Surfaces are at the frontier of every known solid. They provide versatile supports for functional nanostructures and mediate essential physicochemical processes. Intimately related to two-dimensional materials, interfaces and atomically thin films often feature distinct electronic states with respect to the bulk, which is key to many relevant properties, such as catalytic activity, interfacial charge-transfer, and crystal growth mechanisms. To induce novel quantum properties via lateral scattering and confinement, reducing the surface electrons’ dimensionality and spread with atomic precision is of particular interest. Both atomic manipulation and supramolecular principles provide access to custom-designed molecular assemblies and superlattices, which tailor the surface electronic landscape and influence fundamental chemical and physical properties at the nanoscale. Here the confinement of surface-state electrons is reviewed, with a focus on their interaction with molecular scaffolds created by molecular manipulation and self-assembly protocols under ultrahigh vacuum conditions. Starting with the quasifree two-dimensional electron gas present at the $(111)$-oriented surface planes of noble metals, the intriguing molecule-based structural complexity and versatility is illustrated. Surveyed are low-dimensional confining structures in the form of artificial lattices, molecular nanogratings, or quantum dot arrays, which are constructed upon an appropriate choice of their building constituents. Whenever the realized (metal-)organic networks exhibit long-range order, modified surface band structures with characteristic features emerge, inducing noteworthy physical phenomena such as discretization, quantum coupling or energy, and effective mass renormalization. Such collective electronic states can be additionally modified by positioning guest species at the voids of open nanoarchitectures. The designed scattering potential landscapes can be described with semiempirical models, bringing thus the prospect of total control over surface electron confinement and novel quantum states within reach.

Ferromagnetism is the collective alignment of atomic spins that retain a net magnetic moment below the Curie temperature, even in the absence of external magnetic fields. Reducing this fundamental property into strictly two-dimensions was proposed in metal-organic coordination networks, but thus far has eluded experimental realization. In this work, we demonstrate that extended, cooperative ferromagnetism is feasible in an atomically thin two-dimensional metal-organic coordination network, despite only ≈ 5% of the monolayer being composed of Fe atoms. The resulting ferromagnetic state exhibits an out-of-plane easy-axis square-like hysteresis loop with large coercive fields over 2 Tesla, significant magnetic anisotropy, and persists up to T_C ≈ 35 K. These properties are driven by exchange interactions mainly mediated by the molecular linkers. Our findings resolve a two decade search for ferromagnetism in two-dimensional metal-organic coordination networks.

Topological protection shatters in a predicted organic topological insulator by spontaneously reducing its overall symmetry. The first experimental evidence of a 2D-MOF conjugated band is reported, even in absence of edge states.

On-surface metal-organic nanoporous networks generally refer to adatom coordinated molecular arrays, which are characterized by the presence of well-defined and regular nanopores. These periodic structures constructed using two types of components confine the surface electrons of the substrate within their nanocavities. However, the confining (or scattering) strength that individual building units exhibit is a priori unknown. Here, we study the modification of the substrate’s surface electrons by the interaction with a Cu-coordinated TPyB metal-organic network formed on Cu(111) and disentangle the scattering potentials and confinement properties. By means of STM and angle-resolved photoemission spectroscopy we find almost unperturbed free-electron-like states stemming from the rather weak electron confinement that yields significant coupling between adjacent pores. Electron plane wave expansion simulations match the superlattice induced experimental electronic structure, which features replicating bands and energy renormalization effects. Notably, the electrostatic potential landscape obtained from our ab initio calculations suggests that the molecules are the dominant scattering entities while the coordination metal atoms sandwiched between them act as leaky channels. These metal atom transmission conduits facilitate and enhance the coupling among quantum dots, which are prone to be exploited to engineer the electronic structure of surface electron gases.

The electronic structure defines the properties of graphene-based nanomaterials. Scanning tunneling microscopy/spectroscopy (STM/STS) experiments on graphene nanoribbons (GNRs), nanographenes, and nanoporous graphene (NPG) often determine an apparent electronic orbital confinement into the edges and nanopores, leading to dubious interpretations such as image potential states or super-atom molecular orbitals. We show that these measurements are subject to a wave function decay into the vacuum that masks the undisturbed electronic orbital shape. We use Au(111)-supported semiconducting gulf-type GNRs and NPGs as model systems fostering frontier orbitals that appear confined along the edges and nanopores in STS measurements. DFT calculations confirm that these states originate from valence and conduction bands. The deceptive electronic orbital confinement observed is caused by a loss of Fourier components, corresponding to states of high momentum. This effect can be generalized to other 1D and 2D carbon-based nanoarchitectures and is important for their use in catalysis and sensing applications.