  Heterostructures involving graphene and bismuth, with their ability to absorb
light over a very wide energy range, are of interest for engineering
next-generation opto-electronics. Critical to the technological application of
such heterostructures is an understanding of the underlying physics governing
their properties. Here, using first-principles calculations, we study the
interfacial interactions between graphene and bismuth thin-films. Our study
reveals non-intuitive phenomena associated with the moir\'e-physics of these
superlattices. We show a preservation of graphene-derived Dirac cones in spite
of proximity to a substrate with large spin-orbit coupling, a greater influence
of graphene on the electronic structure properties of bismuth, and the
surprising presence of a magnetic solution, only slightly higher in energy (by
several meV) than the non-magnetic structure, possibly validating experiments.
Such subtle and unanticipated phenomena associated with the moir\'e-physics are
expected to play key roles in the practical applications of heterogeneous
assemblies of two-dimensional quantum systems.
