Abstract
We investigate the role of the substrate for the strength of the electron-phonon coupling in Li-decorated graphene. We find that the interaction with a h-BN substrate leads to a significant enhancement from lambda(0) = 0.62 to lambda(1) = 0.67, which corresponds to a 25% increase of the transition temperature from T-c0 = 10.33K to T-c1 = 12.98 K. The superconducting gaps amount to 1.56 meV (suspended) and 1.98 meV (supported). These findings open up a new route to enhanced superconducting transition temperatures in graphene-based materials by substrate engineering.