For the first time, researchers from Vienna University of Technology (TU Wien) have calculated the precise mechanisms of electron emission, finally enabling accurate predictions of how electrons escape from solid materials through a quantum door.
The new research presented in Physical Review Letters explains the complex process that requires not just energy to escape, but also tight maneuvering through a quantum door. Despite its widespread use across many technologies, the effect of electron emission has never been accurately calculable before.
Electron Emission
“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,” said lead author Anna Niggas from the Institute of Applied Physics at TU Wien.
The electrons situated inside any material have varying energy levels. Below a certain threshold, the electrons remain trapped within the solid matter, yet if they receive enough additional energy, they may break the threshold and escape.
“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.”
The Quantum Door
Researchers have long been puzzled by why theoretical expectations for the energy required for an electron to escape did not match real-world observations.
“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,” Niggas said in a statement.
The researchers’ major discovery was that electron emission is not solely a function of energy. Quantum states also determine whether an electron can escape or not. Even if an electron crosses the escape energy threshold, being in the wrong quantum state will block its exit. What the electrons require is a quantum door. Earlier attempts to calculate electron emission failed to account for this crucial factor.
“From an energetic point of view, the electron is no longer bound to the solid,” said Richard Wilhelm, one of the study’s co-authors. “It has the energy of a free electron, yet it still remains spatially located where the solid is. 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,” explained co-author 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.”
Reconsidering Material Design
“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,” Niggas explained.
Intentionally inducing these states will be the design challenge of the future. Some of them require more than five stacked layers to produce the desired quantum states.
By beginning with the newly discovered parameters, future engineers will be able to create layered designs targeted explicitly at generating a quantum door, enabling new levels of technological efficiency.
The paper, “Identifying Electronic Doorway States in Secondary Electron Emission from Layered Materials,” appeared in Physical Review Letters on October 15, 2025.
Ryan Whalen covers science and technology for The Debrief. He holds an MA in History and a Master of Library and Information Science with a certificate in Data Science. He can be contacted at ryan@thedebrief.org, and follow him on Twitter @mdntwvlf.