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Phonon induced Superconductivity of High Temperatures in Electrical Graphene Superlattices

We discuss the BCS theory for electrons in graphene with a superimposed electrical unidirectional superlattice potential (SL). New Dirac points emerge together with van Hove singularities (VHS) linking them. We obtain a superconducting transition temperature $ T_c $ for chemical potentials close to the VHS assuming that acoustic phonon coupling should be the dominant mechanism. Pairing of two onsite electrons with one electron close to the $ {\bf K} $ and the other close to the $ -{\bf K} $ point is the most stable pair formation. The resulting order parameter is almost constant over the entire SL.