Exploring the third dimension in quantum confinement of surface electrons

Quantum confinement of surface electrons in two-dimensional metal-organic networks offers a powerful route to engineer electronic states for quantum and spintronic technologies. Here, we demonstrate the pivotal role of vertical variations in the surface potential on the quantum confinement of surface electrons. We investigate the confinement of both Shockley surface state and image-potential state electrons with their distinct vertical electron density distributions in a Cu-T4PT network on Cu(111). We find a substantial renormalization of the band mass of the image state, whereas the Shockley state remains almost unchanged. This notable divergence arises from 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 beneath the Cu coordination spheres. Our findings demonstrate the essential role of vertical potential engineering in designing quantum-confined states, thereby advancing control over electronic properties and quantum phenomena at the nanoscale.