Researchers at TU Wien have discovered that electrons escaping from solid materials require specific 'doorway states' beyond just sufficient energy, resolving long-standing experimental anomalies. This finding, published in Physical Review Letters, explains variations in electron emission from layered materials like graphene. The insight opens new possibilities for engineering advanced materials.
Electrons in solid materials can gain extra energy, such as from impacts by other electrons, potentially allowing them to break free. This process underpins many technologies but has puzzled scientists for decades due to mismatches between theory and experiments. Anna Niggas, first author from TU Wien's Institute of Applied Physics, notes, '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.'
Traditional models assumed that any electron with enough energy would escape, but observations showed otherwise. For instance, graphene structures with varying layer counts exhibited similar internal electron energies yet different emission behaviors. Prof. Richard Wilhelm, head of the Atomic and Plasma Physics group at TU Wien, explains, 'One might assume that all these electrons, once they have enough energy, simply leave the material. But, as it turns out, that's not what happens.'
The breakthrough reveals that even states above the energy threshold can trap electrons spatially within the solid. Wilhelm adds, '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.' Instead, escape depends on 'doorway states'—specific quantum states that strongly couple to external paths. Prof. Florian Libisch from the Institute for Theoretical Physics states, '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.'
Niggas highlights the implications: '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.' Notably, some doorway states emerge only in stacks exceeding five layers, enabling precise design of layered materials for research and technology. The study appears in Physical Review Letters (2025; 135 (16)), with DOI: 10.1103/qls7-tr4v.