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.
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