Oct 20, 2025 09:54 PM
https://www.tuwien.at/en/tu-wien/news/ne...cht-finden
PRESS RELEASE: Imagine a frog sitting inside a box. The box has a large opening at a certain height. Can the frog escape? That depends on how much energy it has: if it can jump high enough, it could in principle make it out. But whether it actually succeeds is another question. The height of the jump alone isn’t enough — the frog also needs to jump through the opening.
A similar situation arises with electrons inside a solid. When given a bit of extra energy — for example, by bombarding the material with additional electrons — they may be able to escape from the material. This effect has been known for many years and is widely used in technology. But surprisingly, it has never been possible to calculate this process accurately. A collaboration between several research groups at TU Wien has now solved this mystery: just like the frog, it’s not only the energy that matters — the electron also needs to find the right “exit,” a so-called “doorway state.”
A Simple Situation, Puzzling Results. “Solids from which relatively slow electrons emerge play a key role in physics. From the energies of these electrons, we can extract valuable information about the material,” says Anna Niggas from the Institute of Applied Physics at TU Wien, first author of the new study.
Electrons inside a material can have different energies. As long as they remain below a certain energy threshold, they are inevitably trapped within the material. When the material is supplied with additional energy, some electrons exceed this threshold.
“One might assume that all these electrons, once they have enough energy, simply leave the material,” says Prof. Richard Wilhelm, head of the Atomic and Plasma Physics group at TU Wien. “If that were true, things would be simple: we would just look at the electrons’ energies inside the material and directly infer which electrons should appear outside. But, as it turns out, that’s not what happens.”
Theoretical predictions and experimental results did not seem to match. Particularly puzzling: “Different materials — such as graphene structures with different amounts of layers — can have very similar electron energy levels, yet show completely different behaviors in the emitted electrons,” says Anna Niggas.
No Exit Without a Doorway. The crucial insight: energy alone isn’t enough. There exist quantum states that lie above the necessary energy threshold but still do not lead out of the material — and these states had not been accounted for in previous models. “From an energetic point of view, the electron is no longer bound to the solid. It has the energy of a free electron, yet it still remains spatially located where the solid is,” says Richard Wilhelm. The electron behaves like the frog that jumps high enough but fails to find the exit.
“The electrons must occupy very specific states — so-called doorway states,” explains Prof. Florian Libisch from the Institute for Theoretical Physics. “These states couple strongly to those that actually lead out of the solid. Not every state with sufficient energy is such a doorway state — only those that represent an ‘open door’ to the outside.”
“For the first time, we’ve shown that the shape of the electron spectrum depends not only on the material itself, but crucially on whether and where such resonant doorway states exist,” says Anna Niggas. Some of these states only emerge when more than five layers of a material are stacked. This discovery opens up entirely new perspectives for the targeted design and use of layered materials in technology and research.
PRESS RELEASE: Imagine a frog sitting inside a box. The box has a large opening at a certain height. Can the frog escape? That depends on how much energy it has: if it can jump high enough, it could in principle make it out. But whether it actually succeeds is another question. The height of the jump alone isn’t enough — the frog also needs to jump through the opening.
A similar situation arises with electrons inside a solid. When given a bit of extra energy — for example, by bombarding the material with additional electrons — they may be able to escape from the material. This effect has been known for many years and is widely used in technology. But surprisingly, it has never been possible to calculate this process accurately. A collaboration between several research groups at TU Wien has now solved this mystery: just like the frog, it’s not only the energy that matters — the electron also needs to find the right “exit,” a so-called “doorway state.”
A Simple Situation, Puzzling Results. “Solids from which relatively slow electrons emerge play a key role in physics. From the energies of these electrons, we can extract valuable information about the material,” says Anna Niggas from the Institute of Applied Physics at TU Wien, first author of the new study.
Electrons inside a material can have different energies. As long as they remain below a certain energy threshold, they are inevitably trapped within the material. When the material is supplied with additional energy, some electrons exceed this threshold.
“One might assume that all these electrons, once they have enough energy, simply leave the material,” says Prof. Richard Wilhelm, head of the Atomic and Plasma Physics group at TU Wien. “If that were true, things would be simple: we would just look at the electrons’ energies inside the material and directly infer which electrons should appear outside. But, as it turns out, that’s not what happens.”
Theoretical predictions and experimental results did not seem to match. Particularly puzzling: “Different materials — such as graphene structures with different amounts of layers — can have very similar electron energy levels, yet show completely different behaviors in the emitted electrons,” says Anna Niggas.
No Exit Without a Doorway. The crucial insight: energy alone isn’t enough. There exist quantum states that lie above the necessary energy threshold but still do not lead out of the material — and these states had not been accounted for in previous models. “From an energetic point of view, the electron is no longer bound to the solid. It has the energy of a free electron, yet it still remains spatially located where the solid is,” says Richard Wilhelm. The electron behaves like the frog that jumps high enough but fails to find the exit.
“The electrons must occupy very specific states — so-called doorway states,” explains Prof. Florian Libisch from the Institute for Theoretical Physics. “These states couple strongly to those that actually lead out of the solid. Not every state with sufficient energy is such a doorway state — only those that represent an ‘open door’ to the outside.”
“For the first time, we’ve shown that the shape of the electron spectrum depends not only on the material itself, but crucially on whether and where such resonant doorway states exist,” says Anna Niggas. Some of these states only emerge when more than five layers of a material are stacked. This discovery opens up entirely new perspectives for the targeted design and use of layered materials in technology and research.