  There are a large number of atomically thin graphitic films with similar
structure to graphene. These films have a spread of bandgaps relating to their
ionicity, and also to the substrate on which they are grown. Such films could
have a range of applications in digital electronics where graphene is difficult
to use. I use the dynamical cluster approximation to show how electron-phonon
coupling between film and substrate can enhance these gaps in a way that
depends on the range and strength of the coupling. One of the driving factors
in this effect is the proximity to a charge density wave instability for
electrons on a honeycomb lattice. The enhancement at intermediate coupling is
sufficiently large that spatially varying substrates and superstrates could be
used to create heterostructures in thin graphitic films with position dependent
electron-phonon coupling and gaps, leading to advanced electronic components.
