Exploring the third dimension in quantum confinement of surface electrons

Quantum confinement of surface electrons in two-dimensional metal-organic porous networks offers a powerful route to engineer electronic states for emerging quantum and spintronic technologies at the molecular scale. To date, such confinement has been understood primarily in terms of lateral, two-dimensional surface potential landscapes. Here, we demonstrate the pivotal role of vertical variations in the surface potential on the quantum confinement of surface electrons. We investigate the confinement behavior of both Shockley surface state and image potential state electrons with their distinct vertical electron density distributions in an exemplary Cu-T4PT metal-organic porous network on Cu(111). Advanced spectroscopic techniques reveal a substantial band renormalization for the image state electrons, manifested as a significant increase in their effective mass, whereas the Shockley state electrons remain almost unchanged. Such striking divergence is attributed to the distinct three-dimensional potential landscape of the Cu-T4PT network with a strong repulsive potential at the vertical position of the molecular backbone and leaky channels underneath the Cu coordination spheres. Our findings demonstrate the essential role of vertical potential engineering in designing quantum confined states and thus advance the control of electronic properties and quantum phenomena on the nanoscale.