Superconducting critical temperature and softening of the phonon spectrum in ultrathin nb- and nbn/graphene hybrids

Superconductivity is studied in hybrids consisting of ultrathin superconducting film/few layer graphene. Two different superconductors were used at this purpose, Nb and NbN. An increase of the superconducting critical temperature, Tc, is observed when graphene is put into contact with Nb. The largest increase is obtained for the thinnest Nb layer, which has a Tc 8% larger with respect to the single Nb film. In the case of NbN the effect is not so pronounced. Experimental data are discussed by considering the possible modification of the phonon spectrum in the superconductor due to the presence of the graphene. Within an elementary one-dimensional model based on an elastic coupling between nearest-neighbor atoms, we demonstrate that the phonon spectrum in the superconductor is modified at low energies with the subsequent enhancement of the effective electron-phonon coupling constant. While the strong oscillating nature of the electron-phonon interaction, α2(ω), in NbN could lead to the insensitivity of Tc on the low-energy phonons generated by the graphene, the almost constant behavior of α2(ω) in Nb favors the increase of the superconducting critical temperature.