Nanosize pores can turn semimetallic graphene into a semiconductor and, from being impermeable, into the most efficient molecular-sieve membrane. However, scaling the pores down to the nanometer, while fulfilling the tight structural constraints imposed by applications, represents an enormous challenge for present top-down strategies. Here we report a bottom-up method to synthesize nanoporous graphene comprising an ordered array of pores separated by ribbons, which can be tuned down to the 1-nanometer range. The size, density, morphology, and chemical composition of the pores are defined with atomic precision by the design of the molecular precursors. Our electronic characterization further reveals a highly anisotropic electronic structure, where orthogonal one-dimensional electronic bands with an energy gap of ∼1 electron volt coexist with confined pore states, making the nanoporous graphene a highly versatile semiconductor for simultaneous sieving and electrical sensing of molecular species.

Predictions about the electrical conductance across molecular junctions based on self-assembled monolayers (SAMs) are often made from the SAM precursor properties. Collective electrostatic effects, however, in a densely packed SAM can override these predictions. We studied, experimentally and theoretically, molecular tunneling junctions based on thiolate SAMs with an aromatic biphenyl backbone and variable, highly polarizable halogen termini X (S-(C 6 H 5 ) 2 X; X = H, F, Cl, Br, or I). We found that the halogen-terminated systems show tunneling rates and dielectric behavior that are independent of X despite the large change in the electronegativity of the terminal atom. Using density functional theory, we show that collective electrostatic effects result in modulations of the electrostatic potential that are strongly confined spatially along the direction of charge transport, thereby rendering the role of the halogen atoms insignificant for SAMs with conjugated backbones.

Designing platforms to control phase-coherence and interference of electron waves is a cornerstone for future quantum electronics, computing or sensing. Nanoporous graphene (NPG) consisting of linked graphene nanoribbons has recently been fabricated using molecular precursors and bottom-up assembly [Moreno et al, Science 360, 199 (2018)] opening an avenue for controlling the electronic current in a two-dimensional material. By simulating electron transport in real-sized NPG samples we predict that electron waves injected from the tip of a scanning tunneling microscope (STM) behave similarly to photons in coupled waveguides, displaying a Talbot interference pattern. We link the origins of this effect to the band structure of the NPG and further demonstrate how this pattern may be mapped out by a second STM probe. We enable atomistic parameter-free calculations beyond the 100 nm scale by developing a new multi-scale method where first-principles density functional theory regions are seamlessly embedded into a large-scale tight-binding. arXiv:1811.07576v1 [cond-mat.mes-hall]

Controlling the nature of the electronic states within organic layers holds the promise of truly molecular electronics. To achieve that we, here, develop a modular concept for a versatile tuning of electronic properties in organic monolayers and their interfaces. The suggested strategy relies on directly exploiting collective electrostatic effects, which emerge naturally in an ensemble of polar molecules. By means of quantum‐mechanical modeling we show that in this way monolayer‐based quantum‐cascades and quantum‐well structures can be realized, which allow a precise control of the local electronic structure and the localization of electronic states. Extending that concept, we furthermore discuss strategies for activating spin sensitivity in specific regions of an organic monolayer.