Proximity-induced superconductivity in graphene

We propose a way of making graphene superconductive by putting on it small superconductive islands which cover a tiny fraction of graphene area. We show that the critical temperature, Tc, can reach several Kelvins at the experimentally accessible range of parameters. At low temperatures, TTc, and zero magnetic field, the density of states is characterized by a small gap Eg ≤ Tc resulting from the collective proximity effect. Transverse magnetic field Hg(T) ∝ Eg is expected to destroy the spectral gap driving graphene layer to a kind of a superconductive glass state. Melting of the glass state into a metal occurs at a higher field Hg2(T).