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Designing platforms to control phase-coherence and interference of electronwaves is a cornerstone for future quantum electronics, computing or sensing.Nanoporous graphene (NPG) consisting of linked graphene nanoribbons hasrecently been fabricated using molecular precursors and bottom-up assembly[Moreno et al., Science 360, 199 (2018)] opening an avenue for controlling theelectronic current in a two-dimensional material. By simulating electrontransport in real-sized NPG samples we predict that electron waves injectedfrom the tip of a scanning tunneling microscope (STM) behave similarly tophotons in coupled waveguides, displaying a Talbot interference pattern. Welink the origins of this effect to the band structure of the NPG and furtherdemonstrate how this pattern may be mapped out by a second STM probe. We enableatomistic parameter-free calculations beyond the 100 nm scale by developing anew multi-scale method where first-principles density functional theory regionsare seamlessly embedded into a large-scale tight-binding.

Full-scale Simulation of Electron Transport in Nanoporous Graphene: Probing the Talbot Effect