Theory of 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, T c , can reach several Kelvins at the experimentally accessible range of parameters. At low temperatures, T ≪ T c , and zero magnetic field, the density of states is characterized by a small gap E g ≤ T c resulting from the collective proximity effect. Transverse magnetic field H g ( T ) ∝ E g 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 H g 2 ( T ) .