The Third Dimension of the Quantum World: New Ways to Control Surface Electrons – Paper Featured on the Cover of Science Advances
In a recent article in Science Advances, the research group of Prof. Dr. Benjamin Stadtmüller (University of Augsburg), in collaboration with the research group of OPTIMAS spokesperson Prof. Dr. Martin Aeschlimann (RPTU University Kaiserslautern-Landau), demonstrates that the quantum confinement of electrons on surfaces is not determined solely by the lateral structure of a nanolandscape. Instead, a factor that has so far been largely underestimated plays a decisive role: the third dimension of the surface potential. The work was selected as the cover feature of the current issue of Science Advances (Vol. 12, Issue 24).
Electrons on metal surfaces can propagate like free particles along the surface. When they are confined within artificially created nanostructures, so-called quantum states with extraordinary properties arise, forming the basis for future quantum technologies and novel electronic devices. Until now, research has focused primarily on the lateral confinement of this electron motion – that is, on how nanometer-sized honeycomb structures or molecular networks control the in-plane propagation of electrons along a surface.
Within the Collaborative Research Center CRC/TRR 173 Spin+X, the team has now shown for the first time that the vertical extent of the electron wave function is also of decisive importance. To this end, they investigated the quantum confinement of Shockley surface states and image-potential states in a copper-coordinated Cu-T4PT network on a copper surface. The two electronic states differ fundamentally in their spatial distribution perpendicular to the surface, thus providing an ideal model system for studying three-dimensional confinement effects.
Although both states can be confined within the same nanostructure, they exhibit remarkably different behavior. The Shockley states, localized close to the metal surface, experience only comparatively weak quantum confinement. In contrast, the image-potential states, located farther from the surface, become extraordinarily strongly localized. This leads to a drastic change in their electronic properties and, in particular, to an exceptionally strong increase in the effective electron mass.
The theoretical analysis simultaneously provides the explanation for this behavior: the three-dimensional potential at the interface exhibits markedly different strengths at different heights above the surface. Whereas permeable channels form in the immediate vicinity of the surface, through which electrons can partially escape, a nearly closed potential barrier forms at greater distance. Electrons whose wave function resides in this region above the surface are therefore confined much more efficiently.
The results fundamentally extend the previous understanding of the "quantum confinement of electrons." They show that the targeted design of artificial quantum structures must account not only for the lateral structuring but also for the complete three-dimensional potential landscape. This opens up new possibilities for selectively controlling different electronic states within the same nanostructure and deliberately coupling them to one another.
In the long term, this concept could help to generate and manipulate complex quantum states in a targeted manner – an essential prerequisite for future nanoscale quantum technologies and novel architectures of quantum information processing. The results open a new avenue toward the tailored control of electrons on the atomic scale and mark an important step on the path toward future quantum devices.
Exploring the third dimension in quantum confinement of surface electrons
Lu Lyu, Tobias Eul, Wei Yao, Jin Xiao, Mostafa Ashoush, Zakaria M. Abd El-Fattah, Ignacio Piquero-Zulaica, Johannes V. Barth, Martin Aeschlimann, Benjamin Stadtmüller
Science Advances, 2026; Vol. 12, Issue 24: eaed3926
For more information:
Prof. Dr. Benjamin Stadtmüller
Universität Augsburg, Lehrstuhl für Experimentalphysik II
Tel: +49 821 598-3438