the room to get closer to their friends: lots of movement, all kinds of different configurations of the same classroom.
A method that only accounts for small, predictable movements from the original seating — a perturbative method — would completely miss this. It predicts everyone staying more or less in place, getting the behaviour of the room badly wrong.
A nonperturbative method instead looks at all the configurations students can actually reach: all the ways they might rearrange themselves around their assigned spots. There are many of these, so it’s harder to study. But it picks up what’s really going on, including the situations far from the starting point that matter most when students are moving a lot.
In this picture, the students are atoms in a material, and the teacher walking out is like the temperature going up. Atoms, like students, move more when things heat up. While perturbative methods work well in many cases, they fall short when atoms are vibrating strongly, or when small displacements already change things a lot (imagine students sitting next to their friends, where even with the teacher present the class might start getting rowdy). In those situations, a nonperturbative approach is needed to get accurate results, and sometimes to capture qualitatively different behaviour altogether.
Could you describe your career path in a few lines
I did my undergrad at the University of Buenos Aires and then a PhD at Stony Brook University in New York. Then I did postdocs in Rome at Sapienza University, and then a short postdoc in Barcelona, after which I worked briefly for a logistics company. After getting the Marie Curie fellowship, I decided to come back to academia here at the University of Liège.
What led you to choose the scientific path and, in particular, your field of research?
As a kid, I found myself drawn to math and physics. Physics didn’t offer a lot of certainty, and my environment suggested engineering was the safer path, but I felt physics dealt with more fundamental questions: what are things made of, all the way down, beyond the atomic scale? What are the basic laws of nature? I also enjoyed programming and became increasingly interested in areas with stronger potential for technological impact. This led me to open theoretical questions in solid-state physics, which studies the collective behaviour of huge numbers of atoms rather than individual particles. I ended up working mostly on electron-phonon interactions, as I’m doing now in Liège — work that uses some of the same mathematical tools, like Feynman diagrams, that I’d learned earlier while focusing on much shorter length scales. I’ve also worked on other topics, such as how to produce a specific stacking sequence of graphene layers in which superconductivity has been observed.
Funded by the European Union under a Marie Skłodowska-Curie Postdoctoral Fellowship, Project GreenNP No. 101151380