Scientists Solve Decades-Old Puzzle of Electron Emission

Researchers have finally uncovered the missing piece that completes the puzzle. Picture a frog inside a box with a high opening. Whether it can get out depends on its energy: if it can jump high enough, escape is possible in theory. But that alone doesn’t guarantee success, since the frog must also land precisely where the opening is, the journal Physical Review Letters reported.

Simply jumping high is not enough. Scientists have discovered that electrons inside solids face a similar challenge. When the material is given extra energy (for instance, by striking it with other electrons), some electrons gain enough energy to break free. This phenomenon has been recognized for decades and is central to many technologies.

Yet, until recently, researchers could not accurately describe how it happens. A team from several groups at TU Wien has now found the missing piece: like the frog, an electron needs more than energy to escape; it also needs to find the right “exit,” a so-called “doorway state.”

“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.

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.

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