Effective determination of surface potential landscapes from metal-organic nanoporous network overlayers

Determining the scattering potential landscape for two-dimensional superlattices provides key insight into fundamental quantum electron phenomena. Theoretical and semiempirical methods have been extensively used to simulate confinement effects of the two-dimensional electron gas (2DEG) on superlattices with a single scatterer in the form of vicinal surfaces and dislocation networks or isolated structures such as quantum corrals and vacancy islands. However, the complexity of the problem increases when the building blocks (or scatterers) are heterogeneous, as in metal-organic nanoporous networks (MONNs), since additional potentials may come into play. Therefore, the parametrization of the surface potential landscape is often inaccurate, leading to incorrect scattering potentials. Here, we address this issue with a combination of scanning tunneling microscopy/spectroscopy, angle resolved photoemission spectroscopy and Kelvin probe force microscopy measurements together with electron plane-wave expansion simulations on a MONN grown on Cu(111). This experimental-theory approach, enables us to capture the 2DEG response to the intricate scattering potential landscape, and reveals systematic modeling procedures. Starting from a realistic geometry of the system, we determine the repulsive scattering potentials for both molecules and coordinated metal adatoms, the latter contradicting the established simulation framework. Moreover, we reveal local asymmetries and subtle renormalization effects of the 2DEG that relate to the interaction of the MONN and the underlying substrate.