Physicists uncover hidden “doorways” that let electrons escape

Electrons inside solid materials behave in a surprisingly similar way. When they gain extra energy (for instance, when the material is struck by other electrons), they can sometimes break free from the solid. This process has been known for decades and forms the basis of many technologies. However, until recently, scientists had been unable to calculate it with precision. Researchers from several groups at TU Wien have now found the solution. Just as the frog must find the right opening, an electron also needs to locate a specific "exit," known as a "doorway state."

A Simple Setup, Unexpected 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," explains Anna Niggas from the Institute of Applied Physics at TU Wien, the study's first author.

Inside any material, electrons can exist with a range of energies. As long as they stay below a certain energy limit, they remain trapped. When the material is supplied with extra energy, some electrons can surpass this boundary.

"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 models and experimental findings often failed to match. This mismatch was especially puzzling because "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 key discovery is that energy alone cannot determine whether an electron escapes. There are quantum states above the energy threshold that still fail to lead out of the material, a fact missing from earlier 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. Interestingly, some of these states appear only when more than five layers of a material are stacked. This insight offers new opportunities for precisely designing and applying layered materials in both research and advanced technologies.