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.”

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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.”