  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.
