Phonon-mediated superconductivity in graphene and hexagonal boron nitride

Insight into why superconductivity in pristine and doped monolayer graphene seems strongly suppressed has been central for the recent years' various creative approaches to realize superconductivity in graphene and graphene-like systems. We provide further insight by studying superconductivity in doped monolayer graphene based on intrinsic phonon modes and solving the gap equation using a detailed model for the effective attraction based on electron tight binding and phonon force constant models. The various system parameters can be tuned at will, and our results show that the Coulomb interaction induces non-uniform gap textures along the Fermi surface and plays a main role in suppressing superconductivity at realistic dopings. We also perform similar calculations in the gapped hexagonal boron nitride (h-BN), which has direct onset of a large density of states. Somewhat counter-intuitively, however, the dimensionless electron-phonon coupling strength cannot capitalize on this for small charge dopings.